Atomic Physics Methods in Modern Research: Selection of Papers Dedicated to Gisbert Zu Putlitz on the Occasion of His 65th Birthday

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K. Jungmann J. Kowalski I. Reinhard F. Tfiiger (Eds.)

Atomic Physics Methods in Modern Research Selection of Papers Dedicated to Gisbert zu Putlitz on the Occasion of his 65th Birthday

~

Springer

Editors Klaus Peter Jungmann Joachim Kowalski Irene Reinhard Physikalisches Institut, Universit~it Heidelberg Philosophenweg 12 D-6912o Heidelberg, Germany Frank Tr~ger Fachbereich Physik, Universit~t Kassel Heinrich-Plett-Strasse 4o D-34132 Kassel, Germany

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Atomic physics methods in modern research : selection of papers dedicated to Gisbert zu Putlitz on his 65th birthday / K. E Jungmann ... (ed.). - Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Pads ; Santa Clara ; Singapore ; Tokyo : Springer, 1997 (Lecture notes in physics ; 499) ISBN 3-540-63716-8

ISSN oo75-845o ISBN 3-540-63716-8 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved,whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Vertag.Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1997 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement,that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready by the authors/editors Cover design: design&production GmbH, Heidelberg SPIN: 10643850 55/3144-543210 - Printed on acid-free paper

Preface

Many of the significant advances in the course of the development of atomic physics were associated with newly invented scientific methods and experimental tools. Today these techniques are successfully employed in a wide spread variety of highly active areas in modern research, which extend from investigations of fundamental interactions in physics to experiments related to applied issues and technical aspects. With increasing importance they are found in areas outside of classical atomic physics in fields such as nuclear and particle physics, physics of condensed matter and surfaces, physical chemistry, chemistry, medicine and environmental research. The spectrum of methods includes among others optical and microwave spectroscopy, molecular beams, spin resonance, spin echo, particle trapping and tunneling microscopy. Laser spectroscopy is one example of a widely used technique: The fundamental process of light interacting with single atomic particles can be investigated especially profitably. Laser spectroscopy is essential in many high precision experiments for determining most accurate values of fundamental constants and for deriving conclusions on basic interactions which are complementary to results obtained in high energy physics. Optical properties of molecules, small clusters and bulk solid state material can be investigated both for revealing elementary processes and for studying, for example, new concepts of optical data storage. Processes in combustion devices can be characterized. Remote sensing of environmental pollution can be carried out with high sensitivity. Laser optical pumping of noble gases nowadays yields novel opportunities for nuclear magnetic resonance imaging in medical diagnostics. In February 1996 an international symposium on Atomic Physics Methods in Modern Research was held in Heidelberg on the occasion of the 65th birthday of Professor Gisbert zu Putlitz. In his scientific work atomic physics with its great diversity of facets has played an essential role with numerous significant contributions being highly esteemed by the community. The nature of the event inspired the authors of this volume, which is dedicated to Gisbert zu Putlitz. It comprises invited lectures and articles selected to give an overview of the manifold of developments in this area.

VI The editors would like to thank all authors for their articles and W. BeiglbSck for publishing this volume. The assistance of T. Katzenmaier, C. Kr~imer, E. Nowak and M. Zinser of the Physikalisches Institut der Universit~it Heidelberg in preparing this volume is gratefully acknowledged. Financial support for bringing the authors together was provided by the Stiftung Universit~it Heidelberg and the companies ABB, BASF, Fibro, Friatec, Lambda Physics, Spectra Physics and B. Struck. We are grateful to all of them. Heidelberg, August 1997 K. Jungmann J. Kowalski I. Reinhard F. Tr/iger

Contents

T w o - P h o t o n M e t h o d for M e t r o l o g y in H y d r o g e n B. Cagnac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

H i g h Precision A t o m i c S p e c t r o s c o p y of M u o n i u m a n d Simple M u o n i c A t o m s V. W. Hughes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

M u o n i u m A t o m as a P r o b e of Physics Beyond the Standard Model L. Willmann and K. Jungmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

C a n A t o m s T r a p p e d in Solid He Be Used to Search for P h y s i c s B e y o n d t h e S t a n d a r d M o d e l ? A. Weis, S. Kanorsky, S. Land and T.W. H~insch . . . . . . . . . . . . . . . . . . . . .

57

g-Factors of S u b a t o m i c Particles B.L. Roberts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

L a s e r S p e c t r o s c o p y of M e t a s t a b l e Antiprotonic Helium Atomcules T. Yamazaki . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

Polarized, C o m p r e s s e d SHe-Gas a n d Its A p p l i c a t i o n s E. Often . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

105

M e d i c a l N M R Sensing w i t h Laser Polarized 3He a n d 129Xe W. Happer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

121

Test of Special R e l a t i v i t y in a H e a v y Ion Storage R i n g G. Huber, R. Grieser, P. Merz, V. Sebastian, P. Seelig, M. Grieser, P. Grimm, T. Kiihl, D. Schwalm and D. Habs . . . . . . . . . . . . . . . . . . . . . . .

131

R e s o n a n c e F l u o r e s c e n c e of a Single Ion J.T. Hb'ffges, H.W. Baldauf, T. Eichler, S.R. Helm#led and H. Walther . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

141

R e s o n a n c e R a m a n Studies of t h e R e l a x a t i o n of P h o t o e x c i t e d Molecules in Solution on t h e Picosecond Timescale W.T. Toner, P. Matousek, A . W . Parker and M. Towrie . . . . . . . . . . . . .

151

F o u r - Q u a n t u m R F - R e s o n a n c e in t h e G r o u n d S t a t e of an Alkaline A t o m E.B. Alexandrov and A.S. Pazgalev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

t59

VIII

Hard Highly Directional X - R a d i a t i o n E m i t t e d B y a C h a r g e d P a r t i c l e M o v i n g in a C a r b o n N a n o t u b e V. V. Klimov and V.S. Letokhov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

167

Quasiclassical A p p r o x i m a t i o n in t h e T h e o r y of S c a t t e r i n g of Polarized A t o m s E.L Dashevskaya and E.E. Nikitin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

185

I o n B e a m I n e r t i a l Fusion R. Bock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

211

Spin-Echo E x p e r i m e n t s w i t h N e u t r o n s and with Atomic Beams G. Schraidt and D. Dubbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

231

A N e w G e n e r a t i o n of Light Sources for Applications in S p e c t r o s c o p y M. Inguscio, F.S. Cataliotti, C.- Fort, F.S. Pavone and M. Prevedelli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

245

R e m o t e Sensing of t h e E n v i r o n m e n t Using Laser R a d a r Techniques M. Andersson, E. Edner, J. Johansson, S. Svanberg, E. WaUinder and P. Weibring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

257

A p p l i e d Laser S p e c t r o c o p y in C o m b u s t i o n Devices V. Sick and J. Wolfrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

271

T h e Surface of Liquid H e l i u m - an U n u s u a l S u b s t r a t e for U n u s u a l C o u l o m b S y s t e m s P. Leiderer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

283

A s p e c t s of Laser-Assisted Scanning T u n n e l i n g M i c r o s c o p y of T h i n Organic Layers S. GrafstrSm, J. Kowalski and R. Neumann . . . . . . . . . . . . . . . . . . . . . . . . .

295

O p t i c a l S p e c t r o s c o p y of M e t a l Clusters M. VoUmer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

311

N e w C o n c e p t s for I n f o r m a t i o n Storage B a s e d on Color C e n t r e s A. Winnacker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

335

E x c i t o n s a n d R a d i a t i o n D a m a g e in Alkali Halides K. Schwartz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

351

P o l a r i z a t i o n of Negative M u o n s I m p l a n t e d in t h e Fullerene C60: Speculations A b o u t a Null R e s u l t A. Schenck, F.N. Gyax, A. Amato, M. Pinkpank, A. Lappas and K. Prassides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

367

P o s i t r o n i u m in C o n d e n s e d M a t t e r Studies w i t h Spin-Polarized P o s i t r o n s J. Major, A. Seeger, J. Ehmann and T. Gessmann . . . . . . . . . . . . . . . . . . .

381

IX Light-Induced Liberation of Atoms and Molecules f r o m Solid S u r f a c e s F. T r @ e r

...........................................................

On the Shoulders of Giants E a r l y H i s t o r y of H y p e r f i n e S t r u c t u r e Spectroscopy. For Gisbert zu Putlitz P. Br/x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

423

439

Two-Photon Method for Metrology in Hydrogen Bernard Cagnac Laboratoire Kastler-Brossel, Ecole Normale Sup~rieure et Universitfi Pierre et Marie Curie, 75252 Paris Cedex 05, France

1

Introduction

The history of two-photon transitions ( E 2 - E 1 = 2hw) starts with the beginning of quantum mechanics, during this fascinating period around nineteen thirty when all the modern physics was born. The calculation of the twophoton processes was one of the first applications of the time dependent perturbation theory. It was pub!ished in Annalen der Physik in 1931 as the thesis of Maria GSppert-Mayer "Uber Elementarakte mit zwei Quantenspriingen" [1] at the University of GSttingen in Germany. At the end of the paper she thanks professor Born and Weisskopf. Owing to the relatively small probability of such processes, the experimental realization requires a high intensity of the electromagnetic wave. This is the reason why the first experimental observations where done in the radiofrequency range [2,3]. In the optical range, the ruby laser opened in 1961 the era of multiphoton excitation with the experiment of Kaiser and Garret [4] between braod bands in a crystal. The first precise experiment between narrow atomic levels was done by Abella in Cs vapour using thermal tuning of the ruby laser [5]. From 1968 on, the realization of the really tunable dye laser permitted easier experiments [6] and was followed by an explosion of the number of experiments in atomic physics.

2

Two-Photon Method

Figure 1 represents the energy diagram for the process of two-photon absorption, showing the energy defect hAwr = (Er - El) - h~ of the intermediate relay level Er. The square of this energy defect (z~wr) 2 appears in the denominator of the transition probability, calculated in the perturbation theory to 2nd order. (Strictly speaking, it is necessary to carry out the summation over all other levels, but often only one Er has an important contribution). One must compensate the big term (Awr) 2 (the energy defect) in the denominator by a high intensity of the light beam. For that, you can enclose the atoms between two mirrors forming a Fabry Perot cavity. Then the atoms are exposed to two light beams travelling in opposite directions: forward and

Bernard Cagnac

ENERGX

ATOI v -

FRAM :)

E:-'I, BACh(WARD Fig. 1. Energy diagram of a two-photon transition

backward. If you calculate in the rest frame of one particular atom, and if you take into account the Doppler shift of the light frequency due to the velocity v of this atom (the component on the common axis of the two light beams) the apparent frequencies of the two light beams are symmetrically shifted (w + kv), where k is the wave vector, inverse to the wavelength. If the atom absorbs one photon of each oppositely travelling wave, the total amount of the absorbed energy is 2hw independent of the velocity. And the two-photon transition will be Doppler-free. This analysis was done in 1970 by Professor Chebotaev and coworkers in Novosibirsk [7]. In our laboratory, we came later on the same problems [8], but we were interested to study the real feasibility of the two-photon method: the detailed and numerical calculation of the probability showed that the experiment was possible with the low power of dye lasers with very high spectral purity. We analysed the selection rules. We were also able to show that it was possible to overcome the problem of light shifts. We benefited by the vicinity of Professor Cohen-Tannoudji, who had first understood the origin of the light shifts [9], and had the good formulas for their evaluation [10]. The first experiments applying these ideas were carried out almost simultaneously in three groups: in Paris [11], in Harvard [12] and in Stanford [13] in 1974. A review of early experiments can be found in [14]. The proposal for the 1S-2S transition in hydrogen, we gave at this moment [8], was made also independently by Baklanov and Chebotaev [15]. Everybody knows the success obtained later with that experiment by the team of Professor Hgnsch in Garehing [16]. The difficulty was to produce enough light power at the corresponding wavelength of 243nm (two times the L y m a n - a wavelength of 121.5 nm; cf. energy diagram of Fig. 2a showing recent experiments). The 243 nm radiation was produced by frequency doubling pulsed light at 486 nm in a lithium formate crystal.

Two-Photon Method for Metrology in Hydrogen ZERO OF ENERGY [ionizedhydrogen}

I'

~9c

~|

Sw2

Z~ .... M

3/2

D3/2 D5/2 ~ 12=3

~/2

j

i

P312

S C A L E xl I f ULTRAV'IOLK'T

SCALE

I ~3.10~s hcR

x4

~,mb shift

n=2

n=l

-~ [orbit.} 0 ~

(a)

~"'x' ~'~'~.~ .~.,.~='~' ~.,.- O~ (total.]

i12

1

1

I/2

312

2

3/2

5/2

(c)

Fig. 2. Energy diagram of atomic hydrogen showing the transitions recently studied in the indicated laboratories (corresponding wavelengths are indicated at the bottom. a) full diagram from the ground level n = 1 up to ionisation (zero of energy). b) energy scale multiplied by 4 showing the studied transitions from the metastable 2S level, c) fine structure of levels n = 2 and n = 3 depending on the two quantum numbers orbital l and total j.

But the rigorous control of the light frequency during pulses raised m a n y problems. Improvements of such pulsed experiments were obtained via pulseamplified continuous wave (cw) lasers and filtering of the laser pulses. Nevertheless, it is impossible to avoid frequency shifts during the amplification [17]. A detailed study of this frequency chirping effect [18] shows clearly that high precision experiments must be performed with continuous wave light beams.

4

3

Bernard Cagnac

L o n g i t u d i n a l or C o l l i n e a r I r r a d i a t i o n of an A t o m i c Beam

In Paris, the choice was to work in a more conventional range of wavelength, and that permitted to observe in 1985 the first two-photon transition produced with a cw light b e a m in an atomic beam of hydrogen [19], developing the collinear geometry, which has been adopted now in all two-photon precision experiments: the atomic b e a m is irradiated longitudinally, along its own direction, thus producing the m a x i m u m first order Doppler shift, for each of the two counter-propagating laser beams. It does not matter, as the first order Doppler shift is perfectly cancelled. Surely, this collinear geometry increases the very small residual second order Doppler shift; but it increases also largely the interaction time between atoms and light and reduces the transit time broadening below 10 kHz. T h e more conventional wavelengths were found by using the metastabte 2S level of H as the departure of the transitions (instead of arrival; cf. the magnified energy diagram in Fig. 2b). Figure 3 shows the heart of the experiments in Paris for transitions starting from the metastable 2S level of hydrogen: molecular hydrogen is dissociated in a water cooled radiofrequency discharge and the atoms effuse through a nozzle into a first vacuum chamber. A small fraction of them (10 -7) is excited to the metastable 2S state via electron b o m b a r d m e n t . Some of these atoms, deviated through an angle of about 20 ° as a result of the collisions, pass through an aperture into a second vacuum chamber. Another aperture

I Re~ord~ag I~ \

FeedbacA¢

Towards the pumps

Fig. 3. Experimental set up for two-photon transitions from the metastable 2S level, with the longitudinal or colfinear irradiation of the atomic beam.

Two-Photon Method for Metrology in Hydrogen

5

about 50 cm downstream is followed by a detection region in which an electric field is applied to quench the metastable atoms by mixing the 2S and 2P states of neighbouring energy (cf. Fig. 2c) as in Lamb's experiment: the Lyman-~ intensity emitted from the 2P state, recorded with photomultiplier tubes, is proportional to the number of the atoms in the metastable 2S state. The excitation of the resonance is signalled by the depletion of the population of the 2S state as most of the excited atoms fall down in energy to the ground level directly or through the 2P level, avoiding the metastabte 2S state. The apertures help to define the atomic trajectories, a knowledge of which is essential to the interpretation of the atomic spectra. A continuous wave tunable laser propagates along the central axis of the atomic beam. There are, in fact, two intense laser beams as the entire beam apparatus is located inside a high finesse optical cavity. Resonant coupling of the laser light into a TEM00 mode of this cavity ensures both complete overlap of forward and backward beams and enhancement of the optical power available to excite the atoms, both of which are necessary in order to achieve a decent two-photon excitation rate. In the first experiments [19] a dye laser was used, though now a titanium::sapphire laser has replaced it yielding higher power and better frequency stability. In this way, the energy spectral density in the interaction region is equivalent to powers of up to 100 W in a bandwidth of a few kHz. For experiments starting from the 1S ground level, the electron bombardment does not exist; and the hydrogen atoms prepared in the lateral discharge are guided through a Teflon tube [20] to a nozzle, which is a narrow channel centred on the axis of the laser beam. In the case of the transition to the 2S level, like e.g. in Garching, these metastable atoms are also detected at the end of the beam by electrical quenching [21].

4

Light

Shifts

and

Two-Photon

Line

Shapes

A detailed understanding of the line shape is crucial to the success of these experiments. In fact, the most important problem concerning the lineshape comes from inhomogeneous light shifts. When an atom crosses the laser beam, it experiences a varying light intensity and hence a varying light shift. In some instances, this can produce asymmetrical line shapes. However, one can show that if the two-photon transition is far below saturation (two-photon transition probability p(2) ~ < Fe) the light shifts may be much smaller than the natural width F~ [8]. In such cases it is sufficient to work with different optical powers and to extrapolate to zero power. Close to saturation and in precise metrology, one is forced to calculate the light shifts exactly. This was done for example in the experiment on atomic hydrogen performed in Paris on the 2S-nS/nD transitions. The excitation geometry, taken into account in the computer calculation, is indicated in Fig. 4 (the atomic beam is larger than the laser beam). The lineshapes are catcu-

6

Bernard Cagnac o n e particular atomic trajectory

lStdial:)h.

2mldiaph. ,

Fig. 4. Detailed geometry of atomic trajectories through the Gaussian laser beam, taken into account in the computer calculation.

L

lated by summing the contributions of all possible atomic trajectories crossing the laser beams, taking into account the Gaussian distribution of the light power. Figure 5 shows two examples of such lineshapes for the 2S1/2-10S1/2 and the 2S1/2-10D~/2 transitions. As explained previously, these signals appear in absorption. Both signals have asymmetrical lineshapes which are well modelled by calculations. After adjustment of the theoretical curve with the experimental points, the computer is able to calculate the precise true (i.e. unshifted) position of the line [22]. As an illustration we compare in Fig. 6 for each value of the light power: - this true position of the transition (laser frequency) given by the computer calculation after correction of the light shifts - the "brute" half maximum centre of the experimental line The extrapolation of "brute" centres is not exactly linear, whereas the calculated positions are well independent of the light power, which confirms the validity of the theoretical model.

n(2S) n(2S)

(a)

(b) )

! atomic frequency

i

i

i

I

atomicf~uency

Fig. 5. Experimental recordings of two-photon transitions 2S-10S and 2S 10D showing the red-shift for one and the blue-shift for the other in agreement with theory (points are experimental; full lines are theoretical).

Two-Photon Method for Metrology in Hydrogen

7

H a l f - m a x i m u m center of the line 1

- = =:=:-:-::-

....... ! ....... ....... T/i

....... i .......

position

o

<

Light power Fig, 6. Control of the light shift: for each value of the light power inside the Fabry Perot cavity (horizontal axis) the computer indicates on the frequency vertical axis: * small stars: "brute" half maximum centre of the experimental recording, o small circles: corrected "true" position deduced from the theoretical curve.

In the experiments from the 1S ground level, it is not possible to obtain such high power in the ultra-violet cw light b e a m (some m W only), and the two-photon transitions are far below the saturation, corresponding to negligible light shifts. The two-photon transition probability is also very small, but it is applied to the big number of atoms in the ground level and gives enough signal. In the case of the 1S-2S transition, the theoretical linewidth is so small (some Hz) that the width is determined in practice by the transit time of the atoms in the light wave. The team in Garching has strongly reduced the 1S-2S line width by cooling the nozzle from which the atomic b e a m originates, thus reducing the atomic velocities [23], as illustrated in Fig. 7. The shift and asymmetrical shape observed in Fig. 7 is due to the seco.

-~ ~

S~-3skHzj

( =~K

oE

I

-200

-150

-1GO

-50

0

u'v deluning in kHz

50

1C~

Fig. 7. Recordings of the 1S-2S two-photon transition in Garching [23] in a cooled atomic beam, showing the asymmetry due to the second order Doppler effect (points: experimental; full line: theoretical).

8

Bernard Cagnac

ond order Doppler shift and can be exactly modelled. The width decreases as the atomic velocity v, whereas the second order Doppler shift decreases proportional to v 2, the square of the velocity; this is the reason why this shift seems to disappear at the lowest temperature. In all cases, it is possible to determine the true position of the line centre with a precision which is a small fraction of the linewidth (better than one hundredth; probably one thousandth), permitting metrologic measurements. 5

Two

Types

of Experiments

- Transitions

in an

Integer Ratio In fact two types of experiments can be distinguished in optical spectroscopy of hydrogen: 1) Absolute wavelength or frequency measurements of the transitions by comparison with an optical standard, with the aim of determining the Rydberg constant (see next section). 2) Owing to the simplicity of the Rydberg law, governing the energy levels of hydrogen, it is possible to compare directly the frequencies of some transitions which would be in an integer ratio, measuring without any standard the small difference between the high frequency and the harmonic of the low frequency. This second type of experiments permits to determine experimentally the small corrections calculated in the theory, coming from the quantum electrodynamics (Q.E.D.) or from the electron penetration inside the finite volume of the nucleus. These two corrections are particularly important for S levels (l = 0, with a significant probability density to find the electron inside of the extended attraction centre) and are responsible for the energy difference between S and P levels corresponding to the same total quantum number j (see Fig. 2c): they are the so-called Lamb shifts [24]. The Lamb shift of the 2S metastable level could be determined with precision in radiofrequency measurements of the separation 2S-2P [25], whereas the 1S ground level is isolated and its Lamb shift can be only deduced indirectly from the total energy of the 1S level. Table 1 indicates transitions, whose frequencies are in a ratio 4 and which are investigated in various groups in experiments with the aim of measuring the 1S Lamb shift (see Fig. 2a and 2b). If one compares a two-photon transition with a one-photon transition, the two experimental frequencies are only in the ratio 2. If both transitions are two-photon transitions, their frequencies are also in the ratio 4, i.e. one must realise frequency doubling two times in succession for the comparison of frequencies [28,30]. Figure 8 shows the experimental set-up of the most recent experiment, in Paris, for comparison of the 1S-3S transition to 2S6S/6D. Two ring cavities (astigmatically compensated) are used to enhance

Two-Photon Method for Metrology in Hydrogen ~rsttransifion

Z1

Second transifion

Z2

Place, date

9

Reforence

ITwo-Photon IS-2S 243 nm

I photon 2S-4P (saturation)

486 nm 'Stanford 1980

[261

Two-Photon 1S-2S 243 am

1 photon 2S-4P

486 am Oxford 1992

[27]

(crossed beams)

Two-Photon IS-2S 243 am

2-photon-2S-4S/4D 972 nra Garching 1992 and 1994

[281

Two-Photon IS-2S 243 nm

1 photon 2S-4P

486 nm Yale 1995

[291

2-photon 2S-6S/6D 820 nm Paris 1995

[301

(crossed beam)

Two-Photon IS-3S 205 nm

Table 1. Comparison of wavelengths in some hydrogen transitions.

the doubling efficiency in the two successive doubling crystals LBO (from IR to blue) and BBO (from blue to UV). The apparatus for the 2S 6S/6D transition is the same as the one shown in Fig. 3; the apparatus for the 1S3S transition uses a beam source analogous to the one in Garching, but the detection must utilise the red Ha line emitted by the atoms excited to the 3S state and is more noisy (sensitive to parasite light). The values of the 1S Lamb shifts obtained in the most recent experiments are in agreement within the error bars:

L1s --8 172.860 (60) MHz Lls ----8172.827 (51) MHz Lls =8 172.798 (46) M n z

[28] [29] [30]

The interpretation of these values has benefited of the recent advance in theoretical calculations (see section 8). Previously, these values of the 1S Lamb shift seemed to be in favour of the smaller value of the r.m.s, radius of the proton V / ~ = 0.805fm [31]. With the recent theoretical advance in the Q.E.D. calculation, the larger (and more recent) value ~ = 0.862fm [32] is in better agreement. The difficulty in interpreting the Lamb shift value arises from the fact that it mixes two independent corrections (Q.E.D. and nuclear size). One solution would be to work with another nucleus; this is the interest of the project now developed in Yale University to measure the Lamb shift in the He + single ion, where the nucleus (the a particle) has a well known radius [33]. Nevertheless, it is not clear if the effect of the penetrating electron in a composite nucleus can be represented with a single parameter x/(r~).

~0

Bernard Cagnac

UV photomullipliers ~ 82Ohm ~]

I TiS:lLase( [

e~

0 41{)am

.~LBO

v

]

,,~,s,

2S-6S/6D apparatus

205 nm ~_ It trY6Inn Filler--~ Pholomulliplier--~J

1S-3S apparat.s Fig. 8. Experimental set-up for direct comparison of the two-photon transitions 2S-6S/6D (~ = 820nm) and 1S-3S (A = 205nm).

6

F r e q u e n c y Calibration - T h e R y d b e r g C o n s t a n t

In the classical spectroscopic measurements, you compare the wavelength of your particular transition with the well known wavelength of an optical standard using an interferometric apparatus (Miehelson or Fabry Perot). Everybody knows the current optical standards used in the laboratories, i.e. laser stabilised by saturated absorption on a Doppler-free molecular line: I2 near 633nm, or CH4 near 3,39ttm with a He-Ne laser; OsO4 near 10/zm with a CO2 laser. Another secondary standard used in these experiments is the Te2 molecule near 486nm (wavelength of the Balmer-fl line) with a Coumarine dye laser [34]. The absolute measurement of wavelengths or frequencies (it comes to the same thing, as now the light velocity c is fixed) of the hydrogen transitions permits the determination of the Rydberg constant. But one must not forget that, in order to deduce the Rydberg constant from the measured transition frequencies, a theoretical interpretation is necessary, which comprises many small corrections (see table 2) As we have seen in the preceding section, these corrections are particularly important in the S levels (quantum number l=0) which are involved practically in all experiments. In the case of transitions starting from the metastable 2S level, it is possible to use the experimental value of the 2S-2P Lamb shift [25] and to reduce the theoretical calculations to the small corrections in P or D levels; these transitions are more convenient for the Rydberg determination. The transitions from the 1S ground level are better suited for the measurement of the 1S Lamb shift and the deduction of the proton radius, as explained in the preceding section. Figure 9 compares the values of the Rydberg constant determined since the last adjustment of fundamental constants [35]. The horizontal scale of

Two-Photon Method for Metrology in Hydrogen I0¢I237.31~00 200 I I

400 '

cod,,~ I

•

"r~O-eHOVONaS.~n0DI

:',

O/~.pI.IOTON[2S-3P

"~

]

L2~--4p

T'WO-PHOTON

m.zs,fl L

(:~-1 a x o ~

[3s]

I Paz~.sl ~ :

I

[

Yale Yale

t I

•!

1986 1987

i

~- ~ i,#,

Paris 1988

. . . . . -,, -...

_,~....... ~__," ,ff "--..~ vwo-P~ovoNm-zs ~ I

; 1

TWO-~0TON

~-es~

1 -

I

1992_ D6]

i •

I

tl i _,,,: - , , :

Garching199")Faro1988 c o r r e c t e d

[]el Fig. 9. Values measured for the Rydberg constant since 1986. The horizontal scale (in cm -1) is multiplied C39| two times: by 5 and by 8, showing [41 ] the increasing precision with time (the numbers in brackets refer to the references). [4tl ~7I [38I

I Seaz~rd t ~

!

iI_

TWO-PHOTON 2S-SD/10DII2D x8

D

600 800 i,, I i)

Z ,., , ~' x5

19~

11

,

8Ds/z

18D3/z , ~ ~ 2 ("

[4~1

Mean .J

the Rydberg constant is magnified twice (× 5 and x 8) from the top to the b o t t o m of the figure, demonstrating the increasing precision with time. When you exceed the level of precision of 10 -1°, it becomes very difficult to take into account exactly the corrections unavoidable in the interferometric measurement comparing different wavelengths: the reflective phase shift, due to different penetration depths of the evanescent waves inside the coating of the mirrors; the Fresnel phase shift associated to different curvatures of the wavefronts. These effects can be almost negligible only if the two wavelengths are very close to each other. Therefore, for the highest level of precision, it is better to perform direct frequency comparisons with heterodyne techniques. This was the case in the latest measurement in 1993 [44]: one mixes in a lithium iodate crystal (LiIO3) the hydrogen transition frequency (2S-8S/8D, A = 778 nm i.e. u = 385.2 THz) and a standard He-Ne laser stabilised on CH4 (A = 3,39#m i.e. u = 88,4THz), producing the frequency sum 473,6THz, which falls in the vicinity of the frequency of the standard He-Ne laser stabilised on iodine at A = 633 am. The gap of 89GHz between this standard and the frequency sum can be bridged by a triple mixing of the two optical frequencies and the microwave of a Gunn generator in a Schottky diode. These measurements utilised at the beginning the frequency value of the iodine standard determined for the first time in 1983 at the U.S. National Bureau of Standards (NBS) [45]. Its precision has been improved with a new determination in the Observatory of Paris in 1992 [46]. The good agreement between the results obtained in Paris and in Garching using different standards gives confidence in the value obtained for the Rydberg constant: R ~ = 109 737.315 684 1 (41) R ~ = 109737.3156834 (24)

[42] [44]

12

Bernard Cagnac 5D $/2

5Sl/2(Ft=l)-5D~(Fc=3) BTRb T']8 n m

.....

5 P+a / 5

778nm /

P1//

420 nm

P 5Sm+l ._~ V~ 85Rb

S7Rb

1MHz I

!

(a)

I

I

fr~lU~-y

,fits--> Z ~3 +~z.--->1 + 2

(b)

Fig. 10. Principle of two-photon standard in rubidium: a) energy diagram ; b) experimental recording: UV fluorescence at 420 nm versus the laser frequency (points: experimental - full line: fitted Voigt profile).

The precision of the experiment in Paris is limited by the precision of the iodine standard (the width of the Doppler-free line of iodine is rather large, around 5 MHz).

7

D e v e l o p m e n t of a N e w Optical Standard

The problem is to find a new optical standard with a smaller linewidth than iodine, and a wavelength better fitted to the ones used in the hydrogen experiments. The two-photon method has given such a standard with the rubidium atom. Figure 10a shows the energy diagram of the lower levels of the rubidium a t o m with the two-photon transitions. Numerous two-photon transitions have been observed in rubidium, at the beginning of the two-photon method, reaching excited levels with n = 11 to 32 [47] and then up to n = 124 [48]. The lower excited level could not be attained with the dye lasers at that time. Now the Ti::Sapphire laser or the laser diodes working in the near infra-red permit to observe the lower levels. The 5S-5D transition at )~ = 7 7 8 n m is particularly intense because the laser frequency is close to the resonances with 5P1/2 (795 nm) or better 5P3/2 (780 nm). T h a t permits to produce the two-photon transitions with low intensity, without focusing the laser b e a m and to reduce the light shifts to a negligible level. The detection is very easy by collecting the fluorescence light at A = 420 nm in the near UV, emitted in the cascade from the 5P level. Figure 10b shows a particular line chosen inside the hyperfine multiplet [49]; the experimental points are fitted with a Voigt profile. This typical recording is obtained with 100 m W light power each way in an area rt w 2 = 10 m m 2. The width of 500 kHz is ten times smaller than the iodine lines and the signal-to-noise ratio is of the order of 400-500. We have verified

Two-Photon Method for Metrology in Hydrogen ECL

13

~-~merphic plum

Fig. 11.

~eJding

to lock-in ampllfler

Experimental set-up of the two-photon standard (ECL: Extended Cavity laser diode with grating for wavelength selection).

that the position of the line is quasi-independent of the Rb vapour pressure (from 10 -4 Torr to 2.10 -5 Torr by varying the cold point of the Rb cell from 90 °C to 50 °C) and to the change of the cell. The only significant shift is the light shift: in this case, it is much smaller than the line width; and, working with increasing light power up to 600 mW, we have verified that it can be linearly extrapolated. The residual light shift in the case of 100 m W (case of Fig. 10b) is 2 kHz only and can be stabilised with the light intensity. The second step was to build an autonomous standard [50] following the scheme of Fig. 11: The laser diode is mounted in an extended cavity with a grating in order to assure a single mode oscillation. The shape of the light beam is corrected by an amorphic prism before irradiating the Rb cell through 2 or 3 Faraday isolators preventing a spurious feedback to perturb the laser diode. A lateral lens with big aperture collects the UV photons emitted in the return cascade from the 5P level. The two-photon resonance could be observed by simply reflecting the laser beam back onto itself with a mirror without the usual Fabry Perot cavity; but the cavity is better to assure a perfect coincidence of the incoming and return beams. The stabilization is obtained with two servo loops: the fast one reacts on the laser diode current while the slow one controls the piezoelectric transducer (PZT) supporting the grating (Fig. 11). In a set of preliminary measurements the frequency stability has been controlled; the square root of the relative Allan variance is: a(2, r ) / u = 3.1013/V/~

up to

r = 1000sec .

(1)

It is ten times better than a He-Ne laser stabitised on iodine. A preliminary calibration has been done [49], relative to the iodine standard, using the same frequency chain as for the hydrogen experiment [44]. The precision of some kHz is limited by the iodine standard. A new calibration is in development in the Laboratoire Primaire des Temps et Fr6quences (L.P.T.F.) in the Observatory of Paris, using the fact that the rubidium frequency is close to the 13th harmonic of the CO2 laser stabilised on OsO4.

]4

Bernard Cagnac

An optical fiber (less than 3 km) between the Observatory and our university permits to exchange the lightwaves of our Rb standards and to control their stability; it will permit to transfer the calibration without displacement of any standard. The calibration of the hydrogen transition 2S-8S/8D will be obtained by the triple mixing on a Schottky diode of the Ti::Sapphire light wave used for hydrogen, the rubidium light wave, and a 40GHz klystron adjusted to bridge the gap. Surely, that will permit to surpass the precision of 10 -11 . Up to 10 -12 ? - We will see. Anyway, except for the particular transition 1S-2S, taking into account the natural line widths of the hydrogen levels, it seems hardly likely that the experimental precision can be pushed largely beyond 10 -1~. Surely, the highly excited Rydberg levels (particularly "circular" states with l = n - t) are long living; but they are also very sensitive to residual parasitic fields and not adapted to metrology. 8

Confrontation

with

Improvements

of the

Theory

Admitting that the experimental precision can be pushed in the future to the 10 -12 level, these measurements can be interpreted only if the theory reaches the same level of precision, which is not yet the case. Where has the theory arrived now? All calculations start from the formula obtained by Dirac from his relativistic equation [51] modified with the reduced mass/~ = m/(1 + re~M) in place of the true mass m of the electron (M is the proton mass). This modified formula has no exact theoretical justification, as the classical centre of mass has no sense in relativity; nevertheless, it permits to take into account to first order the problem of the nuclear motion. Therefore the binding energy E,~j of the level of quantum numbers n and j is given at zero order by the formula: EnJ :

#c2Z2~ 2

I,.gC2

1

V with

l j(

= J + 2 -

J+

- (Za)2

~

,zo,2

2j + 1

(3)

Ze is the charge of the nucleus (e the elementary charge). (~ = e2/4aotic ,~ 1/137 is the fine structure constant, which gives the order of magnitude of the ratio v/c of the electronic velocity v to the light velocity c. In fact the relativistic calculation and the nuclear motion corrections are intimately intricated and one has to perform an expansion simultaneously in powers of two independent variables m / M and Z a . T h a t explains the

Two-Photon Method for Metrology in Hydrogen

15

five lines in the top of table 2; the well known terms of first order in m/M or in ( Z a ) 2 do not appear in this table, as they are taken into account inside the Dirac formula. This table is intended for non specialists; and for simplification, when we give the order of each term in the expansion, we choose as term of zero order, i.e. as unity, the binding energy E,j (Eq. (2)), which is measured in experiments. (The specialists choose as zero order term the mass energy mc2; i.e. each term must be multiplied by (Za) 2 if you compare with the theoretical formulas, indicated by their reference numbers in some theoretical review papers [52-55].) The radiative corrections, coming from the quantum electrodynamics, necessitate an other expansion in power of c~, which occupies the central part of the table 2. Among these corrections one distinguishes the self-energy (S.E.), the vacuum polarization (V.P.) and the effect of the anomalous magnetic moment, which affects the spin orbit constants in the P and D levels. The most i m p o r t a n t terms correspond to the self-energy in the S states (l = 0) in which the electron has a significant probability density in the nucleus; that raises the degeneracy in l, characteristic for the Dirac formula and produces the so called L a m b shift between the $1/.~ and P1/2 levels (see Fig. 2c). It is yet necessary to calculate the crossed corrections, i.e. radiative corrections to the recoil terms, or recoil corrections to the L a m b shift. The term of lowest order in (m/M)o~(Zo~)2 does not appear in table 2, because it is taken into account by multiplying all radiative corrections with the factor (p/rn) 3 which represents the modification of the wave function at the origin. The terms of higher orders are small but not negligible, and their calculations is not yet quite clear [63,64]. Finally, one must add the correction due to the finite size of the nucleus, which is particularly important for the S levels (l = 0; important electron probability density in the nucleus) and depends on a badly known p a r a m e t e r the r.m.s, proton radius x/(r2). All these calculations use the values of the two parameters rn/M and a. But, since the last adjustment of the fundamental constants [35], the precision has been strongly increased on these two parameters: the electron to proton mass ratio m/M in Penning trap experiments [65], the fine structure constant a in measurement of (g-2) [66] and progresses in its calculation [67]. The present uncertainty on these parameters does not raise problems on the calculation of the energy levels before the 10 -12 level of precision. The limitation comes from the high order necessary in the expansion. The number of terms (or Feynman diagrams) which appear in the expansion increase strongly with the order of the expansion; when you come to the fifth order it can approach a hundred. The calculation is not easy and all terms to the fifth order gave rise in the past years to controversies; the most of which seem now to be settled, owing to very recent advances since two years. These most recent papers are referenced in table 2. The problem arises from the fact that the coefficients found inside some of these terms can be as big as 100, and then these terms are equivalent to

16

Bernard Cagnac

Physical effec~ involved

[S2l 'Order in d~e

~paeston

On;/m"o f

ma~

a~,! -7.=1

n:duced rna~

1

1

E ~ ....

Review- P a l m {531 {5,,1 Sa~tei~ y~ 1990

M~ra" 1995

~admda 1995

(39) (40)

, (19)

(41)

(34)

w,et,k

(2-.4)

(2-7) ~(2-3)

Rela~t~"

(55]

pb.oeon

and

,.,o ~wo

Recoil

(24)

a~xerams

(2-9)

photon

(2-73

(43)

OC.gnms

o~e

loop Radiam,e

~ (Za)~

I0-~

-a(Za)'

to+

~(z~)"

1o-9

(2-10) t2-11)

(C-t)

(2-5) ),a,b.¢

(44)

(36)

(62) • (45) r (50)

S.F_ {21) (23)

$.E.

~' V,P.

[,t61 [4'71 v.P.

(2n

[.561

[5"71

{ss]

[5[[ [S3I oml.~.-tlo~

-a(Za) ~ fc

two Q.E.D.

[59]

to-n

2

(2-1'2)

( ~ ) (Za) z

10-9

(~)~(Za) J

10-|0

(29)

(2-13, (2-153 r (61)

loop diagrams

01)

[61]

(32) (33)

[62]

(37) ~ (38)

{~l [6,t}

(40)

[~]

: Crossed oor~c~ons

m a Za)* (~)~'(

(2-8)

I0"'

(ReL only)

radiative and mvoil m 2~. g l x :

Fimte s g e of nucleus

(2-30)

(2-11)

(64)

(40) I

Table 2. Summary of the power expansion ia the calculation of energy levels.

the terms of preceding order. This was the case in particular for the term in ( a / l r ) 2 ( Z a ) 3 (two loop diagram in the radiative correction) which, after exact calculation, was found ten times bigger than expected, and modified consequently the interpretation of the 1S L a m b shift (see section 5). It remains yet a controversy on the crossed correction of order (re~M)(a/Tr)(Zoo)3 and most of the sixth order terms are unknown. As a consequence, one can now hardly await the 10 -11 precision from the theory.

Two-Photon Method for Metrology in Hydrogen

17

Another limitation comes from the large uncertainty on the proton radius, ( V / ~ , which appears in the nuclear finite size correction (last line of table 2). In fact, the finite size correction and the Q.E.D. corrections are intricately mixed in the exact determination of S levels; and the advances in the Q.E.D. correction will permit to deduce a value of the proton radius. If both theoreticians and experimentalists attain in the future the level of precision of 10 -12 on the totM energy (or a few 10 -7 on the 1S Lamb shift) the proton radius could be determined with a precision better than 1%. On the other hand, the determination of the Rydberg constant can be in some respects independent of the proton radius (and partially of the Q.E.D. corrections) if one utilises some particular combinations of transitions, using the fact that the finite size correction scales as 1/n 3 with successive n levels with the same orbital quantum number I (that is the same for a big part of the Q.E.D. corrections). As it was noticed in [62], for example, the combination (Lls - 8L2s) of the 1S Lamb shift and the 2S Lamb shift is small and quite independent of the proton radius; and the present limit of the theory could nevertheless permit a determination of the Rydberg constant at the 10 -12 level, if the experimentalists continue their advances.

9

Conclusion

At the present time, experimentalists and theoreticians have attained the same level of precision of a few 10 -11 in the determination of the energy levels of hydrogen. One proof is given by the coincidence at this level of precision of the values obtained for the Rydberg constant R ~ from different transitions. Taking into account the big progresses which have been accomplished in the past few years, in experiments and in theory it is possible to hope for further advances in the next years up to a level of 10 -12 with its consequence for the knowledge of the proton radius. The comparisons with other hydrogenic systems (ionic He +, muonium, positronium, ...) surely will help to improve the knowledge of the Q.E.D. corrections and participate to this advancement; these problems are explained in other papers. Nevertheless, it is not sure that it will be possible to pass beyond the experimental limit of 10 -12. Certainly, the exceptional precision of the particular transition 1S-2S will be used in the future for an optical frequency standard with very slow atoms from an hydrogen trap [68]. But the theoretical interpretation, depending on two parameters, R ~ and X / ~ , requires two independent measurements with the same level of precision (supposing that c~ and m / M will follow the same advance...). Anyway, the Rydberg constant R ~ , determined with 10 -12 precision, will remain a corner stone of the adjustments of fundamental constants, far in advance compared to other constants. R ~ is a combination of three fundamental constants m, h and e; two of them h and e are linked by the fine

18

Bernard Cagnac

structure constant a with a precision, better than 10-8; but a third relation at the same level of precision is missing; and m, h and e are known individually with a precision hardly better than 10 -6. Will some advance in the Josephson effect (depending on h/e) be able to bridge this gap? Let me conclude with a personal feeling of perplexity when looking at table 2, which summarizes the calculations: is it not surprising that any correspondence with the reality is obtained after so numerous pages with complicated integrals in the scientific journals and after so many hours of abstract computer work? Nevertheless it works! All right, we believe that physics explains the world and provides us with an understanding of reality i.e. reduces apparent complexity to simplicity. But in what sense is it possible to speak of explanation and understanding when we compare these long and tedious calculations with the spontaneous functioning of any simple electron in all water molecules of the ocean, or in all atoms of the intergalactic clouds?

Note added in proof." The experiments with the new Rb standard and the optical fiber (described in section 7) obtained very recently a new result at a level of 10 -11 for the Rydberg constant R ~ = 109737.3156859 (10) [69].

References [1] Ghppert-Mayer M., Ann.Phys., Lpz 9, 273 (1931) [2] Hughes V.W. et Grabner L., Phys. Rev. 79, 314 and 819 (1950) [3] Brossel J., Cagnac B. et Kastler A., C.R.Acad.Sci.Paris 237, 984 (1953), and J.Physique 15, 6 (1954); Kusch P., Phys.Rev.93, 1022 (1954) and 101, 1022

(1956) [4] Kaiser W., Garrett C.G.B., Phys.Rev.Lett. 7, 229 (1961) [5] Abella I.D., Phys.Rev.Lett. 9,453 (1962) [6] Bonch-Brnevich A.M., Khodovoi V.A., Khronov V.V., JETP Lett. 14, 333 (1971); Agostini P., Ben Soussan P., Boulassier J.C., Opt. Comm. 5,293 (1972) [7] Vasilenko L.S., Chebotaev V.P. and Shish£v A.V., JETP Lett. 12, 113 (1970) [8] Cagnac B, Grynberg G. and Biraben F., J.Physique 34, 845 (1973) [9] Cohen-Tannoudji C., Ann.Phys. 7, 423 et 469 (1962) Alexandrov E.B., BonchBruevich A.M., Kostin N.N., Khodovoi V.A., JETP Lett. 3, 53 (1966) [10] Cohen-Tarmoudji C., Dupont-Roc J., Phys. Rev.A 5, 968 (1972) [11] Biraben F., Cagnac B. et Grynberg G., Phys.Rev.Lett. 32, 643 (1974) [12] Levenson M.D., Blembergen N., Phys.Rev.Lett. 32, 645 (1974) [13] H£nsch T.W., Harvey K., Meisel G. and Schawlow A.L., Optics Comm. 11, 50 (1974) [14] Grynberg G., Cagnac B. and Biraben F., in: "Coherent Non Linear Optics" (Springer) Topics in Current Physics, vol. 21, p 111 (1980) [15] Baklanov E.V. and Chebotaev V.P., Opt.Comm. 12, 312 (1974) [16] H£nsch T.W., Lee S.A., Wallenstein R. and Wieman C., Phys. Rev.Lett. 34, 307 (1975); Lee S.A., Wallenstein R., H/insch T.W., Phys.Rev.Lett. 35, 1262 (1975); Wieman C., H£nsch T.W., Phys.Rev.A. 22, 192 (1980) [17] Tr~hin F., Biraben F., Cagnac B. and Grynberg G., Opt.Comm. 31, 76 (1979)

Two-Photon Method for Metrology in Hydrogen [18] [19] [20] [21]

19

Danzmann K., Fee M.S. and Chu S., Phys.Rev. A 39, 6072-3 (1989) Biraben F. and Julien L., Opt.Comm. 53,319 (1985) Walraven J.T.M. and Silvera I.F., Rev. of Sci.Instr. 53, 1167 (1982) Zimmermann C., Kallenbach R. and H~izlsch T.W., Phys.Rev.Lett. 65, 571-4

(1990) [22] Oarreau J.C., Allegrini M., Julien L. and Biraben F.J., Physique 51, 2263, 2275 and 2293 (1990) [23] Schmidt-Kaler F., Leibfried D., Seel S., Zimmermann C., K6nig W., Weitz M. and HKnsch T.W., Phys.Rev. A 51, 2789 (1995) [24] Lamb W.E. Jr. and Retherford R.C., Phys.Rev. 72, 241-3 (1947) [25] Lundeen S.R. and Pipkin F.M., Metrologia 22, 9 (1986); Hagley E.W. and Pipkin F.M., Phys.Rev.Lett. 72, 1172 (1994) [26] Wieman C.E. and H~insch T.W., Phys.Rev. A 22, 192-205 (1980) [27] Thompson C.D., Woodman G.H., Foot C.J., Hannaford P., Stacey D.N. and Woodgate G.K., J.Phys.B.: At.Mol.Opt.Phys. 25, L1-4 (1992) [28] Weitz M., Schmidt-Kaler F. and H£nsch T.W., Phys.Rev.Lett. 68, 1120-3 (1992); Weitz M., Huber A., Schmidt-Kaler F., Leibfried D. and H~insch T.W., Phys.Rev.Lett. 72, 328 (1994) [29] Berkeland D.J., Hinds E.A. and Boshier M.G., Phys.Rev.Lett. 75, 2470 (1995) [30] Bourzeix S., de Beauvoir B., Nez F., Plimmer M.D., de Tomasi F., Julien L., Biraben F. and Stacey D.N., Phys.Rev.Lett. 76, 384 (1996) [31] Hand L.N., Miller D.G. and Wilson R., Rev.Mod.Phys. 35, 335 (1963) [32] Simon G.G., Schmitt C.H., Borkowski F., Walther V.H., Nucl.Phys. A 333,

381 (1980) [33] Sick I., Phys. Lett. B 116, 212 (1982) [34] Barr J.R.M., Girkin J.M., Ferguson A.I., Barwood G.P., Gill P., Rowley W.R.C. and Thompson R.C., Opt. Comm. 54, 217 (1985) [35] Cohen E.R. and Taylor B.N., Rev.Mod.Phys. 59, 1121 (1987) [36] Biraben F., Garreau J.C. and Julien L., Europhys.Lett. 2, 925 (1986) [37] Zhao P., Lichten W., Layer H.P. and Berquist J.C., Phys.Rev.A 34, 5138

(1986) [38] Zhao P., Lichten W., Layer H.P. and Berquist J.C., Phys.Rev.Lett. 58, 1293 (1987) [39] Beausoleil R.G., McIntyre D.H., Foot C.J., Hildum E.A., Couillaud B. and H£nsch T.W., Phys.Rev./k 35, 4878 (1987) [40] Boshier M.G., Baird P.E.G., Foot C.J., Hinds E.A., Plimmer M.D., Stacey D.N., Swan J.B., Tate D.A., Warrington D.M. and Woodgate G.K., Nature 330, 463-5 (1987) [41] Biraben F., Garreau J.C., Julien L. and Allegrini M., Phys.Rev.Lett. 62,621 (1989) [42] Andreae T., KSnig W., Wynands W., Leibfried D., Schmid-Kaler F., Zimmermann C., Meschede D and H£nsch T.W., Phys.Rev.Lett. 69, 1923-6 (1992) [43] Nez F., Plimmer M.D., Bourzeix S., Julien L., Biraben F., Felder R., Acef O., Zondy J., Laurent P., Clairon A., Abed M., Millerioux Y. and Juncar P., Phys.Rev.Lett. 69, 2326-9 (1992) [44] Nez F., Plimmer M.D., Bourzeix S., Julien L., Biraben F., Felder R., Millerioux Y. and De Natale P., Europhys.Lett. 24, 635 (1993)

20

Bernard Cagnac

[45] Jennings D.A., Pollock C.R., Petersen F.R., Drullinger R.E., Evenson K.M., Wells J.S., Hall J.L. and Layer H.P., Opt.Lett. 8, 136 (1983) [46] Acef O., Zondy J.J., Abed M., Rovera D.G., G6rard A.H., Clairon A., Laurent P., Mill6rioux Y. and Juncar P., Opt. Comm. 97, 29 (1993) [47] Kato Y. and Stoicheff B.P., JOSA 66, 490 (1976) [48] Stoicheff B.P. and Weinberger E., Can.J.Phys. 57, 2143 (1979) [49] Nez F., Biraben F., Felder R. and Millerioux Y., Opt.Comm. 102,432 (1993) [50] Millerioux Y., Touhari D., Hilico L., Clairon A., Felder R., Biraben F. and de Beauvoir B., Opt.Comm. 108, 91 (1994) [51] Dirac P.A.M., Proc.Roy.Soc. A 117, 610 (1928) [52] Erickson G.W., J.Phys.Chem. Ref.Data 6, 831 (1977) [53] Sapirstein J.R. and Yennie D.R., in "Quantum Electrodynamics", edited by T. Kinoshita (World Scientific, Singapore, 1990) [54] Mohr P.J., "Fundamental Physics" in Atomic, Molecular and Optical Physics Reference Book, Drake (ed.) (American Institute of Physics, 1996) [55] Pachucki K., Leibfried D., Weitz L., Huber A., Kgnig W. and H£nsch T.W., Lecture at NATO Advanced Study Institute (Edirne, Turkey) - September 1994 [56] Khriplovich I.B., Milstein A.I. and Yelkhovsky A.S., Physics Scripta T 46, 252 (1993); Fell R.N., Khriplovich I.B., Milstein A.I. and Yelkhovsky A.S., Phys.Lett. A 181, 173 (1993) [57] Pachucki K. and Grotch H., Phys. Rev. A 51, 1854 (1995) [58] Pachucki K., Ann.Phys. (N.Y.) 226, 1 (1993) [59] Molar P.J., Phys.Rev. A 46, 4421 (1992) [60] Eides M.I. and Grotch H., Phys.Lett. B 301,127 and B 308,389 (1993); Eides M.I., Karshenboim S.G. and Shelyuto V.A., Phys.Lett. B 312, 358 (1993); Eides M.I. and Shelyuto V.A., JETP Lett. 61, 478 (1995) [61] Pachucki K., Phys.Rev.Lett. 72, 3154 (1994) [62] Karshenboim S., JETP Lett. 79, 230 (1994) [63] Bhatt G. and Grotch H., Phys.Lett. A 58, 471 (1987) and Arm.Phys. (N.Y.) 178, 1 (1987) [64] Pachucki K., Phys.Rev. A 52, 1079 (1995) [65] Van Dyck R.S., Farnham D.L. and Schwinberg P.B., I.E.E.E. Trans.Instr.Meas. 44, 546 (1995) [66] Van Dyck R.S. Jr., Schwinberg P.B. and Dehmelt H.G., Phys.Rev.Lett. 59, 26 (1987) [67] Kinoshita T. and Lindquist W.B., Phys.Rev. D 42, 636 (1990); Kinoshita T., Phys.Rev.Lett. 75, 4728 (1995) [68] Cesar C.L., Fried D.G., Killian T.C., Polcyn A.D., Sandberg J.C., Doyle J.M., Yu I.A., Greytak T.J. and Kleppner D., Communication to Fifth Symposium on Frequency Standard and Metrology - Woods Hole, October 1995 [69] de Beauvoir B., Nez F., Julien L., Cagnac B., Biraben F., Touahri D., Hilico L., Acef O., Clairon A. and Zondy J.J., Phys.Rev.Lett. 78, 440 (1997); details can be found in the thesis of B6atrice de Beauvoir (Paris, unpublished).

High Precision Atomic Spectroscopy of Muonium and Simple Muonic Atoms Vernon W. Hughes Yale University, Physics Department, J.W. Gibbs, New Haven, CT 06520 USA

Over a period of about 30 years Gisbert zu Putlitz and his colleagues have studied - rapidly and often one by one - some 1015 m u o n i u m atoms, which is equivalent to the number of hydrogen atoms in a bottle of H2 gas with a volume of 0.01 m m 3 at a pressure of 1 atm.

1

Introduction

It's a great pleasure to be able to celebrate Gisbert's 65th birthday with this S y m p o s i u m on Atomic Physics Methods in Modern Research at this great university and in this beautiful city. I first met Gisbert here in Heidelberg in about 1960 when we held the annual Brookhaven Molecular Beams Conference organized by Bill Cohen of BNL which met first here at Heidelberg with Hans K o p f e r m a n n as our host and then at Bonn with Wolfgang Paul as our host. At Heidelberg there were two very competent young associates of Professor Kopfermann who handled the slide projector and related matters. One was Gisbert and the other was Ernst Otten. My next significant meeting with Gisbert was 5 or 6 years later when he visited Yale and we discussed the possibility of his coming to Yale to do research in atomic physics. T h a t Heidelberg meeting and Gisbert's later joining the Yale research faculty was surely one of the most fortunate occasions in my life. It was the beginning of a close scientific collaboration which continues after 30 years. The central theme of our scientific collaboration, which appealed greatly to both of us, was muonium, the #+e- atom, and other related topics in m u o n physics. During Gisbert's memorable stay at Yale research on m u o n i u m was very active for us at the Columbia University Nevis Synchrocyclotron Laboratory where muonium had been discovered in 1960 (Hughes et al., 1960; Hughes et al., 1970). We were involved principally in measurement of the hfs of m u o n i u m in its ground state by microwave magnetic resonance spectroscopy (Thompson et al., 1969; Crane et al., 1971)(Fig. 1). A quite different activity to which Gisbert contributed i m p o r t a n t l y was the organization at Yale of an International Conference on Atomic Physics

22

Vernon W. Hughes

Fig. 1. Experimental setup at Nevis in 1969 showing the Ar gas target and Navy barbettes for shielding.

(ICAP) held at NYU in New York City (ed. by Hughes et al., 1969). Fig. 2 shows Gisbert and L. Wilets at the Conference. Even during the Conference it was not clear that a second ICAP would occur. During a memorable boat trip around Manhattan Kim Woodgate and Pat Sandars agreed to host ICAP 2 at Oxford in 1970. Four years later in 1974 Gisbert hosted ICAP 4 in Heidelberg (ed by zu Putlitz et al., 1975). ICAP has become the principal international conference covering basic atomic physics broadly. The 15th ICAP has just been held in Amsterdam where celebration of the centennial year for the discovery of the Zeeman effect was part of the ICAP program. After the Nevis Synchrocyclotron Laboratory was closed down in the early 1970's and following a short period of muonium research at SREL in Williamsburg, Gisbert and I pursued our muonium experiments at the new meson factories, LAMPF and SIN, where eventually intensity increases of 103 to 104 compared to Nevis were achieved. Fig. 3 shows a three-dimensional electromagnetic coil system - built personally by expert machinist Gisbert zu Putlitz - and used in the study of muonium formation in gases, which was the first published physics research from LAMPF (Stambaugh et al., 1974). The topic I shall talk about is broader than, but includes, muonium. It is high precision atomic spectroscopy of muonium and simple muonic atoms. Several of us: Gisbert and Klaus Jungmann from Heidelberg and Malcolm Boshier and I from Yale have been writing a little article on this topic (Boshier et al., 1996a). My talk includes much of the material we have developed together, but is updated and also includes additional material.

Muonium and Simple Muonic Atoms

F i g . 2. Photograph taken at ICAP in 1968.

Fig. 3. Three-dimensional electromagnetic coil system at LAMPF.

23

24

2 2.1

Vernon W. Hughes

Precision Tests of Q E D Introduction

The principal scientific goal of high precision atomic spectroscopy is to test and study quantum field theory or, more specifically, quantum electrodynamics, the unified electroweak theory and quantum chromodynamics - all now encompassed within the modern standard theory of particle physics. In addition to testing fundamental theory, precision atomic spectroscopy also determines values of fundamental constants including particle masses and magnetic moments, R ~ , ~ and others. Real particles and atoms involve simultaneously the electromagnetic, weak and strong interactions and this often limits the sensitivity of the experimental tests of the theory. Thus for quantum electrodynamics effects of strong interactions or of hadronic structure are at present limiting importantly the QED tests in the simplest one- and two-electron atoms of H and He. With the purely leptonic atoms muonium and positronium the hadronic structure effects are avoided entirely. With simple muonic atoms the hadronic effects can be measured, and hence together with electronic atoms more sensitive tests of QED can be made. As examples we consider briefly the two classic and most important low energy tests of QED - the electron anomalous magnetic moment or g-2 value and the Lamb shift in hydrogen. 2.2

Electron A n o m a l o u s Magnetic M o m e n t and t h e F i n e S t r u c t u r e C o n s t a n t oL

The anomalous g-value a~ = (9 - 2)/2 has been measured to a precision of 3.4ppb (Van Dyck, Jr., 1990) and the QED radiative corrections (Kinoshita, 1990) have been calculated to an even higher precision as a result of a recent improved evaluation of the 6th and 8th order corrections (Kinoshsita, 1996). (This recent evaluation changed the earlier value (Kinoshita, 1995) for radiative corrections by about 50 ppb which is well outside the expected uncertainty.) In order to compare theory and experiment for ae a precise value for the fine structure constant a is needed. Figure 4 shows a plot of the most accurate determinations of a (Kinoshita and Lepage, 1990). In addition to the value recommended by CODATA in the "1986 Adjustment of Fundamental Constants" (Cohen and Taylor, 1987), these include muonium hyperfine structure (Hughes and zu Putlitz, 1990; Mariam et al., 1982), the neutron de Broglie wavelength (Kriiger et al., 1995), the ac Josephson effect (Williams, et al., 1989) (in combination with the gyromagnetic ratio of the proton in water), the quantized Hall effect (Cage et al., 1989), and finally the value obtained from a~ by equating the experimental value to the theoretical expression (Van Dyck, Jr., 1990; Kinoshita, 1996). Determination of a from the neutron de Broglie wavelength is an attractive new method. It involves

Muonium and Simple Muonic Atoms

25

measuring the ratio of Planck's constant to the mass of the neutron (h/mn) from its velocity and de Broglie wavelength and then obtaining cr using the Rydberg constant R ~ and mass ratios and has no theoretical ambiguities. For comparing a~(theor) with a~(expt) the quantized Hall effect now provides the best value with a precision of about 24 ppb. As shown in Fig. 4 agreement of the various ~ values is not too satisfactory. Such a plot is very useful to test our understanding of the different approaches.

CODATA

muonium

his

~

o

I

~

o

Inutlnm

o

i

~

, t

t ac,l & ~'p'

quantum

Hall

t

o

t

a~

-0.40

I

I

I

I

I

-0.30

-0.20

-0.10

0.00

0.10

( a "1 - 1 3 7 . 0 3 6 0 )

0.20

x 104

F i g . 4. R e c e n t d e t e r m i n a t i o n s of t h e fine s t r u c t u r e c o n s t a n t c~.

For a test of QED, rather than rely upon a determination of a involving condensed matter theory it would be preferable to determine a by a method involving the simplest theoretical assumptions such as that from h/mn, or at least from a simple atom which can be treated within QED. The approach involving hiM in which M is the mass of an atom is attractive if adequate precision can be obtained (Weiss et ah, 1993; Martinos e t a h , 1994). For hydrogen the hfs interval Av in its ground state is known experimentally (Ramsey, 1990) with a precision of better than 1 part in 1012 and At, is proportional to cz2. However, the theoretical value for At, has a contribution from proton structure and polarizability of about 30 ppm and an associated uncertainty of about 1 ppm (Sapirstein and Yennie, 1990). Results of a recent evaluation of the proton size and polarizability contribution to At, are shown in Fig. 5 (Unrau, 1996). For muonium ( p + c - ) Au is known experimentally to 36 ppb (Hughes and

26

Vernon W. Hughes Av~ = 1 420 405 751.766 7(9) Hz (1 part in 10~2) AV~

= AVF(I + ~ + ~ ) AVF = 16aZcR I% 3 " #~o ~=

~+

(uncertainty _" 50 ppb)

~ghero~rmr~

(uncem~inty<_50ppb)

2x

rigid)+~(po~nzabmty) = -35.1(7)x104+~pol) ~,=Protonrecoiland smacatre term e e

P ¢,/l//////:vl~o p Two-PhotonExchangeContributionto ~ Due to ProtonSpin Stmcmm 8p(pol)is determin~ by proton spin structure functions Gt(v,Q2) and G~(v,Q2) Recent evaluation (1996) based on present knowledge of Gl and G2 gives ~l~(pol) = (0 -+ 0.4) ppm

Av(exp0 - Av(theor)= (2.4 + 0.7) ppm Fig. 5. Theoretical value of hydrogen hyperfine structure interval Au, indicating contributions of proton structure and polarizability.

zu Putlitz, 1990; Mariam et al., 1982) and the theoretical value including QED and electroweak contributions has been evaluated to 2 0 p p b and no hadronic uncertainties are involved (Kinoshita and Nio, 1994; Kinoshita and Nio, 1996; Karshenboim, 1996). A value for a accurate to 164ppb is obtained, which is limited by our present knowledge of the magnetic m o m e n t ratio which itself is determined from the muonium Zeeman effect. An experiment is in progress at Los Alamos Meson Physics Facility (LAMPF) (Boshier et al., 1995) to improve the value of Au and of and thus determine a to the level of 30 ppb. This on-going experiment will be discussed in more detail later in Section 3.

Pu/Pp,

p~/#v

3Ps

The fine structure of helium in its ls 2s, states is a promising candidate for an accurate determination of a because the 3 p states have a relatively long radiative lifetime of 10-Ts and the fine structure intervals are as large as 30 GHz. (Pichanick and Hughes, 1990) The leading theoretical term is of course proportional to a2Ry. An early determination of a to 0.8 p p m was reported (Pichanick et al., 1968; Lewis et al., 1970; Kponou et al., 1981;

Muonium and Simple Muonic Atoms

27

Frieze et al., 1981). Other recent experiments, particularly those using new precision laser sources, may make possible measurements of the fine structure intervals to a precision of about 50ppb (Shiner et al., 1994; Inguscio et al., 1995; Inguscio et al., 1996; Prevedelli et al., 1996). Calculation of the theoretical values for the fine structure intervals has been made through radiative correction terms of order a T m c ~ In a (Drake and Yan, 1992; Zhang, Yan and Drake, 1996). In order to achieve a theoretical accuracy sufficient to determine a to 25 ppb the order a Z m c 2 term must be calculated. 2.3

T h e L a m b S h i f t in H y d r o g e n

The second basic low energy test of QED is the Lamb shift in H. The interval H ( 2 S 1 / 2 - 2 P 1 / 2 ) has been measured by microwave spectroscopy with an uncertainty of about 9 ppm, and it appears likely that a still higher precision value can be obtained (Pipkin, 1990). Proton structure contributes at the level of 100 ppm, and present uncertainty in the root m e a n square radius < r~ >1/2 of the proton, which has been determined from elastic e p scattering, (Simon et al., 1980; Hand, Miller and Wilson, 1963) results in an uncertainty of 10 ppm in the theoretical value of the Lamb shift. Precise measurements (Weitz et al., 1994; Berkeland et al., 1995; Boirieux et al., 1996) by laser spectroscopy of the 1S-2S transition in H and D determine the Lamb shift in the 1S state and are similarly limited by uncertainty in proton structure. Figure 6 indicates that the Lamb shift measurements can be considered to determine < rp2 > 1 / 2

"small"proton

"big"proton I Lnndeen& Pipkin (2S-2PRF) Hag/ey& Pipkin (2S-2PRF)

~---------_ _ ~ - - - r - - - - - ~ I I ;

I

I I I

Weirs

et

al

(IS Laser)

~------ I-------~

B o ~

et

al

(1S Laser)

I I

"l'nis work

..--.A

m

-30

-20

- 10

I I I

0

(IS Laser)

10

20

30

Deviation from measured Lamb shift (ppm) Fig. 6. Indicating the determination of proton size, < rp2 >1/2 from H spectroscopy. "small" proton < r v2 >x/~ ___0.805(11)fm, "big" proton < rv2 >a/2 = 0.862(12)fm.

28

VernonW. Hughes

There are two approaches to improving the test of QED from the Lamb shift which involve muonium and muonic hydrogen. For muonium this same 1S-2S transition has been observed by laser spectroscopy (Chu et al., 1988; Maas et al., 1994) and the 1S Lamb shift has been determined to 0.8%. It should be possible in the future to achieve very high precision in this measurement where hadronic structure is not involved. The M(2S1/2 - 2P1/2) Lamb shift interval has been measured to about 1% by microwave spectroscopy (Oram et al., 1984; Badertscher, 1985; Hughes and zu Putlitz, 1990; Woodle et al., 1990) and this accuracy could also be substantially improved. Secondly, the Lamb shift in p-p (22S1/2 - 22p1/2) might be studied by laser spectroscopy. (It has been attempted, but so far unsuccessfully (von Arb et al., 1986)). The theoretical level shifts have been evaluated (DiGiacomo, 1969; Pachucki, 1996). In this atom the proton structure effect is very large and an accurate value of < 7~ >1/2 could be measured and then used to improve the theoretical value of the Lamb shift in hydrogen. 3

Current

Muonium

Experiment

at LAMPF

As mentioned in Section 2.1, an experiment is in progress at the Los Alamos Meson Physics Facility (LAMPF) to determine with high precision the hyperfine structure interval Au (to ,-~ 10 ppb) and the muon to proton magnetic moment ratio Pu/#p (to --~ 60ppb) in the ground state of muonium (#+e-). These precision goals correspond to increases in precision for Au and for Pu/Pp by about a factor of 5 compared to present knowledge. The general method of the experiment (Hughes, 1966; Hughes and zu Putlitz, 1990) is microwave magnetic resonance spectroscopy as applied to muonium. It relies on parity nonconservation in the 7r+ --+ #+uu decay to produce polarized p+ and in the p+ -+ e+iuue decay to indicate the spin direction of/~+. The most recent LAMPF experiment provides the present experimental values (Mariam, 1982):

Aue~p = 4 463 302.88(16) kHz (36ppb); Pu/Pp = 3.183 346 1(11) (360ppb) The theoretical expression for Au can be written as: Au(theory) = Av(binding, rad) + Au(recoil) + Au(rad - recoil) + Au(weak) Except for the small term Av(weak) coming from the weak interaction, and a small known contribution arising from hadronic contributions to the photon propagator, this expression arises solely from the electromagnetic interaction of two point-like leptons of different masses in their bound state. The present theoretical value is (Kinoshita and Nio, 1994, 1996; Kinoshita, 1996):

Auth = 4 463 302.38(1.34)(0.04)(0.17)kHz (0.3 ppm) The principal error of 1.34 kHz arises from the uncertainty of Pt,/Pv. The second uncertainty arises from that in c~ based on the electron g-2 experiment,

Muonium and Simple Muonic Atoms

29

and the third is the estimate of the theoretical error in the latest QED calculation (Karshenboim, 1996). Weak neutral current effects associated with Z exchange in the e - p interaction contribute -0.065kHz or 15 ppb and are included in Auth. The experimental and theoretical values for Au agree well:

z~Vth -- Z~Vexp = --0.50(1.4)kHz ; AUth -- A ~ , ~ p = - - ( 0 . 1 1 ± 0 . 3 ) p p m . Allexp

The Breit-Rabi energy level diagram for ground state muonium is shown in Fig. 7. The history of the various determinations of Au and of IzF,/pp is shown in Fig. 8.

H(kG)

0

2 3 4 5 6 7 8 9 101112131415161718192021.22232425 I I I I I I I I I 111111111111111.J

98 5

+,

(F,Mp)

-3 -

(o,o) ~ - - - . . . . . . ~ t / 2 , - i / 2 )

-5 -6 -7

-8-9 H=

(-I/2,1/2)

0

v31

3

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

1

2

3

4

5

6

7

8 X

9

10

11

12

13

14

15

~ -~ a -~ Ip.J +~t~gj J. H-~-

I~ p, ~Ip.H -~ Stng

AV_VI2+V3

2~g;H

16

4 4" AV [-X "4- ( l + X 2 ) trz]

alh = Av = AW/h=4463 M l l z --Y

F=J+

--)

ip. 1

WF=I±I MF 2 2'

= - -AW

4

V. ,

1

- ILBg~tMFH + - ~ A w ~ ] I + 2 M F x

+ X1

Fig. 7. Breit-Rabi energy level diagram for muorfium in its 12S1/2 ground state in a magnetic field.

The new experiment improves on the earlier one (Mariam, 1982) in several ways. First, the p+ b e a m intensity is now larger by a factor of 3 and is 1.107#+/s, with a duty factory of 6 to 9% and has greater purity, achieved principally by use of an E x B separator to reduce the e + background in the beam. Second, the magnetic field from a commercial Magnetic Resonance

30

Vernon W. Hughes

Av {HICaOO-19TO t ~ * t ' ) [*.eppm) 1O0

I

BERK[L[Y*IgTZIFSR. HZO)

I

I

I

YJLE" HEIOELBERG-1977 ( ~ ' , ' 1 [I.4 ppm|

•

SIN - t 9 7 8 ( ~ W . l r z l (O.Sppm)

•

SIN-1981 l ~ n . e . t l (O.5$Ppml

I

._= YALE-NEIO[LS[RG-Ig@2IF.,-) (0.36ppm| LzJ

'oI ; ~ ' ' , ; [ ~ I p p I I0 ll- 3 1 e 3 3 4 0 |

0

22 ppb

2.2 ppbf 196~

1966

)970

197q

1978

1980

1984

1990

Fig. 8. History of muonium Av and

p,,/pp

measurements.

Imaging superconducting magnet system operating in persistent mode provides a field with a homogeneity of better than 1 p p m over the active region of the microwave cavity and with a stability of 0.01 p p m to 0.1 p p m / h r . Third, an electrostatic chopper in the muon beam line provides a muon beam with an on-period of 4 ps and an off-period of 10#s, which allowed the observation of a resonance line from muonium atoms which had lived longer than the 2.2#s mean lifetime v~ of inuons (Boshier, et al., 1995). Such resonance lines can be narrower than the natural linewidth determined by 7~, and indeed narrower than a line obtained by the conventional method by factors of up to 3. The experimental setup is shown in Fig. 9. The longitudinally polarized #+ b e a m of about 26 MeV/c is stopped in a microwave cavity contained in a pressure vessel filled with krypton at a pressure between 0.5 and 1.5 atm. The entire apparatus is in a region of a strong magnetic field of 1.7T. Muonium is formed in an electron capture reaction between #+ and a Kr atom. The e + from p+ decay is detected in a scintillator telescope. Figure 10 shows the MRI solenoid and indicates the characteristics of this precision magnet which is operated in persistent mode. Resonance lines for transitions /'12 and /'34 are observed by sweeping the magnetic field with fixed microwave frequency.

Muonium and Simple Muonic A t o m s

~//////~//////////.Z/~///////~ $hlmCoils

Shielding

ModulationCoil'1"""'"~*a~Pressm'eV~I,~.

]IIL

/ 3 rail MylwW'~ndow~At-Collimllo¢

!,

PosiU-onT,lcscope.,.~Bij~mmr~

~

!L t.

p*

'-T-'

F i g . 9. E x p e r i m e n t a l setup in 1994/95.

• • • • • •

Manufacturer: Operating Field: Field StabiliLy: Length: Clear Bore 9 : Homogeneity: Modulation Coil:

Oxford Mag'aet Technology (OMT) 1.7 Tesla 10 ppb/hr 2.26 m 1.05 m

shimmed to I ppm over 20 cm dsv to scan field over +_50 G

F i g . 10. L A M P F superconducting solenoid 2 T MRI magnet.

31

32

•

Vernon W. Hughes

Idea: Observationofdecayiogs ~ s

actimesT> C.~nven~on~ method

CO~veNr,o.AL ~.ev.oo

I

..,o0 LPt.f~fi..l'3~J'~l~l~]J

I

] ¢

u,CROW,VES e* ¢,aTc e" CO,.C,OeNCE ~

"oLo" . u o . , u . . E T ~ O 0

e ] ''2 ~Vm = (natural)= Z = 145 kHz Old muonium 8Vm (y, Ib~T) I and I~ <~

;qf~,J [ 6-T--',

I

I

~

.,c~ow~,,Es

e*~,T~

~ " co,,c,oc,cE

Svm = 21bt < ~ v m (natural) x

[b~isproportional to microwavemagnetic field

~SeC

Fig. 11. The conventional and old muonium methods of observing resonance lines and the associated linewidths.

The conditions and lineshapes for the conventional and "old muonium" resonances are given in Fig. 11. Observed resonance curves are shown in Fig. 12. It can be seen that a narrower resonance line is obtained for muonium atoms which have lived a longer time. Also wings develop for cases where older muonium atoms are observed and larger signal amplitudes are obtained. During runs in 1994 and 1995 with a total beam time of about 3 months, data were taken with stopping Kr gas pressures of 0.5, 1.0 and 1.5 atm. Some 2,000 sweeps of the resonance line were obtained. Additional data-taking followed in 1996 when resonance lines were obtained by varying the microwave frequency with fixed magnetic field. These data should provide an important check for systematic errors (Boshier et al., 1996b). The scientific importance of a more precise determination of At, and # , / p p includes the following: 1. Most precise test of QED for the two lepton bound state and of the behavior of the muon as a heavy electron. 2. Precise determination of the fundamental constants: muon magnetic moment and muon mass. Also a value of the fine structure constant a accurate to about 30 ppb will be obtained; this accuracy is comparable to that from condensed matter determinations. 3. Precise values of m , and p , are very important for the BNL muon g-2 experiment (Hughes, 1994) and in the determination of the muon neutrino mass m~, (Particle Properties, 1996).

Muonium and Simple Muonic Atoms

~ " 2 2 • 'v12 ~' m',t')CanvlnmOt (l ~H0 321789f215) .~~u ~ ~.0 20 hl o=-81(0.03)G x'/DoF t.o6 DoF 125

'

'

(a )

1~ ~

30

'°

14

6O5) F Z-/{:~ 0.9o

!

-

33

Jr~¢ 6 ? ,1~I,,

FWHM 1121r.~4~ 2(] 15

12

l

10 8

6 200

250

350

300

400

2OO

450

v~-720~kHz) C

4"02-~'97tt'~ec

HO 321479(510)Hz.~1 , ttl IJOG • x'/DoF0.98 f ~llVc~ ~. DoF t26 40 FWHM811d~

( )

"~50

J

3OO

350 4OO 450 v -72000~kHz)

F"'vl2 " ~ 1 3 ~ ) $,92_-6.87$Lu~:

-J 4 °.)

250

' "

'

Ho 32152~ssz~z ~,~ hi I.~G SO 128-3(2.2) / ~ t -/D~ O.99

5O

(d)

3~ 20 2~ 10 0 , I

2OO

~'60

v12

50 4O

250

~

30O

(l~an'o) '

-10

'

350 400 450 v~-72000(kHz) ~

) 7,g2-8.77~t,se~ H0 32229~s3o~tu8 / SO 105.9(3.2) I~1] x'/Dof 1.00 IF1. ,

DoF tins F'WHM 49kHz

'

'"

~

200

250

300

5(

(e)

8.~-9,T/~sec

HO

• hi

~

,I , l f ~ . ~

350 400 450 v~,:72000(kHz)

30

30

2O

2O

10

322292f1336)Hz IJOG

[

, ~:• t.L)

FWI.IM45kI~

)

I0 0

10

-10 2OO

250

30O

350

40O

450

v~,-72000fkI-Iz)

2~

~

3001

3~ v

~

450

:72OO0(kHz)

Fig. 12. Old muonium resonance lines. Observed u12 resonance fines obtained by magnetic field scan w i t h a 1.Satm Kr target. The signal -= (No~+n - N ~ ; ) / N ~ [ % ] in which No~+ (No~n +) is the number of decay e + counts with microwaves on (off). The magnetic field is measured by the proton NMR frequency U~MR. The fitting parameters are the line center Ho, the microwave field amplitude H1 and a scaling factor So. The F W H M for a line obtained by a frequency sweep would be 1.7 times the FWHM in units of u. . . . The solid line fits have been made using measured magnetic field and muon stopping distributions as well as the microwave magnetic field distribution for the cavity mode. (a) Conventional resonance line without the/J+ beam chopped and with a microwave power of 10 W in the cavity. (b)-(f) Old muonium resonance lines with a microwave power of 4 W and different observation times measured from the beam-off time.

34

Vernon W. Hughes

HYDROGEN

MUONIUM F 26 ~ z

F

F F

10 922MFIz |

10 969 ~

,?:-I

2sl/2-

7 T 1o48 MNZ

zP,,, l

I

I ~ . IMHZ I

r lz16

X

/t

lSll2 o

F i g . 13. Energy levels in the n = l and n = 2 states.

Finally, to emphasize the similarity of muonium to hydrogen, Fig. 13 shows their energy levels in the n = l and n=2 states. From the viewpoint of tests of fundamental theory muonium has the distinction of being free of hadronic effects, apart from the very small and well known modification of the photon propagator associated with virtual processes. The energy intervals shown can be measured for both H and M, but for M the measurements are more difficult primarily because few atoms are available, and the precision of the measurements is lower at present.

4 4.1

Laser Spectroscopy of M u o n i u m and M u o n i c Atoms E x p e r i m e n t s D o n e thus Far

The pioneering early experiment was a measurement at CERN on the muonic helium ion, (4He p - ) + , of the 2S to 2P transitions (Bertin et al., 1975a; Bertin et al., 1975b; Carboni et al., 1977). Negative muons were stopped in He gas at a pressure of 40 atm. The negative muons were captured by He into a highly excited state of muonic helium in an Auger process, and after subsequent Auger and radiative capture processes several percent of the stopped /tformed the 2S1/~ state of the muonic helium ion ( 4 H e # - ) + . The decay rate 2S1/~ --+ 1S1/2 through spontaneous two-photon radiative decay is 1.1.105 s- 1 which corresponds to a mean lifetime of 9.1 #s. The experimenters determined

Muonium and Simple Muonic Atoms

35

2Pj/~ 0.1S eV

b)

1.37 eV

tim6"S-*15~"

K

-~ 7o

6 a

t

.2261,eV

I z

~t~

I ,s ,

,

f

~,,

I. •

,

,

.

i ',

' f

"

r'

'

~

-

Fig. 14. a) Energy levels of (4Hep-)+ in n=2 state, b) Observed 2Sl/2 -+2Pi/2 resonance signal.

that the collision quenching rate for the 2S1/2 state in He at 40 atm was less than 8.103 s -1 atm -1 (Carboni et al., 1973). Using a pulsed dye laser at about 8120/~, which was triggered at the time of an individual incoming p - , the transition 2S1/2 -+2P3/2 was induced and then the subsequent 8.2keV Xray from the 2P3/2 --+1S1/2 radiative decay was detected in a NaI detector. Unambiguous resonance lines were observed as the pulsed dye laser was tuned (Fig. 14). Subsequently the 2S1/2 --+2P1/2 resonance was observed in a similar manner. Using the observed resonance wavelengths for these transitions, the dominant QED term, which is due to vacuum polarization, was determined to about 0.1% in agreement with the theoretical prediction. Alternatively, the measurements were used to determine the most precise value for the root mean square radius of the 4He nucleus, < r24He )1/2. Subsequently a fascinating puzzle has arisen about the expected lifetime of the 2S1/2 state of (4He p - ) + in helium at 40 atm pressure, which was the condition for the above experiment. Theoretical estimates indicated that the 2S1/2 state would be rapidly quenched in collisions with He atoms (Mueller et al., 1975). Furthermore several experiments concluded (yon Arb et al., 1984; Eckhause et al., 1986; Rosenkranz et al., 1990) that the lifetime of the 2S1/2 state of (4He#-)+ with respect to quenching in a He collision would be much shorter than 2 ps at 40 atm of He. This called into question how the 2S-+2P transition could have been observed. A possible explanation was

36

Vernon W. Hughes

provided by calculations indicating that a cluster of He atoms centered on the 2S1/=(4He/_t-) + ion might be formed in which the 2S state was stable, although later work showed that this mechanism did not in fact explain the observation (Cohen, 1982). More recently, this idea has developed into a suggestion that at sufficiently high pressures the cluster could form in longlived excited states in which quenching of the 2S state is inhibited (Baracci and Zavattini, 1990). Of course in this case, to test QED one must then know the exact energy levels of the muonic helium ion within the cluster. An unsuccessful attempt was also made recently to observe again the 2S1/p. to 2P1/2 transition at Paul Scherrer Institut (PSI) in Switzerland (Hauser et al., 1992). Hence the puzzle about the lifetime and precise energy levels of ( 4 H e p - ) + in He gas remains. The second laser spectroscopy experiment has been on the muonium 1S-+2S transition. This transition is induced by a two-photon Doppler-free process and detected through the subsequent photoionization of the 2S state in the laser field. The key to success in this experiment was the production of muonium into vacuum from the surface of heated W or of SiO2 powder. The discovery experiment (Chu et al., 1988) was done at the KEK facility in Japan with a pulsed muon beam and an intense pulsed laser system. A subsequent experiment (Maas et al., 1994) done with the pulsed p+ beam at RAL and a similar pulsed laser has improved the signal substantially and has achieved a precision of about 10 - s in the 1S -+ 2S interval, thus determining the Lamb shift in the IS state to about 1% accuracy (Fig. 15). The precision of this experiment should be greatly improved in a new experiment now underway at RAL. This experiment will provide a precise determination of the muon mass from the muonium-hydrogen isotope shift in the transition since this shift is primarily due to reduced mass.

4.2

A d d i t i o n a l P o s s i b l e E x p e r i m e n t s o f Interest

A substantial number of important energy intervals in the simple muonic a t o m s - muonium, muonic hydrogen ( p - p ) , muonic deuterium ( p - d ) and in the muonic helium ions, (4He # - ) + and (3He # - ) + - should be measurable by the method of laser spectroscopy (Jungmann, 1992). The intervals include the 1S-2S interval, fine structure and Lamb shift intervals, and hyperfine structure intervals. They arise from fundamental QED processes and include the fundamental constants of particle masses and magnetic moments as well as the nuclear radii of p, d, 3He and 4He and nuclear polarizabilities. At a more sensitive level electroweak effects appear as well. For electronic atoms these intervals have been measured with high precision over the past 50 years. They have provided fundamental data out of which quantum electrodynamics has been developed and tested. Our knowledge of many fundamental constants and of properties of particles and nuclei also comes from these data.

Muonium and Simple Muonic Atoms

~ = ( a 4 ~ - _ ~ ) USz

,a'~ : ; ~ o o

:"

~o0

.

?;0 8 ; o

37

/

~ o ,d00";,oo u_-v,.CMHz]

Transition Frequency M ( I S - 2 S ) ~ r = 2, 455,529,002(33X46) M]-]z M(1S-2S)QED = 2, 455,528,934(3.6) M]']Z L a m b shifts

[L,s-/-~s] Exrr = 6,98g(33X46) MHz [Lls -/v.s] QED= 7,056.I(1.0) MHz agrees

with QED at the 0.8% level.

Fig. 15. Observed 1S-2S transition in muonium by two-photon laser spectroscopy.

Table 1 lists a number of important transitions in muonium and muonic atoms which might be measured by laser spectroscopy. The physics interest and precision potential are also given, as is a possible pulsed laser system. (The precision potential does not take into account #+ beam intensity limitations and hence in some cases is at present unrealistic.) We note that the size of muonic atoms and their magnetic moments are smaller than for electronic atoms by the mass ratio r n e / m u so that electric dipole and magnetic dipole matrix elements are smaller by m e / m u and hence high laser power is required to induce the transitions. A pulsed high power laser system is required for these experiments.

5

Sources of Pulsed Muons

The ideal experimental facility for future laser spectroscopy measurements on muonium, on muonic hydrogen and on the important muonic helium ions is an intense pulsed low energy muon source, where the pulse length is small compared to the muon lifetime and the repetition rate is similar to that of pulsed high power lasers. Such a facility is in operation with the 800MeV proton synchrotron at Rutherford Appleton Laboratory (RAL) (Cox, 1990). At LAMPF, its high intensity 800 MeV proton linac feeds a proton storage ring which converts the long duty factor (6 to 10%) proton linac beam into a pulsed proton source. A pulsed muon beam could be developed from this

48.4 TIIz (6.2 tun)

43.9 TIIz (6.8 ~ n )

1.6 TI Iz ( 188 pro)

2S-2P

IS, F=0-F=I

3D-3P

muonic hydrogen (H P')

282.7 TIIz, 365.1 Tllz (1.06 ~ n , 822 nm)

(9.85 ~,m)

30.4 Tllz

2S-2P

3D-3P

2S-2P

2,457 Tllz + 819 Tllz 0 2 2 n m + 355 nm)

IS-2Pcontinuum

Frequency-tripled Alexandrite

Laser System (Pulsed)

Free electron laser

Difference frequency generation

Carbon monoxide or nonlinear mixing

Ti:Sapphiro

Carbon dioxide

YAG-pumped Ti:Sapphtre with fourwave mixing in Kr/Ar + doublin~ in BBO 369.6 TIIz. 334.2 Tilz Dye or Tl:Sapphire (812 rim, 898 rim)

2 x1,228.5 Tllz (2 x2,~ nm)

Frequency (Wavelength)

I S-2S

Transition

muonic 3lie (W Slle) *

muonic 'tile ion (it 'tile)+

muonium, M ([a* e )

System

QED vacuum polarization, (insensitive to nuclear structure)

proton charge radius and polarizability

I. proton charge radius and polarizability 2. QED vacuum polarization

3lie nuclear size and poladzahiUty

QED vacuum polarization, (insensitive to nuclear structure)

I. QI-:I) vacuum polari:,arinn 2. ft.-particle charge radius

I. Lamb shift without nuclear structure 2. QED recoil, reduced mass 3. }.t"mass Ultra-slow H" beam

Physics Inlerest

Current Statu!g

Potential (line split to I part in 10 ~)

Approved at PSI

An uncertainty of 10 Gilz improves current knowledge of (r~) 'n (2% level)

Under discussion at PSi. An uncertainty as large as 20 GI Iz improves current knowledge of 2 Ill . (r~)

No transition observed at PSI Test experiment at BNL did not see a clear signal.

to 0.2%

100 (]llz uncertainty (CF~RN): tests vacuum polarization at 0.2% level or determines ~r:~ 'n

Potential for a 6 ppm test of vacuum polarization, all improvement of 1000 Oil cnrrent tests.

Potential for five orders of magnitude improvement beyond this 10 Gtlz.

(~),/2 t o a few partsin 10'

PSI experiment aims for eventual uncertainty of 500 Mllz. giving

Measurement widt uncertainly of 1/5 of linewidth would provide new test of vacuum polarization. Potential for furdrer improvement b~' a factor of 200. Similar to muonic 4lie ion

At least another two orders of magnitude.

60 MIIz uncertainty (RAL) Potential for attolher five orders tests QED to 0.8% and gives m.u of magnitude beyond current to 5 ppm. Order of magnitude result. improvement expected in next RAL experiment Under construction at KEK

T a b l e 1: Possibilities for laser spectroscopy of muonie atoms

m

©

On

GO

Muonium and Simple Muonic Atoms

39

Table 2: Parameters of the positive and negative muon channels at the Rutherford Appleton Laboratory

(RAL), and of future pulsed muon sources proposed at the Los Alamos Meson Physics Facility Proton Storage Ring (LAMPF PSR), the Japan Hadron Project (JHP) and the European Spallation Source (ESS).

Intensity (IMs)

Momentum spread Ap/p

Pulse structure

Spot size

RAL (g÷)

RAL (ix)

3xlO 6

2xlO 5

10%

82ns FWHM at 50Hz

1.2cm x 2cm

JHP(g °)

ESS(p. ÷)

l.TxlO ~

4.5x107

4.5x 107

5% at 40 MeWc

10%

10%

10%

82 ns FWHM at 50 Hz

279 ns FWHM

300 ns

300 ns

FWHM

FWHM

at 40 Hz

at 50 Hz

at 50 H z

3cm x 2cm

1.2cm x 2cm

1.2cm x 2cm

4cm x ,k:m

L A M P F PSR

proton source which would be 1 order of magnitude brighter than the RAL beams (White, 1992). Recent plans in Japan for a Japan Hadron Project (JHP) and in Europe for a European Spallation Source (ESS) (G. Eaton, private communication) could also provide powerful new pulsed muon sources. These machines are discussed in more detail below. At present the Rutherford Appleton Laboratory in England operates a fast-cycling proton synchrotron with 800MeV energy and an average proton current of 200#A. It is used primarily to provide a pulsed spallation neutron source but it also provides a pulsed source of low energy (surface) muons produced from a thin target. Six muon channels are presently available. Measurement of the 1S--+2S transition in muonium is in progress with a pulsed muon beam having the characteristics shown in Table 2. A second source of pulsed muons with a considerably higher intensity could be provided from the Proton Storage Ring (PSR) which is fed by the LAMPF 800 MeV proton linac at Los Alamos. Extraction of the proton beam from the PSR is already provided. A transport line for the proton beam, a target and a muon channel would be needed. The characteristics of the pulsed muon source which would be possible with a muon channel consisting of iron electromagnets are also given in Table 2, which also includes parameters for the possible muon sources at J H P and ESS. Finally, we note one other interesting possibility for the future. Design studies at Brookhaven National Laboratory of a muon injection system for a possible high-energy p+p- collider (R. Palmer, 1996) suggest that very high efficiencies are possible (0.3 muons/proton), indicating that this system may also be useful as a source of pulsed muons. Research supported in part by the U.S. Department of Energy.

40

Vernon W. Hughes

References von Arb H.P. et al., (1984): Phys. Lett. 136 B, 232. von Arb H.P. et al., (1986): Proceedings o] the Workshop on Fundamental Muon Physics: Atoms, Nuclei and Particles, ed. C.M. Hoffman, V.W. Hughes and M. Leon, LA-10714-C, p. 103. Badertscher A. et al., (1985): Atomic Physics 9, ed by R.S. van Dyck, Jr. and E.N. Fortson, (World Scientific) p. 83. Baracci L. and Zavattini E. (1990): Phys. Rev. A 41 2352. Berkeland D.J., Hinds E.A. and Boshier M.G. (1995): Phys. Rev. Lett. 75, 2470. Bertin A. et al., (1975a): Phys. Lett. 55B, 411. Bertin A. et al., (1975b): Atomic Physics 4, ed. G zu Putlitz, E.W. Weber and A. Winnacker (Plenum, New York) p. 141. Boirieux T., et al., (1996): Phys. Rev. Lett. 76, 384. Boshier M.G. et al., (1995): Phys. Rev. A 52, 1948. Boshier M.G., Hughes V.W., Jungmann K., zu Putlitz G. (1996a): Comments Atomic and Molecular Physics 33, 17. Boshier M.G. et al., (1996b): Abstracts ZICAP, Amsterdam, The Netherlands, ThK3. Cage M.E. et al., (1989): IEEE Trans. Instrum. Meas. 38, 284. Carboni G. et al., (1973): Nuovo Cimento 6,233. Carboni G. et al., (1977): Nucl. Phys. A 278 381. Crane T. et al., (1971): Phys. Rev. Lett. 27, 474. Chu S. et al., (1988): Phys. Rev. Lett. 6{}, 101. Cohen J. (1982): Phys. Rev. 25, 1791 and references therein. Cohen E.R. and Taylor B.N. (1987): Rev. Mod. Phys. 59, 1121. Cox S. (1990): Proceedings o.f the Pulsed Muon Workshop (Los Alamos National Laboratory). DiGiacomo A. (1969): Nucl. Phys. B l l , 411; B23,641. Drake G.W.F. and Yan Z.-C (1995): Phys. Rev. A46, 2378. Eckhause M. et al., (1986): Phys. Rev. A 33, 1743. Frieze W. et al., (1981): Phys. Rev. A24, 279. Hand L.N., Miller D.B. and Wilson R. (1963): Rev. Mod. Phys. 35,335. Hauser P. et al., (1992): Phys. Rev. A 46, 2363. Hughes V.W., McColm D.W., Ziock K. and Prepost R. (1960): Phys. Rev. Lett. 5 63. Hughes V.W. (1966): Arm. Rev. Nucl. Sci. 16,445. Atomic Physics, ed by Hughes V.W., Bederson B., Cohen V.W., Pichanick F.M.J., (1969): (Plenum Press, NY,). Hughes V.W. et al., (1970): Phys. Rev. A1, 595; A2, 551. Hughes V.W. and zu Putlitz G. (1990): Quantum Electrodynamics, ed. T. Kinoshita (World Scientific, Singapore) p 822. Hughes V.W. ((1994): A Gift o] Prophecy, ed. E.C.G. Sundarshan (World Scientific, Singapore) p. 222. Inguscio M. et al., (1995): Proceedings of the IEEE Frequency Control Symposium. Inguscio M. et al., (1996): Submitted to Physiea Scripta, Special issue in honor of Prof. G. Series. Jungmann K., (1992): Z. Phys. C56, $59.

Muonium and Simple Muonic Atoms

41

Karshenboim S.G. (1996): Z. Phys. D 36, 11. Kinoshita T. (1990): Quantum Electrodynamics, ed. T. Kinoshita (World Scientific, Singapore) p. 218. Kinoshita T. and Lepage G.P. (1990): Quantum Electrodynamics, ed. T. Kinoshita (World Scientific, Singapore) p. 81. Kinoshita T. and Nio M. (1994): Phys. Rev. Lett. 72, 3803. Kinoshita T. (1995): Phys. Rev. Lett. 75, 4728. Kinoshita T. (1996): Rep. Prog. Phys. 59, 1459. Kinoshita T. and Nio M. (1996): Phys. Hey. D 53, 4909. Kponou A. et al., (1981): Phys. Rev. A24, 264. Kriiger E., Nistler W. and Weirauch W. (1995): Metrologia 32, 117. Lewis S.A. et al., (1970): Phys. Rev. A2, 86. Maas F.E., et al., (1994): Phys. Lett. A 187, 247. Mariam F.G. et al., (1982): Phys. Rev. Lett. 49,993. Martinos J.M., Nahum M. and Jensen H.D. (1994): Phys. Rev. Lett. 72,904. Mueller R.O. et al., (1975): Phys. Rev. A l l , 1175. Oram C.J. et al., (1984): Phys. Rev. Lett. 52, 910. Pachucki K. (1996): Phys. Rev. A53, 2092. Palmer R. 1996: (private communciation) "Review of Particle Properties" 1994:, Phys. Rev. D50, 1173. Pichanick F.M.J. et al., (1968): Phys. Rev. 169, 55. Pichanick F.J.M. and Hughes V.W. (1990): Quantum Electrodynamics, ed. T. Kinoshita (World Scientific, Singapore) p 905. Pipkin F. (1990): Quantum Electrodynamics, ed. T. Kinoshita (World Scientific, Singapore) p 696. Prevedelli M. et al., (1996): Optics Communciations 125 231. Atomic Physics 3, ed by zu Putlitz G., Weber E.W. and Winnacker A. (1975): (Plenum Press, NY) Ramsey N.F. (1990): Quantum Electrodynamics, ed. T. Kinoshita (World Scientific, Singapore) p 673. Rosenkranz J. et al., (1990): Ann. Phys. 47, 667. Sapirstein J.R. and Yennie D.R. (1990): Quantum Electrodynamics, ed. T. Kinoshita (World Scientific, Singapore) p 560. Shiner D., Dixson R. and Zhao P. (1994): Phys. Rev. Lett. 72, 1802. Simon G.G. et al., (1980): Nucl. Phys. A333 381. Stambangh R.D. et al., (1974): Phys. Rev. Lett. 33 568. Thompson P.A. et al., (1969): Phys. Rev. Lett. 22, 163. Unrau P. (1996): Ph.D. Thesis, Spin Dependent Nucleon Structure at Intermediate Q2 Massachusetts Institute of Technology. Van Dyck, Jr R.S., (1990): Quantum Electrodynamics, ed. by T. Kinoshita (World Scientific, Singapore) p. 322. Weiss D.C., Young B.C. and Chu S. (1993): Phys. Hey. Lett. 70, 2706. Weitz M. et al., (1994): Phys. Rev. Lett. 72, 328. White H. (1992): LAMPF Pulsed Lepton Source, Los Alamos National Laboratory. Williams E.R. et al., (1989): IEEE Trans. Instrum. Meas. 38, 233. Woodle K.A. et al., (1990): Phys. Rev. 41, 93. ZhangT, Yan Z.-C and Drake G.W.F. (1996): University of Windsor preprint.

T h e M u o n i u m A t o m as a P r o b e of P h y s i c s beyond the Standard Model L. Willmann* and K. Jungmann Physikalisches Institut der Universit/it Heidelberg, Philosophenweg 12, D-69120 Heidelberg, Germany

1

Introduction

Precision measurements on atomic systems have played an important role in the course of the development of modern physics. In many cases they have lead to discoveries which had significant impact on the understanding of the physical laws of nature. The explanation of the carefully measured electromagnetic spectrum of atomic hydrogen by the Schr6dinger equation was a great success for quantum mechanics. The observed fine structure was included in the solutions to the Dirac equation which demonstrated the necessity of a relativistic description of the atomic structure. Precise investigations of the hydrogen Balmer-a line revealed a faint nearby line [1] which was the discovery of deuterium through its spectroscopic isotope shift. A small deviation of the measured hyperfine splitting in hydrogen [2] from the value predicted in Fermi's theory on the 0.1% level could be explained by the anomalous magnetic moment of the electron. This discovery together with the observation of the Lamb-shift (22S, - 22Fx ) in hydrogen [3] has initiated and boosted the development of t]ae modern field theory of quantum electrodynamics (QED). The unification of the weak and electromagnetic interactions in the electroweak standard model was strongly supported by the observation of parity violation in precise spectroscopic measurements in heavy atoms. Today electroweak processes examined both at high energies [4] at the LEP electronpositron storage ring collider at CERN, Geneva, Switzerland, and in atomic parity violation experiments in heavy atoms, e.g. in cesium and thallium [5, 6], have ascertained the power of the unified electroweak theory which is valid over a range of 10 orders of magnitude in momentum transfer. Today the standard model appears to be a very successful effective description of all known interactions between particles and no significant deviation from it could be established so far. Its predictions are subject to high precision experiments which allow to extract a set of intrinsic parameters including the masses in the leptonic and the quark sectors and mixing angles between different quarks. However, there still remain unresolved questions within this sophisticated theoretical framework like the number of interactions, the number of lepton and quark generations or the nature of parity violation. Partic-

7

44

L. Willmann and K. Jungmann

ularly the question of lepton number conservation is investigated by various experiments, since no underlying symmetry could be discovered to be associated with it yet. The muonium atom (M=It + e - ) , the bound state of a positive muon It+ and an electron e - , can be considered a light hydrogen isotope. This fundamental system is ideally suited for investigating bound state quantum electromagnetic theory and it renders the possibility to test fundamental concepts of the standard model. The spectroscopic measurements of electromagnetic transitions like the hyperfine interval in the ground state or the ls-2s energy splitting are generally considered precise tests of QED and are used to infer accurate values of fundamental constants [7]. In addition, they may be used to extract information on fundamental symmetries. For example, the latest measurement of the ls-2s energy interval [7, 8] can be regarded as the best test of the charge equality of leptons from different particle generations at a level of 10 - s relative accuracy [9]. The system offers further unique possibilities to search for yet unknown interactions between leptons, in particular, since the close confinement of the bound state allows its constituents a rather long interaction time which is ultimately limited by the lifetime r u = 2.2Its of the muon.

2

Test

of Lepton

Number

Conservation

A spontaneous conversion of muonium into antimuonium (M = # - e +) would violate additive lepton family (generation) number conservation by two units. This process is not provided in the standard model like others which are intensively searched for, e.g. It --+ e7 [10], It --4 eee [11], It - e conversion [12] or the muon decay mode It+ - 4 e + + u u +-P7 [13]. However, in the framework of many speculative theories, which try to extend the standard model in order to explain some of its not well understood features, lepton number violation is a natural process and muonium to antimuonium conversion is an essential part in several of these models (Fig. 1) [14-19]. Traditionally, muonium-antimuonium conversion is described as an effective four fermion interaction with a coupling constant GM~ which can be measured in units of the Fermi coupling constant of the weak interaction GF [20]. Many of the speculative models would allow a strength of the interaction as large as the experimental bound at the time they were created. In minimal left-right symmetric theory muonium and antimuonium could be coupled through a doubly charged Higgs boson A++. In this case even a lower bound has been predicted for GM~, provided the muon neutrino mass m,~, were larger than 35 keV/c 2 [14]. With the present experimental limit of m , , <_ 170 keV/c 2 [21] the coupling constant GM~ should be larger than 2- 10 -4 GF. This figure would even increase for an improved bound on m ~ . For neutrinos being Majorana particles a coupling between muonium and antimuonium is possible by an intermediate pair of neutrinos. A limit on

The Muonium Atom as a Probe of Physics beyond the Standard Model #+

45

#-

A++

Wa.. '.. WL

~+

e

(a)

(b)

#+

e+

#+

.

~N m

IX++ #-

e

#-

(c)

e-

¢+ (d)

Fig. 1. Muonium-antimuonium conversion can be described in various theories beyond the standard model. The interaction could be mediated by (a) a doubly charged Higgs boson A ++ [14], (b) heavy Majorana neutrinos [15], (c) a neutral scalar ~b~v [16], which could be for example a supersymmetric r-sneutrino P~ [18] or (d) a dileptonic gauge boson X ++ [19].

the effective coupling can be estimated based on the Majorana mass limit of the electron neutrino which has been deduced from experimental searches for neutrinoless double fl-decay [22] to GM~ < 10-hGF [15]. Supersymmetric theories allow an interaction to be mediated by a 7-sneutrino PT, the supersymmetric partner of the 7.-neutrino. The predictions are G M ~ < 10-2GF for a mass value rn~r of 100 G e V / c 2 [18]. Some of these speculative theories need to introduce neutral scalar bosons to explain the mass spectrum in the leptonic sector. These models predict a coupling strength of 10-2GF which is in the range of the sensitivity of present experimental search [16]. In the framework of grand unification theories (GUT) muonium-antimuonium conversion could be explained by the exchange of a gauge boson X ++ which carries both an electronic and a muonic lepton number. B h a b h a scattering experiments at P E T R A storage ring at DESY in Hamburg, Germany, bounded the mass of this dileptonic particle to mx++/g3t >_ 340 G e V / c 2, where g3l depends on the particular s y m m e t r y and is of order unity [23]. This can be translated into GM~ _< 10-2GF.

3

The Conversion Process

Muonium and antimuonium are neutral atoms which are degenerate in their energy levels in the absence of external fields. In 1957 Pontecorvo suggested the possibility of a muonium to antimuonium conversion process even before the a t o m had been formed for the first time by V.W. Hughes and his coworkers in 1960 at the NEVIS cyclotron of Columbia University, New York, USA [24]. He proposed a coupling by an intermediate neutrino pair state in analogy to the K ° - K ° oscillations, which were discovered at that time [25].

46

L. Willmann and K. Jungmann

Any possible coupling between m u o n i u m and its a n t i a t o m will give rise to oscillations between the two species. For atomic s-states with principal q u a n t u m number n a splitting of their energy levels =

8GF

GM~-

(1)

v%2~a03 @ is caused, where a0 is the Bohr radius of the atom. For the ground state equals 1.5-10 -12 e V - ( G M ~ / G r ) which corresponds to 519 Hz for G M ~ = GF. We note that this value is three times larger than the uncertainty reported for the best measurement of the m u o n i u m ground state hyperfine structure interval [26]. Therefore, the interpretation of precise measurements of the hyperfine structure must include considerations on how such a process would affect the accuracy under the particular experimental conditions [27]. A system starting at time t -- 0 as a pure state of m u o n i u m could be observed in the antimuonium state at a later time t with a probability of (Fig. 3)

(~_~.) e-A~,t

pM~(t) = s i n 2 ~t

(~t~ 2

~' \ 2 h )

-

"¢ ~,t,

(2)

where A, = 1 / % is the muon decay rate. The approximation is valid for a weak coupling as suggested by the known experimental limits on GM~. In this case the process should be considered a conversion rather than an oscillation. The m a x i m u m of the probability for a decay as a n t i m u o n i u m is found at tm~x = 2/A,, while the ratio of antimuonium to m u o n i u m continuosly increases with time. The total conversion probability integrated over all decay times is

PM~=2-5610 -5

\--~F J

"

(3)

This demonstrates the advantage of experiments in which the system is allowed an extended time interval (a duration of order r , or longer) for developing a conversion. The degeneracy of corresponding states in the a t o m and its a n t i a t o m is removed by external magnetic and electric fields which can cause a suppression of the conversion and a reduction of the probability PMM"T h e influence of an external magnetic field depends on the interaction type of the process. The reduction of the conversion probability has been calculated for all possible interaction types as a function of field strength (Fig. 3) [28, 29]. In the case of an observation of the conversion process the coupling type could be revealed by measurements of the conversion probability at two different magnetic field values. The conversion process is strongly suppressed for m u o n i u m in contact with matter, since a transfer of the negative muon in a n t i m u o n i u m to any other a t o m is energetically favored and breaks up the s y m m e t r y between

The Muonium Atom as a Probe of Physics beyond the Standard Model

47

0.5

e "Xgt

0.45

0.4 0.35 "~ 0.3 0.25 0.2 0.15 0.1 0.05 0

xlO 8 for P'-~MM= 1.8

• 1 0 -2

= 1000

0

1

2

3

4

5

"'"'"" 4..

6

7

8

9 10 time [ps]

Fig. 2. Time dependence of the probability to observe an antimuonium decay for a system which was initially in a pure muonium state. The solid line represents the exponential decay of muonium in the absence of a finite coupling. The decay probability as antimuonium is given for a coupling strength of GM~- = 1000 by the dotted line and for a coupling strength small compared to the muons decay rate (dashed line). In the latter case the maximum of the probability is at 2 muon lifetimes. Only for strong coupling several oscillation periods could be observed.

m u o n i u m and antimuonium by opening up an additional decay channel for the antiatom only. In gases at atmospheric pressures the conversion probability is about five orders of magnitude smaller than in vacuum [30] mainly due to scattering of the a t o m s from gas molecules. In solids the reduction amounts to even 10 orders of magnitude. Therefore a sensitive experiment will benefit largely from employing muonium atoms in vacuum.

4

History

of Experimental

Search

There is a strong connection between experimental searches for nmonium to antimuonium conversion and the development of efficient sources of m u o n i u m atoms. In the earliest experiment in 1967 at the NEVIS cyclotron [31] muons were stopped in a Ar noble gas target of pressure 1 a t m with a technique similar to the one which was used in the discovery of nmonium. A large fraction of the muons forms m u o n i u m by electron capture. A conversion process would be indicated by K s X-rays originating from an argon a t o m after the transfer of the negative muon from antimuonium. A sensitivity of G'M~ < 5800 GF (95% C.L.) could be reached which was mainly limited by the strong suppression of the conversion in gases. One year later M¢ller scattering was investigated at the Princeton-Stanford electron storage rings at Stanford, USA. An analysis of the channel

48

L. Willmann and K. Jungmann

"

0.61 ~

.

.~. . . . .i. . . .0. . . . .". . . . 8. . . . .~. . . . . . . . . . . . . . . . . .

~0.4 F 0

effective Hamiltonianform: ~ (V-+A)×(VT-A)or (STP)x(ST-P)

l-

0.2 ~-

~

l-~

10

10

-2

GM~< 1 G F

~ ' ~

(v~A)~(v+~)or(S~PNs-+P)

_ ~_i~....p~,~ .... --ss ss

-3

"",

10

........ ,

-1

1

........ ,

10

......... ,

10

........ ,

2

.\ ..,.~-~

3

........

4

10 10 10 magnetic field [G]

5

Fig. 3. The muonium to antimuonium conversion probability depends on external magnetic fields and the coupling type. Recent independent calculations were performed by Wong and Hou [16] and Horikawa and Sasaki [29].

e- + e- --+ # - + p - , which is essentially the same physical process as muonium-antimuonium conversion, yielded nearly two orders of magnitude higher sensitivity on the coupling strength [32]. 1 Significant increases in sensitivity could be achieved after 1980 by taking advantage of newly developed sources of muonium in vacuum. At the Los Alamos Meson Physics Facility (LAMPF) in Los Alamos, USA, muonium in vacuum could be produced by a beam foil technique from thin aluminum foils. The velocity-resonant nature of the electron capture process causes typical kinetic energies of the atoms of a few keV. The corresponding high velocities and finite dimensions of the apparatus restricted the time interval available for the conversion. Antimuonium could have been discovered by secondary electrons and muonic X-rays from a bismuth catcher foil. The coupling constant GM~ could be limited to below 7.5 GF (90% C.L.) [33]. The discovery of muoniurn formation in fine grain SiO~ powders [34, 35] with about 60 % efficiency [36], after stopping muons from a surface beam stimulated experimental work at the Tri University Meson Facility (TRIUMF) in Vancover, Canada, in the early 80's. The signature for antimuonium was the detection of X-rays after capturing the negative muon in a calcium host atom. The data were analyzed under the assumption that the muonium atoms escape from the grains into the intergranular voids and yielded GM~ _< 42 GF (95% C.L.) [37]. With a more complete understanding of the behaviour of muonium atoms inside of a powder target a reanalysis of the Today e- + e - scattering experiments would have to run for approximately 1 year at LEP beam energies and luminosities to reach a sensitivity similar to a modern muonium-antimuonium conversion experiment in medium energy laboratories.

The Muonium Atom as a Probe of Physics beyond the Standard Model

49

data limited the coupling constant GM~ to less than 20 GF (95% C.L) [38]. The observation of a few percent of the muonium atoms leaving SiO2 powder target surfaces with thermal energies at TRIUMF [38] and at at the Paul Scherrer Institut (PSI) in Villigen, Switzerland [39], was a major breakthrough in the mid 80's. It has boosted experimental efforts searching for muonium to antimuonium conversion and has been employed in all new approaches since. At TRtUMF an experiment using thermal muonium in vacuum requested a signature consisting of X-rays generated by the transfer of the negative muon to a host atom and followed by the delayed decay of a radioactive tantal nucleus created by nuclear muon capture. A sensitivity of GM~ ~ 0.29 GF (90% C.L.) could be reached [40]. The thermal kinetic energy of the muonium atoms corresponds to a velocity of 7.4(1) mm/ps [39]. This assures that the atoms will stay in a small volume of about 100 cm 3 for several natural lifetimes T, and allows for long times for the conversion to antimuonium. At the Phasotron accelerator in Dubna, Russia, another experiment has been carried out using muonium in vacuum from a SiO2 target. The only signal required was the observation of a single energetic electron from the negative muon's decay in a narrow momentum band of 6.3 MeV/c right below the maximum possible momentum 53 MeV/c of the decay electron in muon decay. A limit of GM~ < 0.14GF (90% C.L.) was deduced after one single event has been observed to fulfill the weak required criterion [41].

5

Coincidence

Signatures

of the Atom's

Decay

Major progress was achieved using a new powerful and clean signature requesting the coincident detection of both constituents of the antimuonium atom in its decay. This method was developed and applied for the first time in an approach at LAMPF, where a magnetic spectrometer was used to search for an energetic electron from the p - decay. The positron, which is expected to be left behind from the atomic shell with a mean kinetic energy corresponding to the system's Rydberg energy [42], could be electrostatically extracted from the interaction region and registered on a microchannel plate (MCP) detector. A limit of GM~ < 0.16 G~- (90% C.L.) could be established [43]. The latest experiment at PSI (Fig. 5) [44, 45], implemented major improvements over the LAMPF setup. The solid angle for the detection of the energetic electron was increased by three orders of magnitude to 70 % of 4zr by using a cylindrical magnetic spectrometer equipped with five concentric proportional chambers and a 64-fold segmented hodoscope which was constructed from the former SINDRUM I detector. The atomic positron is electrostatically accelerated and guided in a momentum selective transport system parallel to the magnetic field lines to a position sensitive MCP with resistive anode readout [46]. The tracks of these particles can be traced back

50

L. Willmann and K. Jungmann

Fig. 4. Top view of the apparatus at PSI. The observation of the energetic electron from the p - decay in the antiatom in a magnetic spectrometer with a magnetic field strength 0.1 T is required in coincidence with the detection of the positron, which is left behind from the atomic shell of the antiatom, on a MCP and at least one annihilation photon in a CsI calorimeter.

to the interaction region for reconstructing a decay vertex providing an additional suppression of background. Further the annihilation radiation of the positrons can be observed in a 12-fold segmented undoped, highly pure CsI crystal calorimeter (Fig. 5). One of the design goals for the setup was to achieve as high as possible s y m m e t r y for the detection of both, antimuonium and muonium, in order to reduce the systematic uncertainties arising from corrections for efficiencies and acceptances of the detector subsystems. The production of the a t o m s has been monitored by reversing all electric and magnetic fields regularly every few hours for half an hour. The setup at PSI has a significantly higher sensitivity for observing the decay of muonium atoms in vacuum than to those decaying inside of the production target, as it allows the coincident detection of a fast and a slow particle after the decay. Therefore a new determination method for the muonium production yield could be uniquely exploited. It is based on a model established in independent dedicated experiments [39], which assumes that

The Muonium Atom as a Probe of Physics beyond the Standard Model

51

the atoms are produced inside of the SiO2 powder at positions given by the stopping distribution of the muons. A one dimensional diffusion process describes the escape of the muonium a t o m s into vacuum where their velocities follow a Maxwell-Boltzmann distribution. The distribution of time intervals between a stop of a muon and the detected decay of a m u o n i u m a t o m in vacu u m includes full information on the a t o m ' s production rate (Fig. 5). Using an effective diffusion equation for the movement of atoms inside the target parallel to an axis (y) orthogonal to the target surface the time distribution is derived for a diffusion length l = ~ which is small compared to the target thickness a

2-v~.

DM

• exp ( • /0 t dr' fo ~ dy S(y)x/~Tg (a -- y)

(a - - y)2

4T~MM :7, )

,

(4)

with DM the diffusion constant, fM the fraction of muons stopped with a density S(y) inside of the target and forming muonium. There is no muonium in vacuum at t = 0. The m a x i m u m of r ~ M v a c ( t ) is approximately at 1.5 ps which is about the average time of diffusion for the muonium atoms in the target. The spectra contain a small exponentially decaying background arising from muon decays within the target which can be associated with the release of a secondary electron from the target material. Numerical fits (Fig. 5) typically yield a few percent of n m o n i u m a t o m s in vacuum with respect to the incoming muons. For a flat stopping distribution S(y) and target thickness a large compared to the diffusion length l an analytical integration results in ngv~c(t) = f g

exp(--Aut)

D~

(5)

The expression contains the diffusion constant DM only as a part of the normalization factor. An intermediate result from the PSI experiment, which is carried out in a two step approach, is available [45] on the basis of an effective measurement time of 210 hours during which 1.4(1) • 10 ~ muonium atoms decayed inside of the fiducial volume of diameter 9 cm and length 10 cm. No decay of an antimuonium a t o m was observed. There are no entries in a 20 ns wide window around the expected time of flight of 70 ns for the positrons from the atomic shell (Fig. 6). The apparent structure around tTOF--te×p~ct~a = --50 ns arises from the allowed rare decay mode #+ --+ e+e+e-ueP£ in which one of the positrons is released with low kinetic energy, while the electron is detected in the magnetic spectrometer. Due to their significantly higher initial m o m e n t a positrons from these processes arrive at earlier times at the M C P and can be significantly distinguished from possible antimuonium decays. A small part of this observed background signal is due to positrons from normal muon

52

L. Willmarm and K. Jungmann

~100

0

2000

4000

6000 tdecay

8000

[ns]

Fig. 5. In the setup at PSI the detection of decays of muonium atoms in vacuum is favored compared to decays of muons inside of the target. The distribution of time intervals between the detection of an incoming muon in the beam counter and the observation of the decay of an atom in vacuum carries information on the efficiency of the muonium production. The dashed line represents an exponentially decaying background.

decay which experience B h a b h a scattering in any structural component in the target region. The probability for a conversion in a 0.1 T magnetic field is PM~(0.1 T) < 2.8-10 -9 (90% C.L.), where corrections have been applied to account for differences in detection efficiencies while measuring the m u o n i u m production yield and while searching for antimuoniuna. For (V =t=A) × (V =k A) type interactions, the conversion probability is suppressed in a magnetic field of 0.1 T to 35% of the zero field value. This leads through Eq.(3) to an upper limit of GM~ _( 1.8. 10 -2 GF (90% C.L.). For diteptonic gauge bosons X ++ in G U T models a tight new mass limit of Mx++/93t > 1.1 T e V / c 2 (90% C.L.) can be extracted. This bound exceeds significantly the one deducted from high energy Bhabha scattering [23]. With these results from the first step of the PSI experiment models with dilepton exchange [19] as well as models with heavy leptons and radiative generation of lepton masses appear to be less attractive [16]. This is a nice examples for contributions of research using atomic objects for solving problems in the domain of particle physics.

6

O u t l o o k for F u t u r e E x p e r i m e n t s

The measurements in the second stage of the experiment at PSI promise further advances. Among the m a j o r improvements are a detector for positrons with four times enhanced efficiency [46] and a beam line (~Eh) with 5 times

The Muonium Atom as a Probe of Physics beyond the Standard Model

(a) events with abs(troF-texp,~d ) _<10PS

15

53

(b) events with abs(Rd, ~) _< 12mm

~4 i ~"

10

2

o~

..... :, '

..

, o

..

no~ "

'

Rdc a

°1oo

[Clll]

tl

nnnn_~,',

~.~ n n n . n .

o

loo

tTOF -texpected

Ins]

Fig. 6. The number of events with identified energetic electron and slow positron as a function of (a) the distance of closest approach Rdc~ between the electron track in the magnetic spectrometer and the back projection of the position measured at the MCP and (b) the difference of the positron's time of flight tTOF to the expected arrival time texpect,a. The signal at earlier times is due to the allowed decay channel/z --+ 3e2v and Bhabha scattering. It is smeared out because of the different acceleration voltages used. No event satisfied the required coincidence signature. The dotted and dashed curves correspond to a simulated signal for GM~ = 0.05 GF-

higher muon flux. D a t a have been collected for some 1300 hours and a preliminary result [47] is available which sets in (V ± A) × (V + A) coupling an upper limit of GM~ _< 3.2 - 10 - a GF (90%C.L.). This provides an even more stringent test for speculative extensions to the standard model, in particular to the left-right symmetric models predicting a lower bound on GM~ [14]. In order to increase the sensitivity of detecting a possible conversion process of m u o n i u m into antimuonium considerably in the future a new experimental approach will be required. The present setup has come close to the limits imposed by the available muon fluxes at present meson factories, realistic durations of running times and the rate capabilities of available proportional wire chambers. The number of accidental coincidences is expected to become a serious problem for higher beam rates. At present, possible improvements to the existing setup at PSI appear to promise only marginal progress. However, at future highly intense pulsed muon sources one could take advantage of the time evolution of the conversion signal which increases quadratically in time (Eq. 2). Therefore a detection scheme could be envisaged which again uses the powerful coincidence detection of both constituents of antimuonium and which starts to look for antimuonium decays a few muon lifetimes after the formation of the system. It should be noted that final state interaction in muonium decay could mimic an antimuonium decay, when energy is transfered from the positron of the #+ decay to the electron in the atomic shell (internal B h a b h a scattering). An energy transfer of more than 10 MeV while the positron remains with less than 0.1MeV kinetic energy has a probability of well below 10 -11 [44]. However, this process can be distinguished from an antimuonium decay by

54

L. Willmann and K. Jungmann

the characteristic energy spectra of the detectable particles as in the case of potential background from the allowed p --+ 3 e 2 u decay. Therefore, there is no principle limitation which could prevent much more sensitive searches beyond the present bounds.

Acknowledgements We are indebted to Prof. G. zu Putlitz for his constant support, advice and encouragement during our work on this appealing subject in the framework of international collaboration. * Present address: Department of Physics, Massachusetts Institute of Technology, Cambridge, MA. 02139

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L. Willmann and K. Jungmann

[34] G.M. Marshall, J.B. Warren, D.M. Garner, G.S. Clark, J.H. Brewer and D.G. Fleming, Phys.Lett. A65,351 (1978). [35] Cabot Corporation, "Cab-O-Sil Properties and Functions", technical report, Cab-O-Sil Division, Tuscola, IL (1988). [36] R.F. Kiefl, J.B. Warren, C.J. Oram, G.M. Marshall, J.H. Brewer, D.R. Harshmann, and C.W. Clawson, Phys.Rev. B26, 2432 (1982). [37] G.M. Marshall, J.B. Warren, C.J. Oram and R.F. Kiefl, Phys.Rev. D25,

1174 (1982). [38] G.A. Beer, G.M. Marshall, G.R. Mason, A. Olin, Z. Gelbark, K.I:{. Kendall, T. Bowen, P.G. Halverson, A.E. Pifer, C.A. Fry, J.B. Warren and A.R. Kunselman, Phys.Rev.Lett. 57, 671 (1986). [39] K. Woodle, K.-P. Arnold, M. Gladisch, J. Hofmann, M. Janousch, K.P. Jungmann, H.-J. Mundinger, G. zu Putlitz, J. Rosenkranz, W. SchMer, G. Schitt, W. Schwarz, V.W. Hughes and S.H. Kettell, Z.Phys. D9, 59 (1988), see also: A.C. Janissen, G.A. Beer, G.R. Mason, A. Olin, T.M. Huber, A.R. Kunselman, T. Bowen, P.G. Halverson, C.A. Fry, K.IR. Kendall, G.M. Marshall and J.B. Warren, Phys.Rev. A42, 161 (1990). [40] T.M. Huber, A.R. Kunselman, A.C. Janissen, G.A. Beer, G.R. Mason, A. Olin, T. Bowen, P.G. Halverson, C.A. Fry, K.R. Kendall, G.M. Marshall, B. Heinrich, K. Myrtle and J.B. Warren, Phys.Rev. D41, 2709 (1990). [41] V.A. Gordeev, A.Yu. Kiselev, N.P. Aleshin, E.N. Komarov, O.V. Miklukho, Yu.G. Naryshkin, V.A. Sknar, V.V. Sulimov, [.I. Tkach, V.M. Abazov, V.A. Baranov, A.N. Bragin, S.A. Gustov, N.P. Kravchuk, T.N. Mamedov, I.V. Mirokhin, O.V. Savchenko and A.P. Fursov, JETP Lett. 59, No. 9, 589 (1994). [42] L. Chatterjee , A. Chakrabarty, G. Das and S. Mondal, Phys.Rev. D46, 46

(1992). [43] B.E. Matthias, H.E. Ahn, A. Badertscher, F. Chmely, M. Eckhause, V.W. Hughes, K.P. Jungmann, J.R. Kane, S.H. Ketell, Y. Kuang, H.-J. Mundinger, B. Ni, H. Orth, G. zu Putlitz, H.R. Sch~ifer, M.T. Witkowski and K.A. Woodle, Phys.Rev.Lett. 66, 2716 (1991). [44] K. Jungmann, B.E. Matthias, H.-J. Mundinger, J. Rosenkranz, W. Sch/ifer, W. Schwarz, G. zu Putlitz, D. Ciskowski, V.W. Hughes, R. Engfer, E.A. Hermes, C. Niebuhr, H.S. Pruys, R. Abela, A. Badertscher, W. Bertl, D. Renker, H.K. Walter, D. Kampmarm, G. Otter, R. Seeliger, T. Kozlowski and S. Korentschenko, PSI proposal R-89-06 (1990). [45] R. Abela, J. Bagaturia, W. Bertl, R. Engfer, B. Fischer yon VVeikersthal, A. Grossmann, V.W. Hughes, K. Jungmann, D. Kampmann, V. Karpuchin, I. Kisel, A. Klaas, S. Korentschenko, N. Kuchinsky, A. Leuschner, B.E. Matthias, R. Menz, V. Meyer, D. Mzavia, G. Otter, T. Prokscha, H.S. Pruys, G. zu Putlitz, W. Reichart, I. Reinhard, D. Renker, T. Sakelashvilli, P.V. Schmidt, R. Seeliger, H.K. Walter, L. Willmann and L. Zhang, Phys.Rev.Lett. 77, 1950 (1996). [46] P.V. Schmidt, L. Willmann, R. Abela, J. Bagaturia, W. Bertl, B. Braun, H. Folger, K. Jungmann, D. Mzavia, G. zu Putlitz, D. Renker, T. Sakelashvilli and L. Zhang, Nucl.Inst.Meth. A376, 139 (1996). [47] P.V. Schmidt, doctoral thesis, Heidelberg, unpublished (1997); see also: H.P. Wirtz, doctoral thesis, Zfirich, unpublished (1997).

Can A t o m s Trapped in Solid H e l i u m Be U s e d to Search for Physics B e y o n d the Standard Model? A. Weis, S. Kanorsky, S. Lang and T.W. H/insch Max-Planck-Institut fiir Quantenoptik, Hans-Kopfermann-StraBe 1, 85748 Garching, Germany

Introduction Since the 1960's experiments using atomic physics techniques have played an ever increasing role in testing fundamental elementary particle theories. In particular studies of atomic processes in which the fundamental symmetries P (mirror inversion, parity) and T (time reversal) are violated have yielded physical insights which are complementary to the information gained from nuclear and high energy physics experiments. One of the most sensitive ways to test T-symmetry is the search for permanent electric dipole moments of elementary particles which cannot exist if P and T are good symmetries. In the past four decades experiments aimed at the detection of such moments have been carried out on the neutron and on various atoms (Ramsey 1994). While reaching spectacular sensitivities all of these experiments have so far measured values of the dipole moments which are compatible with zero. In quest for a radically new experimental approach to the dipole moment search in atoms we have been led to consider paramagnetic atoms trapped in condensed 4He as a promising new sample. The scope of the present paper is to review the knowledge we have gained in the past years on the properties of this novel sample and to discuss its applicability to an experiment searching for T-violation. In order to motivate the interest in atomic electric dipole experiments we will start by giving a brief general account of the role played by atomic physics experiments in the investigation of the discrete symmetries P and T. We will show that the search for permanent electric dipole moments is a search for physics beyond the standard model of electroweak interactions. After reviewing the state-of-the-art of the experimental results in this field we will outline the general principles common to all electric dipole experiments. The major part of the paper will be devoted to a detailed discussion of the novel approach to the search for electric dipole moments pursued by our team at the Max-Planck-Institut fiir Quantenoptik (MPQ) in Garching since a couple of years.

58

Can Atoms Trapped in Solid Helium Be Used ... ?

Violations of Discrete Symmetries Parity Violation In 1957 several experiments observed that parity is violated in ~-decay, i.e. in processes which are governed by the weak interaction. The subsequent development of the standard model of electroweak interactions - a unified description of electromagnetic and weak interactions - in the 60's and the experimental observation of weak neutral currents in neutrino scattering experiments in the early 70's gave rise to the speculation that atomic properties should also be affected by the weak interaction and that parity violation should be observable in atomic physics. In a seminal paper C. and M.-A. Bouchiat showed in 1974 (Bouchiat and Bouchiat 1974) that heavy atoms are particularly sensitive to contributions from weak interactions (Z 3 law), and that modern laser spectroscopic techniques would have the sensitivity required to measure such effects. In the two decades since, parity violation was measured in various heavy atoms. All experimental results are in perfect agreement with the predictions from the standard model, the most precise experiments reaching an accuracy of 2.5% (for a review see e.g. Bouchiat 1991). The origin of parity violation in atoms is a quantum-mechanical interference of two (neutral current) amplitudes describing the interaction of the electron with the nucleus; one being the electromagnetic Coulomb interaction mediated by virtual photons, and the second being the weak interaction mediated by the neutral intermediate vector boson Z°. The fascinating aspect of the atomic parity experiments is the fact that table top experiments allow to observe effects induced by the Z° at q2 values (q = four-momentum transfer between photon and electron) which are ten orders of magnitude below the ones used in accelerator experiments. The next generation of atomic parity violation experiments aims at pushing the sensitivity to the 1% level and even beyond (Bouchiat 1991, Moriond 1994). This level of precision will allow the study of a number of new phenomena, such as nuclear spin dependent P-violating effects , the nuclear anapole moment (a P-violating nuclear property), as well as radiative corrections to the standard model. Atomic parity violation is thus expected to provide further tests of the standard model. Time Reversal Invariance While the parity symmetry and the various manifestations of its violation are nowadays well understood in the frame of the standard model, time reversal symmetry remains rather obscure. So far only a single experimental evidence for T-violation was found (decay of the long-lived component of the K ° meson). In the 50's Purcell and Ramsey had already pointed out (Purcell 1950) that there was no a priori reason to a s s u m e the conservation of discrete symmetries and that such a belief must be based oil experiment. In 1950 they proposed to search for an electric dipole moment (EDM) of the neutron as a test of P-conservation. After the fall of parity in 57 they argued further that T conservation was still a strong argument against the existence of permanent EDM's in elementary particles. The search for P and T violating electric dipole moments in atoms and the

EDM Experiments

59

neutron is now widely recognized to be one of the most sensitive ways to test T-symmetry (Ramsey 1994). The standard model can accomodate T-violation through a complex phase factor (Kobayashi-Maskawa mixing angle). However, the magnitudes of the electron and neutron electric dipole moments predicted by this naeehanism are 8 - 9 orders of magnitude below the current experimental sensitivities. When considering that, averaged over the past 30 years, the experimental sensitivity has been lowered by of one order of magnitude every 8 years, there is little hope that the experiments wilt ever be able to test standard models predictions. On the other hand there are several reasons to believe that the standard model is not the ultimate theory of electroweak interactions 1. For this reason several extensions of the standard model or alternative theories have been developed in the .past decade, some of them predicting values for the electron or neutron EDM's which are well within the reach of modern EDM experiments or their future extensions (Barr 1994, Bernreuther and Suzuki 1991). In this sense the hunt for the EDM of an elementary particle is probably the most promising way to search for physics beyond the standard model, or, as Steven Weinberg, one of the fathers of the standard model has put it: "... may be that the next exciting thing to come along will be the discovery of a neutron 07" atomic or electron electric dipole moment. These electric dipole moments . . . s e e m to me to offer one of the most exciting possibilities for progress in particle physics." 2. Because of the smallness of the standard model predictions any non-zero result in an EDM experiment would be a clear indication for physics beyond the standard model.

EDM Experiments State-of-the-art The neutron EDM has been chased by N. Ramsey and his collaborators for more than 40 years, first with neutron beam magnetic resonance techniques and more recently with ultracold neutrons trapped in a neutron "bottle" (Smith et al 1990, Ramsey 1994). This series of experiments, which counts among the longest ongoing experimental effort in the history of modern physics, has recently been resumed at the ILL in Grenoble after a long shut-down of the reactor. Atomic physics has entered the scene of T-violation experiments in the 60's, with a first experiment that set an upper limit on the EDM of the laaCs atom using a conventional Ramsey magnetic resonance method. More and more refined techniques have been developed since, in particular by applying optical methods to spin polarize the samples and to detect the magnetic resonance. Nowadays the sensitivities of EDM experiments in atoms and the neutron have now reached comparable levels. In Table 1 we compare the present upper limits for the EDM of the neutron and of various atoms, as well as the inferred EDM's of the electron and the proton. t For a discussion of arguments see e.g. the review papers by Barr (Barr I994, Barr 1993). 2 cited in (Barr 1994)

60

Can Atoms Trapped in Solid Helium Be Used ... ?

T a b l e 1. Experimental upper limits for permanent electric dipole moments taken from a recent compilation (Ramsey 1994). Numerical values ai-e given in traits of 10-2r e cm. neutron

t99Hg

129Xe

2OST1

133Cs

system EDM

< 90

< 0.63

< 210

< 2 300

< 20 000

inferred electron EDM

-

<44

< 2104

<3

<90

T h e atomic experiments can be seen to fall in two categories, viz. experiments on diamagnetic atoms (Hg, Xe) and experiments on paramagnetic atoms (Cs, T1). The former give lower limits on the atomic EDM from which mainly information on T-violating processes within the nucleus or in the electron-nucleus interaction can be deduced, while the latter are more sensitive to contributions from an EDM of the electron. Atomic EDM's Electric dipole moments d are measured via their interaction - d . E with a static electric field E . The acceleration of charged particles by strong electric fields therefore precludes the direct measurement of the EDM of particles such as the proton or the electron. If one tries to counteract this acceleration by other forces, as in bound systems of charged particles such as atoms, the total electric field at the particle's location will vanish and the individual particles will no longer experience a dipole interaction. This simple fact, which was first pointed out by Ramsey and Purcell in the 50's was generalized in the 60's by Schiff (Schiff 1963) in a form usually referred to as the Schiff Theorem. The i m p o r t a n t point of Schiff's paper was however the remark that the above considerations no longer hold when the motion of the particles is relativistic, when other than electrostatic forces act on the particles or when the charge distribution within the particles differs from the EDM distribution, conditions which are met in heavy atoms. Sandars (Sandars 1966) was the first to calculate the atomic dipole m o m e n t due to a dipole nmment of the electron and found that for heavy paramagnetic atoms the above discussed screening is actually an antiscreening, usually referred to in terms of the enhancement factor R = datom/detection. Note that this phenomenon is closely related to the well-known Sternheimer correction which describes the screening/antiscreening of external electric filed gradients experienced by the nucleus in an atom. Typical values of R are 120 for 133C8and -600 for 2°STl. The atom as a whole can only have a significant EDM contribution from the electron EDM if the atom has a non-zero electronic angular m o m e n t u m J. In diamagnetic atoms with J = 0 (such as 199Hg or 129Xe) the main EDM contribution comes from nuclear EDM's, which are not enhanced, due to the nonrelativistic motion of the nucleus. This explains why paramagnetic atoms are more sensitive to electron EDM's (cf Table 1).

Atoms in Solid 4He

61

G e n e r a l principles of E D M e x p e r i m e n t s All EDM experiments share several common principles which rely on the fact that if a particle has both magnetic/~ and electric d dipole moments, these have to be oriented parallel or antiparallel to the particle's angular momentum J . The spin precession frequency of the particle when placed in parallel/antiparallel magnetic and electric fields B and E is then given by

where WL--

tt.B h

is the Larmor frequency and

WE --

d.E h

its electrical

equivalent; the relative orientation of the fields is given by ~ = / ) • ~J. The various EDM experiments differ by the techniques used to detect the precession frequency and its EDM induced change. Most experiments use magnetic resonance techniques, while some recent atomic EDM experiments use magnetic level crossing techniques. The experimental sensitivity is determined by the phase angle ¢ = COprr accumulated during the coherent spin precession time r. Sensitive experiments thus call for large electric fields and long interaction times (spin relaxation times) r, i.e. narrow magnetic resonance lines. Experiments in diamagnetic atoms use nuclear magnetic resonance (NMR), while experiments on paramagnetic atoms detect electron spin resonance (ESR). Nuclear spin polarized samples are known to have spin relaxation times which are orders of magnitude larger than electronic spin relaxation times. This explains why experiments on diamagnetic atoms usually yield lower limits for atomic EDM's.

A t o m s in Solid 4He A t o m s in H e I I In 1991 one of us (S.K.) proposed to use spin polarized paramagnetic atoms implanted into superfluid 4He (HelI) as a radically novel sample to search for atomic EDM's. This proposal was motivated by the perspective that liquid He could serve as a trap for the implanted atoms, where long storage times in an isotropic, non magnetic environment would allow long coherent spin precession times and hence very narrow electronic magnetic resonance lines. In addition superfluid He was known to hold electric field strengths in excess of 1O0 kV/cm and presented furthermore the advantage of being ideally suited for the implementation of superconducting magnetic field shields which allow to isolate the sample from magnetic perturbations from the laboratory enviromnent. Moreover, the matrix itself has vacuum-like properties for the electromagnetic fields used in the experiments, be they static E or B fields, optical fields in the visible or near-infrared spectral regions, or radio-frequency and microwave fields. The idea of using matrix-isolated atoms was triggered by the reading of a series of

62

Can Atoms Trapped in Solid Helium Be Used ... ?

papers in which a team from the University of Heidelberg described a technique which had allowed them for the first time to implant foreign atoms into superfluid Helium and to observe recombination fluorescence, as well as laser-induced fluorescence from a variety of atomic species. The team was directed by G. zu Putlitz. In 1991 we started at MPQ in Garching a project aimed at the investigation of magneto-optical effects in paramagnetic atoms in condensed Helium. In the past the main interest of the only team working in the field (Heidelberg) was concentrated on the development of implantation techniques and on the study of optical properties of implanted species (Reyher et al. 1986, Tabbert et al. 1995). At the time it was not known whether atoms in HeII could be spin-polarized by optical pumping nor whether it would be possible to observe magnetic resonance in such atoms. Inspired by the Heidelberg work we designed a double bath cryostat which became operational in 1992. In a first series of experiments we studied optical spectra of Ba atoms in superfluid He. These studies have yielded two important results. On one hand the study of the pressure shift of the Ba resonance lines allowed us to infer quantitative informations on the structure of the atomic trapping sites in He (Kanorsky et al. 1994a, Kanorsky and Weis 1996). On the other hand we discovered a novel and simpler implantation technique for foreign atoms. An energy of approximately leV is required for an atom to penetrate into superfluid He. For this reason atoms cannot be implanted into liquid He from an atomic beam hitting the liquid-vapor interface of a He bath. The Heidelberg technique consisted in creating atomic ions above the He bath either by a discharge or by laser ablation. We chose the laser sputtering method in which ablated positive ions are accelerated electrostatically into the superfluid volume, where they are made to recombine with electrons extracted by field emission from a tunneling microscope tip. During our experiments we found that when the He level in the inner chamber rose above the target, the ablation process worked equally well, and that even when no voltage was applied to the field emission tip, a strong atomic LIF signal could be detected (Arndt et al. 1993). A similar technique was developped independently at the same time by a team at the university of Kyoto (Fujisaki et al. 1993). This important discovery thus opened the road to extend the experiments from the liquid phase of He to its solid phase (Kanorsky et al. 1994b). Starting in 1993 we therefore focussed our efforts first on pressurized superfluid and afterwards exclusively on solid He matrices. The latter offers the great advantage that it allows to obtain atomic trapping times ranging from minutes (Cs) to hours (Ba). Implantation

o f a t o m s i n t o solid H e

The original experiments were done in a double bath cryostat, in which the temperature is lowered to 1.5 K by evaporative cooling. Fig. 1 shows a schematic diagram of the cryostat used in our recent experiments. The major features are a single bath and a pressure cell with optical access fi'om 5 sides. The cell has optical access through five fused silica windows. Soft copper gaskets instead of In wire rings were used to seal the windows in order to avoid distortions of the magnetic fields applied with three pairs of superconducting Hehnholtz coils (not shown ill Fig.i) located outside of the cell. Two pairs

Atoms in Solid 4He

63

capillary

to pump

f Nd-YAG (2¢o)

~ I ~- ' \ - - - - ~ ~

J !iiii:~ ~ ~spectroscopy -' ']'~ F'--- cloudwith implantedatoms

Fig. 1. Schematic diagram of the cryostat used for the spectroscopy of atoms in solid 4He (left) and blown-up view of the pressure cell (right). The ablation laser can be focussed either onto the target for the implantation process or into the atomic cloud in order to dissociate clusters.

of coils inside the cell were used to produce the oscillatory magnetic fields. A/zmetal ( C R Y O P E R M 10) cylinder closed on one side shields laboratory magnetic fields at a level of raG. Optional additional features of the cell are resistive temperature and pressure sensors. At a temperature of 1.7 K a pressure of 27 bar has to be applied in order to solidify He (Fig.2). The required pressure is controlled by a room temperature pressure tank connected to the cell by a capillary. The ablation laser (frequency doubled Nd-YAG) is focussed through the top window onto the metal target located at the b o t t o m of the cell. By the deposited heat (typically 40 mJ per pulse at a rate of 10 Hz) the solid helium melts in the vicinity of the target. At the same time atoms are ablated into this liquid region and trapped therein in a conically shaped region after resolidification of the helium. Details of this implantation technique have been given elsewhere (Arndt et al. 1995a).

64

Can Atoms Trapped in Solid Helium Be Used ... ?

31 3O -~

29

"~

28 27 26 25

1.4

1.5

1.6

1.7

1.8

1.9

T (K) Fig. 2. p-T phase diagram of condensed 4He The spectroscopy laser 3 is sent through the cloud of implanted a t o m s and the fluorescence light - collected at right angles with respect to the direction of the laser b e a m - is filtered by an interference filter and detected with a cooled photonmttiplier. We observe a decrease of the fluorescence intensity on a time scale of minutes which we attribute to atomic diffusion and cluster formation. An efficient way to regenerate the atomic signal is to occasionally focus a few pulses of the ablation laser into the region where the atomic cloud and the spectroscopy laser overlap. Optical properties

o f a t o m s in c o n d e n s e d 4 H e

The optical properties of immersed foreign a t o m s can be described the so-called bubble model (Bauer et al. 1990). We only briefly review here its basic features; an extensive discussion can e.g. be found in (Kanorsky and Weis 1996). The interaction of tile implanted foreign a t o m with the m a t r i x a t o m s is characterized by a strong (hard-core type of) repulsive potential 4 and a weak van der Waals attractive potential. The repulsion expels He a t o m s from the location of the atomic defect, thus creating a bubble-shaped cavity. The shape of this bubble reflects the s y m m e t r y of the atomic wave function and its size is determined by the balance of the Pauli repulsion on one side and the bubble surface tension and pressure-volume work required for the bubble creation on the other side. The optical absorption-emission cycle (Fig.3) can now be understood as follows: Consider an a t o m with a spherically symmetric ground state located in a spher3 depending on the implanted species we used dye lasers, a Ti:Sapphire laser or diode lasers. 4 due to the Pauli principle

A~oms in Solid ~He

65

ically symmetric cavity. During the optical absorption process the shape of the cavity does not change as a consequence of the Franck-Condon principle.

~/. ....

.HI,

S S I ~ J S] H ~ t S ~ N I ~ . , , .

1p|'~¢~;~{~;~

.

®

................

6pl/;

......

.

.

.

.

.

.

.

.

.

...........

,[,

........... ISo

.

® iiil

.. . . . . .. . . .

.

.

.I S o .

.

.

.

.

.

.

.

.

""" ......

681/2

Fig. 3. Schematic representation of the bubble evolution during the absorptionemission cycle of Ba (a) and Cs (b) atoms in condensed He The atomic wave function of the excited state occupies a larger volume and thus exerts a stronger pressure on the cavity wall. The energy of the system is minimized by a shape relaxation of the bubble, which adopts to the symmetry of the atomic wave function. It becomes oblong for the aspherical 1P1 state of excited Ba and stays spherical in the case of the excited 2P1/2 state of Cs. This shape relaxation process is fast (ps) as it involves the displacement of He atoms by a few /1~at the speed of sound in He. The atom then decays in the relaxed bubble, and again, the shape does not change during this emission process. The cycle is completed by a relaxation of the bubble towards its initial state. As a consequence the optical excitation line is strongly perturbed and shows a large blue shift (40 nm for the Cs D1 line) and a strong broadening (several nm), while the emission line is less shifted and less broadened. From an experimental point this large Stokes shift is very convenient as it allows to efficiently discriminate against scattered laser light in laser induced fluorescence experiments. The above qualitative arguments can be put into a quantitative form and give a reasonable description e.g. of the lineshapes of excitation lines in pressurized He (Kanorsky et al. 1994a, Kanorsky and Weis 1996).

66

Can Atoms Trapped in Solid Helium Be Used ... ?

O p t i c a l p u m p i n g a n d spin r e l a x a t i o n t i m e The observation that the bubble model gives a satisfactory description of the optical spectra of Ba atoms in solid helium let us expect that the repulsion exerted by atoms in spherically symmetric ground states is stronger than the helium binding energy. As a consequence we expected that the symmetry of the trapping site to be determined by the symmetry of the atom-helium interaction rather than by the crystalline structure of the matrix 5. The absence of local crystalline field gradients resulting from the spherical symmetry of the cavity, together with the diamagnetic character of the matrix (neither the He nucleus nor its electron shell carry magnetic momenta) are necessary conditions for the creation of a large degree of spin polarization of implanted atoms. We tested this hypothesis in optical pumping experiments on implanted paramagnetic Cs atoms. Cs was the atom of choice for these studies, on one hand because it has a readily accessible resonance line in the near infrared with a large oscillator strength, and on the other hand because it is a promising candidate for a future EDM experiment. Optical pumping is a very efficient method for the creation of spin polarization in atoms. Due to the large homogeneous linewidth (3~optical 400 A~h.].,.) of the optical absorption line the hyperfine structure/-3~hJ.s, of the transition remains completely unresolved. When Cs atoms are illuminated with circularly polarized light resonant with the Dl-transition (6S1/2, F = 3,4 -+ 6P1/2, F = 3,4), the optical field couples to all the Zeeman sublevels of the ground state with the exception of the IF=4, MR=4) state, which is thus a dark state for circularly polarized light. After several absorption-emission cycles most of the population will be transferred to the dark state; in which both nuclear and electronic spins are fully polarized as IF=4, ME - - 4 ) - - I J = l / 2 ,

Mj = 1/2)1I=7/2, M r = 7/2).

The build-up of polarization, i.e. the increase of dark state population can be conveniently detected by the observation of a decrease in fluorescence. We have measured the longitudinal spin relaxation time T1 by the method of "relaxation in the dark". The technique consists of first polarizing the sample by optical pumping, and then turning off the exciting light, upon which the spins are allowed to relax "in the dark". The fluorescence level found immediately after turning the pump light back on after a variable dark time is a measure of the polarization which has survived the dark period. The results showed that the spin relaxation times were indeed very long. Values for T1 the range of 1 - 2 seconds were found (Arndt et al. 1995b) with magnetic holding fields as low as 10 mG (Fig. 4). The T1 values showed no significant magnetic field dependence up to 7 G, but scattered slightly from sample to sample. We assume tha.t impurities, such as paramagnetic Cs clusters are responsible for the observed depolarization rate of 1 s -1. These relaxation times are among the longest ever measured for electronic spin polarization. However, these long relaxation times could only be observed with a.toms implanted in the isotropic b.c.c, phase of the matrix. In 5 Deviations from this expectation will be discussed below

Atoms in Solid 4He

67

the (anisotropic) h.c.p, phase almost 1000 times smaller T1 times were observed (Fig. 4) indicating additional relaxation processes in that phase (see below).

1.0 IN,

'

{

'

t

'

0.8~-{-~-~

0.6:

I

'

I

--

holt mamx: bcc l--

"4

/

°4 i 0.2

(a)

0.0

,

l

0.0

,

{

0.5

t 1.0~

,

I

,

{

1.0

'

,

{

1.5

2.0

(s) '

J

0.8

,

I

'

1

{

host matrix: hcp

=

(4)

m

0.6-

L

"~ 0.4 "~, e-

_

0.0

(,b) I

0

2

,

I

,

4

I

6

,

I

8

,

I

10

tdark(ms)

Fig, 4, Measurement of longitudinal spin relaxation times in b.c.c, matrix (a) and h.c.p, matrix (b). Solid lines represent fits with exponential decay curves.

Optically detected magnetic resonance Having shown that a large degree of long-lived spin polarization can be created in Cs atoms isolated in solid 4He we have investigated magnetic resonances in the Cs ground state. In these experiments a longitudinal magnetic holding field B0 stabilizes the polarization build up by optical pumping. A linearly polarized magnetic field oscillating at the frequency wrf resonantly destroys spin

68

Can Atoms Trapped in Solid Helium Be Used ... ?

polarization when ¢zrf = ~0, where w0 is the Larmor precession frequency in the static field. The magnetic resonance is detected via the resonant increase of the fluorescence. In our early experiments (Arndt et al. 1995b, Weis et al 1995) we have observed in this way magnetic resonance lines with typical widths of a few kHz, corresponding to effective values for the transverse relaxation time T2 of 100 #s. T h e relatively large linwidths were determined by magnetic field inhomogeneities. In a recent rebuilding of the experimental chamber we have shielded the pressure cell from laboratory fields and have improved the homogeneity of the applied fieldS. The results were very satisfying and have yielded resonance linewidths which are 2-3 orders of magnitude narrower than in the previous experiments. Fig. 5 shows a typical example of such resonances.

i

i

i

i

i

i

i

.-_ 0.28 e-I

.~ 0.24

: FWHM = 15 Hz

~9

=

0.16

\

/

0.20

\

\

J

F=4 40

-20

F=3

0' , 2t0 , 4O , , 60 , , 8~ , v - v (Hz) rf

0

Fig. 5. Optically detected electron spin resonance in Cs atoms in b.c.c. 4He. The magnetic field Bo was 42.5 mG, corresponding to a resonance frequency Vo of 14.89 kHz. The line splitting is due to the nuclear magnetic moment.

The linewidth in this particular case is 15 Hz and still does not reflect the intrinsic transverse relaxation time, but is rather due to power broadening from tile optical p u m p i n g process. In order to infer the intrinsic T2 value we have performed a magnetic resonance experiment in the time domain. Fig. 6 shows a typical free-induction (FID) decay signal obtained by a sudden switching of the orientation of the longitudinal holding field by 90 degrees. Note that Fig.5 is basically the Fourier transform of Fig. 6. The FID decay time is of course also shortened by the optical p u m p i n g process and is on the order of 10 ms for the particular case shown in Fig.6. The FID technique allows however to perform an " F I D in the dark" type of experiment analogous to the one used to measure T1. Here again the laser is switched off a few FID periods after the flipping of the magnetic field so that the decay occurs in the dark. By varying the dark time one

Atoms in Solid 4He

69

can thus measure the intrinsic transverse relaxation time. In this way we have obtained T2 times exceeding 100 ms. The reason why T2 is'approximately one order of magnitude shorter than Tt is not clear at present, but may probably be traced back to magnetic field inhomogeneities at the level of a few #G. Planed spin echo experiments will probably help to clarify this point.

I

0.4

~

--~ -

!

- long

!

y~-Z

s

0.3

0.2

0.1

0.0 I

0.00

i

I

,

0.01

l

0.02

L

0.03

t (s) Fig. 6. Free induction decay of Cs ground state spin polarization in transverse magnetic field

Magnetometrie

sensitivity

One of the experimental problems regarding a possible EDM experiment is the fact that the atomic signal degrades as a consequence of cluster formation, thus posing severe normalization problems if signals recorded with electric fields of opposite polarities are to be compared. A possible way to circumvent this problem is the use of a dispersively-shaped resonance signal in an active feed-back loop which keeps the detuning u0 - ur] nulled. In this way any signal change affects only the gain in the feed-back loop and does not show up as a signal change. Flecently we have performed first tests with such an arrangement. The technique is based on a spin precession driven by a if-field as shown in Fig 7. Here the static magnetic field is oriented at 45 ° with respect to the optical pumping direction and a linearly polarized r.f. field resonantly drives the spin precession. The fluorescence is detected with a phase sensitive amplifier tuned to the r.f. frequency. This scheme has the further advantage that high modulation frequencies can be used, thus suppressing low-frequency noise in the sytem. A typical spectrum recorded with this arrangement is shown in Fig. 8.

70

Can Atoms Trapped in Solid Helium Be Used ... ?

fluorescence detection

X

y/

z

~0

.'"'~

1

lock-in

Q circ. pol. light

Brf(t)

S

Fig. 7. Experimental arrangement used to observe driven spin precessmn

I

I

i

I

I

[

i

0.4 0.3 0.2 ..a

0.1

z5

0.0 -0.1 -0.2 -0.3 -40

t

i

-30

-20

,

I

,

-to

I

,

0

I

lo

,

I

20

,

I

30

,

40

r e - v ° (Hz) Fig. 8. Driven spin precession recorded with integration time of 1 second/point. Inset shows data scatter near center of resonance (to = 4 0 k H z ) .

Tile analysis of the curve shows that we can detect frequency changes of approx. 10 mHz with an integration time of 1 second. This corresponds to magnetic field changes of 28 nG. Note that this is a preliminary first result obtained

Atoms in Solid 4He

71

without optimizing system parameters. It is nevertheless very promising in view of an EDM experiment as we will discuss below. T o w a r d s a n E D M e x p e r i m e n t w i t h Cs a t o m s in s o l i d 4 H e

Statistical considerations. The noise in the data of Fig.8 is predominantly determined by instabilities of the magnet current supply and fluctuations of the imperfectly shielded laboratory magnetic fields. The planed implementation of a superconducting magnetic shield and the integration of the current supply in a feed-back loop should allow to suppress these noise sources and hence to improve the magnetometric sensitivity AB. Using Eq. 1 the sensitivity ._4d to electric dipole moments can be directly expressed in terms of A B through

Ad = l i A B l E Using E = lOOkV/crn and I*/h = 1.4MHz/G we get Ad = 1.6. l0 -21 e c m with an integration time of 1 second. Typical total integration times in EDM experiments are 100-200 hours. If we assume that the sensitivity B d scales with the integration time T as Ad(T) = Ad(lsecond) T -t/2 we obtain

Ad(lOOhours) = 2.7.

10 - 2 4

ecm.

from the present results. When comparing this value to the upper limit of the EDM in paramagnetic atoms set in the past by the Amherst (Cs) (Murthy et al. 1989) and Berkeley (T1) (Commins et al. 1994) teams Ad(laacs) < 9.10 .24 and Ad(2°STl) < 2 . 1 0 -24 ecru we see that our present apparatus is already quite competitive. We stress once more that there are several realistic possibilities to further increase the sensitivity. Besides the above mentioned reduction of the magnetic noise, the signal can be further enhanced by optimization of the fluorescence detection system. We anticipate that an improvement by one to two orders of magnitude seems to be quite realistic. Systematic effects. Tile statistical considerations presented above were based on the assumption that the EDM experiment can be carried out in an electric field of 100 k V / c m . So far we have not tried to apply any electric field to our samples. While condensed He is known to hold electric fields in excess of 100 kV/cm the question whether this is also true for our doped He samples remains open and will definitely require an experimental answer. Several systematic effects that can mimic an EDM have to be considered. Any effect which has the same signature as an EDM (as e.g reversal of sign under a reversal of E) will contribute to the systematics, but may be suppressed by using further reversals of system parameters, such as the magnetic field or the handedness of the pumping light. Motional fields. Compared to beam experiments EDM experiments on trapped species offer the great advantage that sytematic effects arising from the motional magnetic field seen by atoms moving through tile electric field are absent.

72

Can Atoms Trapped in Solid Helium Be Used ... ?

hnperfect field reversal. EDM's are inferred from a change of the Larmor precession frequency under a reversal of the electric field.: A change A E of the field magnitude upon reversal mimics an EDM. For an ultimate limit of Ad = 10--95e em the maximum tolerable value is A E = Adios(~) = 1 m V / c m , where a(2) is the static electric tensor polarizability of the ground state, which, for S-states arises only in third order of perturbation. The T1 EDM experiments have shown that this effect can be dealt with (Commins 1994). Leakage currents. Leakage currents between the field electrodes produce magnetic fields, which may affect the spin precession. As these fields reverse with the plate voltage, they can also mimic an EDM. As we have no experience with electric fields yet we cannot make a quantitative statement about this effect at present. Gravitational effect. The atom is held within the He bubble by its electron cloud. Due to gravity the nucleus of the atom will therefore be displaced from the center of mass of the electron cloud, and thus give rise to an atomic electric dipole m o m e n t dgravity whose magnitude can be estimated by

dg,.~,ity= ( S ez S} = 2M~tomge ](PIzIS)I2 E, - Ep If we consider only the admixture of the closest P state we obtain for Cs dg .... ity ~ 2. lO-~3ecm. This value is approximately two orders of magnitude larger than the ultimately sought sensitivity to EDM's. It will therefore put severe constraints on the control of the electric field orientation. On the other hand the gravity induced dipole moment is ideally suited to test our apparatus, as it has a well known orientation and is of a magnitude which can already be accessed with our present sensitivity. Matrix effects. We remind that in the pressure and temperature range of our experiments solid helium has two crystalline structures (Fig.2): an isotropic body cubic-centered (b.c.c.) phase and an anisotropic uniaxial hexagonal close-packed (h.c.p.) phase. In the h.c.p, matrix the lattice constants are in the ratio of 1.6:1. An interesting question, not addressed so far by theorists, is whether the Pauli repulsion between implanted atom and the He matrix is strong enough for the atom to impose a spherical shape on the bubble, or whether the bubble shape is influenced by the anisotropy of the matrix far from the local trapping site. We have several experimental evidences that the bubbles in h.c.p, are indeed deformed. On one hand we have observed (in h.c.p.) A M F = 2, 3 forbidden magnetic resonance lines which indicate a breakdown of the cylindrical s y m m e t r y imposed by the magnetic field and thus evidence the existence of all additional local axis. Further evidence is that the spin relaxation times are two to three orders of magnitude smaller than in b.c.c, which again may be explained by a

Atoms in Solid 4He

73

'?

",:-.:-"::..::......

i':-:

Fig. 9. Electric dipole moment induced by gravity.

spin coupling to local fields. The strongest evidence is our recent observation of magnetic resonances in zero magnetic field, which we attribute to a quadrupolar splitting of the hyperfine Zeeman sublevels due to the interaction of the nuclear electric quadrupole moment with electric field gradients present in deformed bubbles. The analysis of these effects is still in progress and should allow to infer from the quadrupole splitting the strength of the field gradients and, together with model calculations, to determine the size of the bubble deformation. First estimates show that the deformations are small compared to the bubble size. The complete absence of all the effects discussed here in the b.c.c, phase should allow us in the future to ascertain with very high accuracy the degree of sphericity of the bubbles in that phase.

Summary In this paper we have reviewed tile information gained in the past three years in a novel approach to high resolution spin physics in matrix-isolated atoms. We hope to have convinced the reader that these samples - besides being interesting by themselves - have very promising applications in view of an experiment testing fundamental symmetries. To the best of our knowledge our laboratory has remained so far the only one investigating foreign atoms in solid lie matrices. We do hope that in future more researchers will be attracted by these most f~scinating novel samples.

74

Can Atoms Trapped in Solid Helium Be Used ... ?

Acknowledgement s The authors acknowledge the contributions of M. Arndt, who, during his Ph.D. work has set up the low-temperature lab at MPQ and who was in charge of all the experiments in the early stage of the project. We also thank R. Dziewior, S. Liicke, and S.B. Ross who have provided valuable contributions at different stages of the experiments reported above.

References Arndt M., Kanorsky S.I., Weis A., and Hansch T.W. (1993): Can Paramagnetic Atoms in Superfluid Helium be Used to Search for Permanent Electric Dipole Moments?, Phys.Lett. A174, 298 Arndt M., Kanorsky S.I., Weis A., and Haensch T.W. (1995a): Implantation of Metal Atoms into Solid Helium, Z.Phys. B98, 377 M. Arndt, S.I. Knnorsky, A. Weis, and T.W. Haensch (1995b): Long Electronic Spin Relaxation Times of Cs Atoms in solid 4 He, Phys.Rev.Lett. 74, 1359 Burr S. (1993): A Review of CP Violation in Atoms, Int.J.Mod.Phys. A8, 209 Barr S. (1994): Atomic Electric Dipole Moments and CP Violation, in XXIXth Rencontres de Morion& (Editions Frontieres) Bauer H., Beau M., Friedl B., Marchand C., Miltner K. and Reitner H.J. (1990): Laser Spectroscopy of Alkaline Earth Atoms in HeII, Phys. Lett. A146, 134 Bernreuther W. and Suzuki M. (1991): The Electric Dipole Moment of the Electron, Rev.Mod.Phys. 63, 313 Bouchiat M.A. and Bouchiat C.C. (1974): Weak Neutral Currents in Atomic Physics, Phys.Lett. 48B, 111 Bouchiat M.A. (1991): Atomic Parity Violation, a Low Energy Test of the Electroweak Standard Model, in it Atomic Physics 12 ed. by R.R. Levis and J.C. Zorn, p 399 Commins E.D., Ross S.B., DeMille D., and Regan B.C. (1994): Improved Experimental Limit on the Electric Dipole Moment of the Electron, Phys.Rev.A50, 2960 Fujisaki A., Sano K., Kinoshita T., Takahashi Y., and Yabuzaki T. (1993): Implantation of neutral atoms into liquid helium by laser sputtering, Phys.Rev.Lett. 71, 1039 Kanorsky S.I., Arndt M., Dziewior R., Weis A., and H~inseh T.W. (1994a): Pressure Shift and Broadening of the Resonance Line of Barium Atoms Trapped in Liquid Helium, Phys.Rev.B 50, 6296 Kanorsky S.I., Arndt M., Dziewior R., Weis A., and H/insch T.W. (1994b): Optical Spectroscopy of Atoms Trapped in Solid Helium, Phys.Rev.B49, 3645 Kanorsky S. and Weis A. (1996): Atoms in Nano-Cavities, Les Houches Summer School Quantum Optics of Confined Systems, (Kluver). Moriond (1994): see various contributions in XXIXth Rencontres de Moriond, (Editions Frontieres } Murthy S.A., Nrause D., Li Z.L., and Hunter L.R. (1989): New Limits on the Electron Electric Dipole Moment from Cesium, Phys.Rev.Lett. 63,965 Purcell E.M. and Ramsey N.F. (1950): On the Possibility of Electric Dipole Moments for Elementary Particles and Nuclei, Phys.Rev. 78,807 Ramsey N.F. (1994): Electric Dipole Tests of Time Reversal Symmetry, in Atomic Physics 14, ed. by D.J. Wineland, C.E. Wieman, and S.J. Smith, pp 3-17 Reyher M.J., Bauer H., Huber C., Mayer R., SchMer A., and Winnacker A. (1986): Spectroscopy of Barium Ions in [IeII, Phys.Lett. A l l S , 238

References

75

Sandars P.G.H. (1966): Enhancement Factor for the Electric Dipole Moment of the Valence Electron in an Alkali Atom, Phys.Lett. 22, 290 Schiff L.I. (1963): Measurability of Nuclear Electric Dipole Moments, Phys.Rev. 132, 2194 Smith K.F. et al. (1990): A Search for the Electric Dipole Moment of the Neutron, Phys.Lett. B234, 191 Tabbert B. et al. (1995): Atoms and Ions in s~tperfluid helium. L Optical spectra of atomic and ionic impurities, Z.Phys. B97, 425 Weis A., Kanors.ky S.I., Arndt M., and H£nsch T.W. (1995): Spin Physics in Solid Helium: Experimental Results and Applications, Z.Phys. B98, 359

g-Factors of S u b a t o m i c Particles B. Lee Roberts Department of Physics, Boston University, Boston, MA 02215, U.S.A.

1

Introduction

The measurements of magnetic moments of subatomic particles have provided fundamental information about particle structure, as well as information on the nature of the underlying theories of QED and QCD. While all of the stable spin ½ particles have anomalous magnetic moments, i.e. their g-factors are not exactly equal to 2, only the electron and muon appear to be pointlike. The anomalous moments of these two leptons are dominated by the lowest order radiative correction 2-'~, which is a small correction to the Dirac moment of 1. The proton, neutron and other baryons have large anomalous moments, which we have come to realize are related to their internal structure. Classical electromagnetic theory predicts that a magnetic dipole moment will be produced by a current loop. If the current is caused by a charged particle such as an electron orbiting about a nucleus, the dipole moment tL can be related to the angular momentum L through e_L_L .

/~ ----gl 2m

(1)

The proportionality constant gl, which is called the "gyromagnetic ratio", is the ratio of the magnetic moment to the angular m o m e n t u m and is equal to unity for an orbital angular momentum. For an intrinsic spin angular momentum, where we assume that the magnetic moment is proportional to the spin, 1 the moment is given by ~,, = g , ( ~ ) S

.

(2)

The g-factor for the electron was first measured in 1922 by Stern and Gerlach [1, 2] with a beam of silver atoms. In 1927 Phipps and Taylor [3] used the Stern-Gerlach technique on hydrogen, and clearly demonstrated that the effect was a result of the spin of the electron, and not an atomic effect. The value of g determined from these experiments was consistent with g -- 2. The relativistic Dirac formalism [4] of 1928 predicted that g is exactly 2. Since the g-factor need not be exactly 2, one can write g as the sum of two parts, g = g0 + gl (3) 1 The subscript on g, is almost always omitted.

78

B. Lee Roberts

where 90 = 2 is the Dirac value, and gl represents a correction/addition to the simplest theory. In terms of the 9 factors, the magnetic m o m e n t can be written as

(go + g~) eh P -

2

2m

(4)

where m is the particle's mass. For a positive particle, this is written as eh p = ( 1 + a) 2m

(5)

where the first term is called the Dirac m o m e n t and the second is the Pauli or anomalous moment. The first term is the charge in units of the electron charge, (q/e = -l-l, 0), and the Pauli m o m e n t can be written as a = (

) -=- ~- .

(6)

The quantity (eh/2m) is called a magneton; (eh/2rne) = liB is called the Bohr magneton, and (eh/2mp) = ]2u is called the nuclear magneton. Baryon magnetic moments are usually quoted in nuclear magnetons. In addition to these two magnetons, the Particle D a t a Tables [5] also use the muon magneton (eh/2mu). The first indication that g might not be exactly equM to two came from the proton, not the electron. In 1933, well in advance of the discovery of an anomalous 9 factor for the electron, O. Stern and co-workers [6] showed that the proton had a magnetic m o m e n t of (2.5 -4- 10%) PN, which we now know to be 2.79284739(6)/~N [5]. Thus 9p = 5.58 rather than the expected value of 2. Stern et al. also measured the deuteron m o m e n t , Pd : 0 . 8 , which suggested to some people that perhaps the neutron m o m e n t p,~ was ~ --2/2N. In 1940 L. Alvarez and F. Bloch [7] showed that the neutron had a magnetic m o m e n t of (-1.935 =t=0.02)#N rather than zero, which might have been expected naively. In the conclusion to their paper they say: "The fact alone t h a t pp differs from unity and pn differs from zero indicates that, unlike the electron, these particles are not sufficiently described by the relativistic wave equation of Dirac and that other causes underly their magnetic properties." [7]. These large anomalous m o m e n t s remained inexplicable until the 1970s. While it must have become clear that these anomalies could result from internal structure of the proton and neutron, a quantitative calculation was impossible. As late as 1967 in a discussion about the Schwinger term (see below) and the large proton anomaly, J.J. Sakurai states "However, if we consider these particles are complicated objects surrounded by virtual meson clouds, the failure of the simple prescription does not seem surprising." [8]. Even with the development of unitary s y m m e t r y [9] in 1961 which made it possible to derive relationships among the magnetic m o m e n t s of the baryon

g-Factors of Subatomic Particles

79

Fig. 1. The lowest order radiative correction to g.

octet [10], it was not clear if quarks were genuine constituents, or simply convenient mathematical devices. Only in 1969, with the deep inelastic e - p scattering experiments at SLAC [11] did the community begin to take the quark-parton model seriously. We now know that hadrons are made of quarks, and these large anomalous moments are the result of the internal quark structure of the proton and neutron. One of the early successes of the SU(6) model was the prediction that tLp /~n

_

3 2

(7)

which is experimentally found to be -1.460. In the next section we return to the topic of hyperon moments. In 1948 Kush and Foley [12] showed that g of the electron was not exactly 2, but was g~ : 2(1.001 19 ~ 0.000 05) . (8)

This difference from two was explained by the lowest order radiative correction (Fig. 1) to go, which was first calculated by Schwinger [13]. He obtained gl-

~r

-- 2(0.001 16...) ,

(9)

where a is the fine-structure constant, in excellent agreement with experiment. This correction is now usually couched in terms of Feynman diagrams, and the Schwinger term is represented by the diagram in Fig. 1. Schwinger's calculation represented one of the first in the new field of quantum electrodynamics, which has now become a calculational industry. The QED calculations of gl of the electron have now been carried out to tenth-order by Kinoshita [14]. When the electron g-factor was measured by Kush and Foley, the value was determined to be slightly greater than 2. The electron anomalous moment is now measured to an experimental accuracy of a few parts per billion [15], and is well described by quantum electrodynamics calculation [14]. To the

80

B. Lee Roberts

level of measurement, only photons and electrons contribute, and gl ~- 1 × 10 -3. There is no evidence to date, both from g-factor measurements or e+e scattering, to indicate that the electron has any internal structure. To conclude this section, we briefly describe two phenomena which have been exploited in the measurement of magnetic moments: precession in a magnetic field, and fine-structure splitting in atomic energy levels. If a magnetic dipole with dipole moment/~ is placed in a magnetic field, it will experience a torque "r=~xB . (10) This fact has been exploited in the measurement of most magnetic moments. We detail how it permitted measurement of hyperon g-factors. The magnetic moment is along the spin direction, and will precess in a magnetic field. One starts with a polarized beam of hyperons which is injected into a magnetic field. After the region of magnetic field, hyperon decays are observed. For these two-body weak decays, the distribution of the decay baryons relative to the hyperon spin is given (in the CM frame) by (1 + a P c o s O )

,

(11)

where P is the beam polarization and a is the decay asymmetry parameter. From the distribution of decay products one can tell how far the spin has precessed. The magnetic moment manifests itself in atomic spectra through finestructure splitting. In the simplest picture of the hydrogen atom, the atomic electron sees a proton orbiting about it which produces a magnetic field like a current loop. The magnetic moment of the electron interacts with this magnetic field with the interaction energy

Hint : -/~ " B .

2

2.1

(12)

E x o t i c A t o m M e a s u r e m e n t s of t h e ~ and ~ g-Factors Exotic Atoms

Hydrogen-like atoms with a single p - or 7r- captured into atomic states were postulated in 1947 [16], in response to the experiments of Conversi Pancini and Piccioni [17]. The first clear observations of x rays from such an atom was made by Camac, McGuire, Platt and Schulte with a beam of zr- from the Rochester cyclotron [18]. The first detailed study of x-rays from muonic atoms was carried out by Fitch and Rainwater at the Nevis cyclotron [19]. By the late 1960s,/3 and K - atoms had been observed and studied also. The principle is simple. A beam of the negative particles from an accelerator is degraded in energy and brought to rest in a target. When a negative particle slows down to roughly the velocity of the outer atomic electrons, it

g-Factors of Subatomic Particles

81

is captured into a high atomic level with principal quantum number given by n ,., X / ~ / m ~ . It then cascades towards the atomic Is state, first by Auger emission, and then by radiative transitions. Experimentally, one looks for x rays in coincidence with a stopped beam particle. Since the 1960s, most such experiments have used solid-state Ge(Li) photon detectors, which typically have a (FWHM) resolution - ~ ,-~ 7 x 10 -3 in the energy range 100 to 700 keV, and absolute photopeak efficiency of 10 - 20%. More recently, bent crystal spectrometers, which have even better resolution, have been employed to study low-Z pionic, muonic and kaonic atoms. Since the Bohr radius of this exotic atomic system n2

r,~ -

(13)

mZa

depends inversely on the orbiting particle's reduced mass, the heavy negative particle is soon inside of the cloud of atomic electrons and the modification of the Coulomb potential of the nucleus by these electrons becomes a very small correction. This system is very close to a hydrogen-like atom. For nuclei heavier than He, the orbiting particle can have a substantial overlap with the nucleus. The cascades of ~'-, K - and i5 atoms with nuclear charge Z > 2 are observed to terminate before the K~ x ray is observed. If one calculates the fine-structure splitting for a hydrogen-like atom of nuclear charge + Z e , and includes a Pauli moment term, the energy splitting is given by [2(1] • (ZoO 4 m (14)

A E n ' t = ( 2 +gl) ~n3

e(e+l)

where n is the principal quantum number and ~ is the orbital angular momentum. This calculation is done in the "Pauli approximation" and is accurate up to (and including) terms of relative order (f~/c) 2, where ~ is the expectation value of the electron velocity. 2 The total angular m o m e n t u m is J = L + S, and the total angular mo1 For (g0/2 + gl) < 0 the state with mentum quantum number is j = ~ + ~. highest total angular momentum j lies highest in energy. The difference in weighting between the two terms in Eq. 14, (go + 291), arises from the famous factor of two from Thomas precession [21], which subtracts off an amount from the fine-structure splitting which is exactly half that expected from the Dirac moment term. This fine structure splitting should be compared with the Bohr energy m(Z~)2 n2

En -=- -

(15)

For g = n - 1, n >_ 2, the splitting relative to the total energy is AE,,,_I

(Za) 2 _~

En

(16)

2n2(u - 1)

2 The mean velocity O/c is approximately Zc~/n.

82

B. Lee Roberts

(9,8)

/ /

fi2, i0

TM

(-}

t

Fig. 2. A portion of the atomic cascade. The energy separations are not to scale. In the blow up, the fine-structure states are labelled + for j = g + ½, - for j = g - !2 ~ and the Dirac and Pauli moments are both assumed to be negative.

where the Pauli m o m e n t contribution has been neglected. For the 2p state of h y d r o g e n this ratio is 6.6 × 10 -6. T h e basic features of the a t o m i c cascade are given in Fig. 2. T h e population of the circular (those with ~ = n - 1) energy states tends to become enhanced over the statistical 2 l + 1 weighting as the cascade proceeds towards lower q u a n t u m states. T h e circular transitions, i.e. those between circular states, tend to d o m i n a t e the experimental spectrum. This can be understood by considering the three E1 transitions shown in Fig. 2 which are labelled c~, /~ and 7, where a is the circular transition. T h e radiative transition probability depends on ~3 times the dipole m a t r i x element. T h u s the A n = --2 transition labelled fl is preferred over the "noncircular" A n = - 1 transition labelled 7A s s u m i n g a statistical p o p u l a t i o n of the fine-structure states, the spin flip transition b can be shown to be weak for transitions between two adjacent levels of large principal q u a n t u m n u m b e r [22]. T h e intensity ratio for the three c o m p o n e n t s of a circular transition (i.e. from (n, ~) = (n -4- 1, n) -+ (n, n - 1)) is given by a : b : c = 2n 2 + n -

1 : 1 : 2n 2 - n -

1

(17)

where n is the principal q u a n t u m n u m b e r of the lower state. For n = 10 this ratio is 209 : 1 : 189, where we assume t h a t the state of highest j lies highest. If the a n o m a l o u s m o m e n t were the opposite sign to the Dirac m o m e n t , these two c o m p o n e n t s could reverse in energy (see Eq. 14). Experimentally one

g-Factors of Subatomic Particles

83

would observe two x-ray lines separated in energy by an amount equal to the difference in fine-structure splitting of the upper and lower states.

2.2

Measuring g-Factors with Exotic Atoms

The first measurements of the hyperon magnetic moments were carried out at the Brookhaven AGS and the CERN PS in the late 60s and early 70s. Since the hyperon energies were low, as was the average polarization, these experiments were quite difficult, and did not yield precise measurements. Furthermore, the magnetic moment of the S - , which has a decay asymmetry parameter (cr = -0.068 + 0.008), see Eq. 11, was impossible to measure using these low energy beams. The development of constituent quark models motivated by QCD [2329] permitted theorists to make definite predictions for the moments of the baryons in the SU(3) flavor octet, usually with the proton moment as input to the calculation. Thus in the mid 1970s, the measurement of hyperon magnetic moments became an important testing ground for these models of the quark structure of the baryons. Motivated by the desire to measure the Z - moment, a group working at the Brookhaven AGS developed a new technique for measuring the magnetic moments of the antiproton (p) and ,U-. Since the traditional precession technique did not work for either of these particles (the p does not decay) the exotic atom technique was invented. From Eq. 14 we can see that the x-ray lines observed from # - , p and Z'- will exhibit fine-structure splitting and one can measure the magnetic moment by measuring this splitting. In practice, this technique is useful only for particles with a large anomalous moment, which excludes a precision measurement of the muon moment by this technique. Since the fine-structure splitting goes as ( Z a ) 4 n -5, one wishes to look at the lowest transition not affected by the strong interaction, and in the highestZ target possible. One must choose targets with no static quadrupole moment, i.e. nuclear spin 0 or ½, to eliminate hyperfine structure which would interfere with a measurement of the fine-structure. Even with high-Z nuclei, the finestructure splitting is almost never experimentally resolved, so one has to be very careful to measure the detector resolution and lineshape independently under the same conditions as the data are collected. A deformed nucleus such as 238U, which does not have a static quadrupole moment, can still cause dynamic E2 effects [30]. While the total centroid for the/3 energy levels is shifted, the individual fine-structure components are shifted together to within 8 eV, which was negligible and could be included as a small correction in the analysis. The experimental resolution is such that except for the/5(n = 11 --+ n = 10) transition in uranium, which is shown below, the two components are not well resolved. On the other hand, since the shape and intensities of the two components are known, the chi-square of a fit with no splitting is larger than

84

B. Lee Roberts

I DiracOnly 12.5

(10,9,+)

(,o,s,+)

(

8 '°.°t-

N .~ 5 . 0 -

All Corrections

~ 2.5 0.0

Pauli Moment

-

(Q)

(b)

(c)

Fig. 3. Relative positions of the energy levels of the Pb ,U-(n = t0,~ = 9) and (n = 10, g = 8) states. The states are labelled by (n,e,:J=) where

1 (a) shows the pure Dirac levels, the -4- gives the total j = £ 4- ~. (b) shows the inclusion of all corrections except the anomalous moment, and (c)

shows the fully corrected levels assuming that p ( E - ) = -1.11PN

the m i n i m u m value, which occurs at some finite splitting, by as much as 100 for combined d a t a sets. For small subsets it is larger by at least 10 units as will be shown below. To determine the intensities of the non-circular transitions relative to the circular ones, it is necessary to carry out a simulation of the exotic a t o m cascade [31]. Since the An = - 2 transitions are experimentally observed, their observed intensities relative to the An = - 1 transitions can be reproduced by the cascade calculation by adjusting the initial population and the strong interaction parameters. In addition to the Pauli m o m e n t term, other corrections such as vacuum polarization [32], nuclear polarization [33] and electron screening [34], were included by integrating the Dirac equation [35]. In Fig. 3 we show the effect of these corrections to the Dirac energy levels for S - Pb. Note that the degeneracy of states with the same total angular m o m e n t u m is lifted by the inclusion of these corrections. It has been pointed out that the g-factor of a bound particle is decreased relative to its free value [36]. This effect has been demonstrated [37] to be considerable for a p - bound in the l s level of a high-Z muonic atom. In the experiments discussed below, the lowest principal q u a n t u m state considered was the n = 10 state, where the effect was estimated to be smaller than 0.1% and was neglected. The first magnetic m o m e n t measured with this technique was the p moment measurement carried out at the Brookhaven AGS in the s u m m e r of 1972

g-Factors of Subatomic Particles

85

300

o~ I-- 2 0 0 o o

I00

0~

I

366

I

I

:570

I

I

374

ENERGY (keV)

Fig.4. The/5(n = 11 ~ n --- 10) transition in depleted U. The two fine-structure components can clearly be seen. The non-circular contribution to this transition is negligible.

[38]. In Fig. 4 the #(n = 11 -+ n = 10) transition is shown for a depleted uranium target. For this transition the non-circular intensity is negligible. The solid curve through the d a t a is a free fit of two Gaussians plus background to the data. The measured fine-structure splitting is consistent with a magnetic m o m e n t of p(p) = -2.79, the value expected from the C P T theorem which requires particles and antiparticles to have magnetic m o m e n t s with the same magnitude but opposite in sign. The intensity ratio obtained from the fit is consistent with the expected ratio of 209 : 189. The combined # m o m e n t obtained from the two early experiments [38, 39] was p(#) = (--2.795+0.018)#N. The current value of the 15 magnetic m o m e n t is dominated by an experiment [40] which utilized the unique capabilities of the L E A R facility at CERN to measure the fine-structure splitting in the /5(11 --+ 10) transition in Pb. T h a t experiment obtained the result (-2.800 + 0.0090)pg. While the value of the # m o m e n t is firmly predicted by the C P T theorem, the ~ - m o m e n t was scarcely predicted at all when this technique was developed. Since the Z - lifetime is too short to produce a b e a m and bring it to rest, it was necessary to use a stopped K - beam to produce hyperons through the reaction K - + N -+ ,U- + rr, where N is a nucleon in the target nucleus. Although weak ~ - x rays had been observed in the spectra from low-Z kaonic atoms, Z - x rays had never been seen in high-Z atoms, which would be necessary to measure the magnetic m o m e n t . The first observation of ~ - x rays from high-Z atoms was reported at Brookhaven in 1973 [41] where a limit was placed on the magnetic m o m e n t . With more data, it was possible to measure a value for the magnetic m o m e n t [42], which

86

B. Lee Roberts

7°°0 F

,

6°°° I-

t

=+

soool-f

+

T

f

4oo01.- l I

=

~

|r,

® t

°u .... r, lljL. 1000 -

T+°+ i + ++-

h

~~,~

0~

100

"+

~

t

_~

t

£

I

I

200

300

400

,500

600

ENERGY ( keY} Fig. 5. The x-ray spectrum from kaons stopping in a laminar W target.

was p(~U-) = ( - 1 . 4 8 + 0.37)#N. A similar result was obtained in a second experiment by a Columbia-Yale collaboration [43]. A follow-up experiment at Brookhaven (E723) used a laminar target with sheets of Pb or W placed in a liquid hydrogen bath. A K - beam was stopped in this target, and the reaction K-

+ p -4 ~-

+ ~r+

B . R . = 46%

(18)

was used to produce Z - in the target. The monoenergetic 7r+ was stopped in a range telescope and the 7r+ -4 p+ -4 e + decay chain was observed to tag 2 - production. The x-ray spectrum in coincidence with stopped K - is shown in Fig. 5, and the tagged spectrum is shown in Fig. 6. The Z - (11 -4 10) transition in W is shown in Fig. 7. The tagging improves the 2 - x-ray signalto-noise by a factor of 20 to 30 over the first experiments. To combine all the data, the maps of ~2 vs. fine-structure splitting for the two targets and three detectors were added together. The resulting map showed a one standard deviation preference for the negative sign. The final result [44] was p ( ~ - ) = (-1.105 ± 0.029 + 0.010)#N, where the first error is statistical and the second systematic. Of course, the biggest difference between the first and second generation experiments is signal-to-noise, whose importance cannot be underestimated in such a difficult measurement. With the discovery of polarization in the hyperon beam at Fermilab [45], it became possible to perform precision magnetic moment measurements there, and eventually the S - moment was measured by the precession technique in the same time frame as E723. The current world average [5] is # ( S - ) = (-1.160-t-0.025)pN. The difficulty of this particular measurement is reflected in the fact that the world average includes a scaling up of the combined error

g-Factors of Subatomic Particles

87

200

IZ :::)

0

loo

T

50

,

r

1

-

g

~, t

t

I

i

100

200

300

400

riO(

700

ENERGY(keY) F i g . 6. The tagged spectrum from kaons stopping in a laminar W target.

by a scale factor of 1.7, since the three most precise experiments (E723 and the two most recent Fermilab experiments) do not agree well with each other. All of the hyperon magnetic moments have now been measured well [5]. The models have been further refined. While a specific calculation may come closer to predicting one of the magnetic moments better than the other calculations, the proper test is to look at how one model predicts the whole set. With that criterion, the agreement is only at the 10% level.

3

A N e w E x p e r i m e n t to M e a s u r e t h e M u o n g - F a c t o r

For the muon and electron, the strong interaction contribution to the magnetic moment is very small. The QED calculations of their anomalous moments represent a calculationat tour de force. While the g-factor of the electron has provided a testing ground for QED, the anomalous magnetic moment of the muon has provided an even richer source of information. The muon's mass of 105.7 MeV is quite large compared to the electron's mass of 0.511 MeV, and heavier virtual particles can contribute in a measurable way to its anomalous moment. The relative contribution from heavier particles to the muon anomaly scales as (m~/m~) ~, and in a series of three elegant experiments [46-48] virtual muons and quarks (pions) have been shown to contribute at measurable levels. The current experimental accuracy is not sufficient to observe the W and Z ° gauge boson contributions. At present there is good agreement between experiment and theory [49], and there is no indication of any substructure to the muon.

88

B. Lee Roberts

:1 5ot 160.

°:

150. 140

10

130

-z

.t5

-i

0

-o.s

6.s

i

3O4

1.5

3O6

~{£'1 (Nuclear Magnetons}

(a)

(b)

Fig. 7. (a) A X2 map from a fit to a tagged sample of the W - S - ( 1 1 --+ 10) transition. There are 116 degrees of freedom. (b) The best fit to the observed S transition, corresponding to the X2 minimum. Both the circular and noncircular fine-structure doublets are shown separately. This figure contains ,-- 7% of the total data taken.

Unlike the short lived hyperons, the muon's long lifetime permits a b e a m to be stored in a storage ring, and the spin rotation frequency can be measured. While the decay #+ --4 e+~,ue is a three-body decay, the highest energy positrons go along the electron spin direction, and the parity violation in the weak decay permits one to determine the direction of the spin vector. A charged particle moving in a uniform magnetic field will execute cyclotron motion with the orbital cyclotron frequency we =

eB

(19)

m7

The spin precession frequency in a magnetic field is given by ~

=

geB 2m

eB + (1 - ~ / ) - m"/

,

(20)

with the Larmor and T h o m a s precession terms explicitly separated. Thus the spin vector of a charged particle moving in a uniform magnetic field will precess, relative to the m o m e n t u m vector, with a frequency wa, which is given by the difference between the orbital cyclotron frequency wc and the spin precession frequency we. ~za :

~v~ - w~ :

e

--aB

(21)

m

is directly proportional to the anomalous m o m e n t and independent of the particle's m o m e n t u m . For particles with a Pauli m o m e n t of the same sign

g-Factors of Subatomic Particles

89

as the Dirac moment, the spin vector will lead the m o m e n t u m vector. Experimentally one measures the precession frequency of a particle's spin in a known magnetic field, and determines the magnetic moment. In a real experiment, the field B in Eq. 21 is the average field seen by the ensemble of muons in the storage ring. Vertical focussing must be provided to keep the muon beam stored, which can be accomplished with magnetic multipoles, or with an electrostatic quadrupole field. However, if magnetic multipoles are used, it is difficult to know the average B field to the accuracy needed for a precision measurement of a~. In a region in which both magnetic and electric fields are present, the relativistic formula for the precession is given by [50]

~oa-

dOR _ e dt ~n

[ (') a,B-

a,

72-

1

/3xE

1

'

(22)

where OR = (s,/3) is the angle between the muon spin direction in its rest frame and the muon velocity direction in the laboratory frame. The other quantities refer to the laboratory frame. If the muon beam has the "magic" value of 3' = 29.3, the electric field does not change the relative orientation between the spin and momentum vectors. Thus the precession of the spin relative to the momentum is determined entirely by the magnetic field, and one can use electrostatic quadrupoles for vertical focussing. The magnetic field can be a pure dipole field and can be determined very accurately. This technique was used in the third CERN experiment [48] and will be used in the new experiment at Brookhaven. The famous CERN experiments measured # = 1.001 165 9230 (85) ( e h / 2 r n u ) , a precision of -t-7.3 parts per million (ppm) for a~. While this result tested QED to a high level, and showed for the first time the contribution of virtual hadrons to the magnetic moment of a lepton, this sensitivity was not sufficient to observe the contribution of the W and Z ° gauge bosons. A new experiment [51], is being constructed to measure ( 9 - 2 ) of the muon to better than =k0.35 ppm in order to measure the electroweak contribution to ( 9 - 2). The first data collection run will take place in 1997. This experiment has been described in some detail elsewhere [52, 53], and only a few comments will be made here. The goal of the experiment is to verify the standard model prediction, and to search for physics beyond the standard model. The theoretical value of a u consists of contributions from QED [49], virtual hadrons [54, 55], and virtual electroweak gauge bosons [56-58]. Taking the value of (~ from the electron (9 - 2) experiment [59], the total QED contribution is a QED = 116 584 706(2) × 10 -11. The QED part is calculated to a precision of a few parts per billion, and the agreement between the calculated and measured (g - 2) values for the electron gives us great confidence ill the QED calculation. The hadronic correction cannot be calculated from first principles but can be calculated using dispersion theory and data from e+e - --4 hadrons.

90

B. Lee Roberts

The total hadronic contribution is tL# _Had . ~ 6882(154) x 10 -11. The two recent evaluations [54, 55] agree that the current error on this contribution is ~ 5=1.3 ppm. The latter authors estimate that this error can be reduced to (,-~ 5=59 x 10 -11) or ,.o +0.5 p p m after CMD2, the new Novosibirsk experiment, has finished the analysis of their data. To further reduce this theoretical error, additional e+e - d a t a from x/~ = 1.4 GeV (the m a x i m u m energy for CMD2) to above the J / ¢ threshold will be needed, or perhaps theoretical calculations in this energy region can further reduce this error [60]. The theoretical limit seems to be set by the contribution from hadronic "light by light" scattering [61], aHad(lbl) = --52 (18) × 10 -11, which has an uncertainty of 5=0.15 ppm. This contribution cannot be estimated from data, but might be improved by a lattice QCD calculation. While the single W and Z loop calculations have been available for some time [56], recent higher order calculations which include both fermionic [57] and bosonic [58] two-loop contributions, obtain a higher order contribution which turns out to be surprisingly large. The first order weak contribution of 195(4) x 10 - i t is reduced to 151(4) x 10 -11 (1.3 p p m of au) when the second order terms are included. Since the ability to calculate loop diagrams is intimately tied to the renormalizeability of the theory, this measurement will provide an important test of the renormalization prescription. = 116 591 739 (154) ×10 -11 The total theoretical prediction is a Th~orv u where the theoretical error of 5=1.3 p p m is dominated by the uncertainty on the hadronic vacuum polarization. Since (g - 2)u is very sensitive to W and p substructure, as well as supers y m m e t r y in the mass region below 130 GeV or any SUSY model with large tan/3, a result which agrees with the standard model will place significant new limits on physics beyond the standard model [52, 62]. The experimental goal is nominally stated as a precision of +0.35 ppm, a factor of twenty better than the C E R N experiment. With the option of direct muon injection into the ring, which requires a full aperture kicker to store the muon beam, one m a y be able to do much better. If the estimates of the incident muon flux and capture efficiency into the storage ring for direct muon injection are correct, then the final result for a t could reach a statistical sensitivity of 5=0.12 p p m at the end of the d a t a collection. This statistical error of 5=0.12 p p m happens to be equal to the current estimate of the experimental systematic errors, and the collaboration is studying ways of reducing systematics further. While this statistical error would represent a ten standard deviation measurement of the electroweak contribution, the uncertainty in the current evaluation of the hadronic contribution is much larger, and will need to be improved to realize the full potential of the final experimental result.

g-Factors of Subatomic Particles

4

91

Conclusions

The anomalous g-factors of the muon and electron have played an i m p o r t a n t role in the development of QED, and in our understanding of the nature of these leptons. The current precision of the electron anomaly makes it one of the most precisely measured quantities in nature, and one could argue that QED is so well understood that this measurement can be used to provide the best measurement of the fine-structure constant. The muon g-factor has measurable contributions from virtual hadrons, and soon we hope to measure the W and Z ° gauge boson contributions. This new measurement also opens a window for the discovery of new physics beyond the standard model. For a full interpretation of this experiment, additional data, and calculations, will be needed to permit a more precise evaluation of the hadronic vacuum polarization contribution to a , . Baryon magnetic m o m e n t s is another subject altogether. Because of the difficulties of calculating low energy phenomena in QCD, it is necessary to resort to QCD inspired phenomenological models, which describe the situation to about 10%, decades away from the spectacular agreement between theory and experiment for the leptons. Nevertheless, when the constituent quark models were being developed in the 70s, hyperon magnetic m o m e n t s played an important role in testing their validity. Perhaps some day, computing power will increase to the point where lattice calculations of the static baryon properties can reach an accuracy which would permit a meaningful comparison with experiment. Acknowledgement. I have learned much about exotic atoms from the collaborators listed in the references, especially M. Eckhause, J. Miller, and It. Welsh, as well as from C.3. Batty, M. Blecher and M. Leon who are not listed. The early exotic atom work described here was done in friendly and beneficial competition with C.S. Wu and her collaborators. I am grateful to K. Johnson and S. Glashow for interesting discussions on magnetic moments and baryon structure. T. Kinoshita and W. Mareiano have been invaluable resources on the theory of the muon g-factor. I wish to thank D.W. Hertzog and Y.K. Semertzidis for their helpful comments on this manuscript.

References [1] O. Stern, Z. Phys. 7 (1921) 18. [2] W. Gerlach and O. Stern, Z. Phys. 8 (1922) 110, Z. Phys. 9 (1922) 349, Z. Phys. 9 (1922) 353 and Ann. Phys. 74 (1924) 45. [3] T.E. Phipps and J.B. Taylor, Phys. Rev. 29 (1927) 309. [4] P.A.M. Dirac, Proc. Roy. Soc. 117 (1928) 610, and 118 (1928) 341. [5] Particle Data Group, Review of Particle Properties, Phys. Rev. Dh0 (1994) 1173. [6] R. Frisch and O. Stern, Z. Phys. 85 (1933) 4, and I. Estermann and O_ Stern, Z. Phys. 85 (1933) 17.

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[7] Luis W. Alvarez and F. Bloch, Phy. Rev. 57 (1940) 111. [8] J.J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley, Reading Massachusetts (1967), p. 110. [9] See M. Gell-Mann, C.I.T. Report CTSL-20 (1961) unpublished, and Y. Ne'eman, Nucl. Phys. 26 (1961) 222, which are reprinted in the classic collection of articles The Eightfold Way, M. Gell-Mann and Y. Ne'eman ed., Benjamin, New York, 1964. [113] S. Col.eman and S.L. Glashow, Phys. Rev. Lett. 6 (1961) 423. [11] E.D. Bloom, D.H. Coward, H. DeStaebler, J. Drees, G. Miller, L.W. Mo, R.E. Taylor, M. Breidenbach, J.I. Friedman, G.C. Hartmann and H.W. Kendall Phys. Rev. Lett. 23 (1969) 930, and M. Breidenbach, J.I. Friedman, H.W. Kendall, E.D. Bloom, D.H. Coward, H. DeStaebler, J. Drees, G. Miller, L.W. Mo, R.E. Taylor, Phys. Rev. Lett. 23 (1969) 935. [12] P. Kush and H.M. Foley, Phys. Rev. 74 (1948) 250. [13] J. Schwinger, Phys. Rev. 73 (1948) 416, and Phys. Rev. 76 (1949) 790. [14] A review of these calculations is given in T. Kinoshita, Quantum Electrodynamics (Directions in High Energy Physics, Vol. 7), T. Kinoshita ed., World Scientific 1990, p 218. These calculations are constantly being extended. [15] R.S. Van Dyck, Jr., P. Schwinberg, and H. Dehmelt, Phys. Rev. Lett. 59 (1987) 26 and in Quantum Electrodynamics, T. Kinoshita ed., World Scientific, 1990, p. 322. [16] E. Fermi, E. Teller and V. Weisskopf, Phys. Rev. 71 (1947) 314, and E. Fermi and E. Teller, Phys. Rev. 72 (1947) 399. [17] M. Conversi, E. Pancini and O. Piccioni, Phys. Rev. 71 (1947) 209. [18] M. Camac, A.D. McGuire, J.B. Platt and H.J. Schulte, Phys. Rev. 88 (1952) 209. [19] V.L. Fitch and J. Rainwater, Phys. Rev. 92 (1953) 789. [20] H.A. Bethe and E. Salpeter, Quantum Mechanics of One- and Two- Electron Atoms, (Springer-Verlag, 1957). The discussion of magnetic moments and freestructure splitting begins in section 10. [21] L.H. Thomas, Nature 107 (1926) 514. [22] See Bethe and Salpeter, op. cit. p. 273. [23] A. De Rujula, H. Georgi and S.L. Glashow, Phys. Rev. D12 (1975) 147. [24] T. DeGrand, R.L. Jaffe, K. Johnson and J. Kiskis, Phys. Rev. D12 (1975) 2060. [25] N. Isgur and G. Karl, Phys. Rev. D21 (1980) 3175. [26] G.E. Brown, M. Rho and V. Vento, Phys. Lett. 84B (1979) 383. [27] S. Theberge and A.W. Thomas, Nucl. Phys. A393 (1983) 252, and references therin. [28] J. Franklin, Phy. Rev. D30 (1984) 1542. [29] Z. Dziembowski and L. Mankiewicz, Phys. Rev. Lett. 55 (1985) 1839. [30] M.Y. Chen, Y. Asano, S.C. Cheng, G. Dugan, E. Hu, L. Lidofsky, W. Patton, C.S. Wu, V. Hughes and D. Lu, Nucl. Phys. A254 (1975) 413. [31] The most modern code, which includes the strong absorption of the orbiting hadrons is by M. Leon and R. Seki, Phys. Rev. Lett., 32 (1974) 132. The code for muonic atoms written by J. H/iffner, Z. Phys. 195 (1966) 365, was widely used in the 1960s. The basic atomic physics is given in Y. Eisenberg and D. Kessler, Nuovo Cim. 19 (1961) 1195. They discuss strong absorption

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of orbiting hadrons in Phys. Rev. 123 (1961) 1472 and Phys. Rev. 130 (1963) 2352. The most recent review of cascade calculations is by C.J. Batty and R.E. Welsh, Nucl. Phys. A589 (1995) 601. [32] J. Blomqvist, Nucl. Phys. B48 (1972) 95. [33] T.E.O. Ericson and J. H/finer, Phys. Lett. 40B (1972) 459. [34] P. Vogel, At. Data Nuc]. Data Tables 14 (1974) 599 and P. Vogel eta]. Phys. Lett. B70 (1977) 39 and references therein. [35] E. Borie, Phys. Rev. A28 (1983) 555 and references therein. We are grateful to E. Borie for a copy of her code. [36] H. Margenau, Phys. Rev. 57 (1940) 383, and K.W. Ford, V.W. Hughes and J.G. Wills, Phys. Rev. 129 (1963) 194. [37] T. Yamazaki, S. Nagamiya, O. Hashimoto, K. Nagamine, K. Nakal, K. Sugimoto and K.M. Crowe, Phys. Lett. 53B (1974) 117. [38] J.D. Fox, P.D. Barnes, R.A. Eisenstein, W.C. Lain, J. Miner, R.B. Sutton, D.A. Jenkins, R.J. Powers, M. Eckhause, J.R. Kane, B.L. Roberts, M.E. Vislay, R.E. Welsh, and A.R. Kunselman, Phys. Rev. Lett. 29 (1972) 193. The final analysis of these data is reported in B.L. Roberts, Phys. Rev. D17 (1978) 358. [39] E. Hu, Y. Asano, M.Y. Chen, S.C. Cheng, G. Dugan, L. Lidofsky, W. Patton, C.S. Wu, V. Hughes and D. Lu, Nucl. Phys. A254 (1975) 403. [40] A. Kreissl, A.D. Hancock, H. Koch, Th. KShler, H. Poth, U. Raich, D. Rohmann, A. Wolf, L. Tauscher, A. Nilsson, M. Suffert, M. Chardalas, S. Dedoussis, H. Daniel, T. yon Egidy, F.J Hartmann, W. Kanert, H. Plendi, G. Schmidt and J.J. Reidy, Z. Phys. C37 (1988) 557. [41] J.D. Fox, W.C. Lain, P.D. Barnes, R.A. Eisenstein, J. Miller, R.B. Sutton, D.A. Jenkins, M. Eckhause, J.R. Kane, B.L. Roberts, R.E. Welsh, A.R. Kunselman, Phys. Rev. Lett. 31 (1973) 1084. [42] B.L. Roberts, C.R. Cox, M. Eckhause, J.R. Kane, R.E. Welsh, D.A. Jenkins, W.C. Lam, P.D. Barnes, R.A. Eisenstein, J. Miller, R.B. Sutton, A.R. Kunselman, R.J. Powers and J.D. Fox, Phys. Rev. Lett. 32 (1974) 1265, and Phys. Rev. D12 (1975) 1232. [43] G. Dugan, Y. Asano, M.Y. Chen, S.C. Cheng, E. Hu, L. Lidofsky, W. Patton, C.S. Wu, V. Hughes and D. Lu, Nucl. Phys. A254 (1975) 396. [44] D.W. Hertzog, M. Eckhause, K.L. Giovanetti, J.R. Kane, W.C. Phillips, W.F. Vulcan, R.E. Welsh, R.J. Whyley, R.G. Winter, G.W. Dodson, J.P. Miller, F. O'Brien, B.L. Roberts, D.R. Tieger, R.J. Powers, N.J. Colella, R.B. Sutton, and A.R. Kunselman, Phys. Rev. Lett. 51 (1983) 1131, and Phys. Rev. D37 (1988) 1142. [45] G. Bunce, R. Handier, R. March, P. Martin, L. Pondrom, M. Sheaf[, K. Heller, O. Overseth, P. Skubic, T. Devlin, B. Edelman, R. Edwards, J. Norem, L. Schachinger and P. Yamin, Phys. Rev. Lett. 36 (1976) 1113. [46] G. Charpak, F.J.M. Farley, R.L. Garwin, T. Muller, J.C. Sens and A. Zichichi, Nuovo Cim. 37 (1965) 1241. [47] J. Bailey, W. Bartl, B. von Bochmann, R.C.A. Brown, F.J.M. Farley, M. Giesch, H. JSstlein, S. van der Meer, E. Picasso and R.W. Williams, Nuovo Cim. 9A (1972) 369. [48] J. Bailey, K. Borer, F. Combley, H. Drumm, C. Eck, F.J.M. Farley, J.H. Field, W. Flegel, P.M. Hattersley, F. Krienen, F. Lange, G. Leb~e, E. McMillan,

94

[49] [50]

[51]

[52] [53]

[54] [55] [56]

[57] [58] [59] [60] [61] [62]

B. Lee Roberts G. Petrucci, E.Picasso, O. Runolfsson, W. yon Riiden, R.W. Williams and S. Wojcicki, Nucl. Phys. B150 (1979) 1. T. Kinoshita and W.J. Marciano in Quantum Eleetrodynamics (Directions in High Energy Physics, Vol. 7), T. Kinoshita ed., World Scientific 1990, p. 419. V. Bargmann, L. Michel and V.L. Telegdi, Phys. Rev. Lett. 2 (1959) 435, are generally given credit for this formula. As noted by J.D. Jackson in ClassicM Electrodynamics, (John Wiley & Sons, New York, 1975), p. 556, Thomas published an equivalent equation in 1927. Brookhaven National Laboratory AGS E821: D.H. Brown, R.M. Carey, E. Efstathiadis, E.S. Hazen, F. Krienen, J.P. Miller, O. Rind, B.L. Roberts*, L.R. Sulak, W.A. Worstell, J. Benante, H.N. Brown, G. Bunce §, J. Cullen, G.T. Danby, C. Gardner, J. Geller, L. Jia, H. Hseuh, J.W. Jackson, R. Larsen, Y.Y. Lee, R.E. Meier, W. Meng, W.M. Morse*, C. Pai, I. Polk, S. Rankowitz, J. Sandberg, Y.K. Semertzidis, R. Shutt, L. Snydstrup, A. Soukas, A. Stillman, T. Tallerico, F. Toldo, K. Woodle, T. Kinoshita, Y. Orlov D. Winn, A. Grossmann, K. Jungmann, G. zu Putlitz, P.T. Debevec, W. Deninger, D.W. Hertzog, S. Sedykh, D. Urner M.A. Green, U. Haeberlen, P. Cushman, S. Giron, J. Kindem, D. Maxam, D. Miller, C. Timmermans, D. Zimmerman, L.M. Barkov, D.N. Grigorev, B.I. Khazin, E.A. Kuraev, Yu.M. Shatunov, E. Solodov, K. Nagamine, K. Endo, H. Hirabayashi, S. Ichii, S. Kurokawa, Y. Mizumachi, T. Sato, A. Yamamoto, K. Ishida, S.K. Dhawan, F.J.M. Farley, M. GrossePerdekamp, V.W. Hughes*, D. Kawall, R. Prigl, and S.I. Redin (*Spokesmen, §Project Manager). B.L. Roberts, Z. Phys. C56 (1992) S101. V.W. Hughes, et al., Proc. 10th International Symposium on High Energy Spin Physics, Nagoya, 9-14 November 1992, T. Hasegawa, N. Horikawa, A. Masaike, S. Sawada ed., p. 717. S. Eidelman and F. Jegerlehner, Zeit. Phys., C:67 (1995) 585. W.A. Worstell and D.H. Brown, (1996), Phys. Rev. D54 (1996) 3237, and Muon (g-2) technical note # 220 (1995). W.A. Bardeen, R. Gastmans and B Lautrup, Nucl. Phys. B46 (1972) 319; R. Jackiw and S. Weinberg, Phys. Rev. D5 (1972) 157; I. Bars and M. Yoshimura, Phys. Rev. D6 (1972) 374. A. Czarnecki, B. Krause and W.J. Marciano, Phys. Rev. D52 (1995) R2619. A. Czarnecki, B. Krause and W.J. Marciano, Phys. Rev. Lett. 76 (1996) 3267. T. Kinoshita, Phys. Rev. Lett. 75 (1995) 4728. W. Marciano, private communication. M.Hayakawa, T. Kinoshita and A.I. Sanda, Phys. Rev. Lett. 75 (1995) 790 and Phys. Rev. D54 (1996) 3137. See the review by Kinoshita and Marciano, oF). cit. for a more complete discussion.

Laser Spectroscopy of Metastable Antiprotonic Helium Atomcules Toshimitsu Yamazaki CERN, CH-1211 Geneva, Switzerland and Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo, 188 Japan

1

Discovery

of Long-lived

Antiprotons

in Helium

The lifetime of an exotic atom/molecule sets a natural time window which constrains the precision of spectroscopy through the natural width. The high precision studies of muons, muonic atoms and muonium have been facilitated by their long enough lifetime of 2.2 ps. Before 1991 such a favourable situation had not been conceived for antiprotonic atoms. We knew well that even the positron and positronium are short-lived in matter and that the antiproton is destined to annihilate in matter in a few picoseconds via the strong interaction. A surprising situation emerged in 1991, when the University of Tokyo group discovered at KEK that about 3 % of antiprotons stopped in liquid helium survive for microseconds [1], 106 times longer than usually believed. This experiment had been triggered by a preceding one in which they encountered accidentally the longevity of K - mesons in liquid helium [2] while they were searching for £7 hypernuclei [3]. The longevity of negative mesons in liquid helium was suggested by Condo [4] based on their anomalously large free decay components. Condo proposed the formation of metastable exotic atoms X - e - H e 2+ with large principal and orbital quantum numbers (n, l), and this peculiar atom was studied theoretically by Russell [5]. Although Russell calculated the lifetime of antiprotonic helium atoms to be in the microsecond region, it was hardly believed that such metastable atoms are stable in high density medium like liquid helium. So, this extremely interesting subject had remained untouched nearly for two decades till the discovery in 199I. Immediately, a new experimental group (called PS205) was formed to study this phenomena comprehensively by using the Low Energy Antiproton Ring (LEAR) of CERN, which provides a superb beam for this purpose. This monoenergetic low energy antiproton beam made experiments even with gas targets very efficient and productive. In the first period (1991-93) they measured delayed annihilation time spectra (DATS) precisely in various phases of helium and also studied the effect of admixture of other atoms and molecules [6, 7, 8, 9, 10]. Although the information obtained from systematic studies of DATS indicated that the longevity is due to the formation of metastable atoms ~e- He 2+ (=~He +), it is rather "macroscopic" and "integral", and no

96

Toshimitsu Yamazaki

direct proof of the proposed atom was obtained. We needed a new "microscopic" and "differential" method with which individual states and transitions of the metastable atoms can be identified. In 1993 a new breakthrough emerged. The PS205 group succeeded in the first laser resonance experiment on the antiprotonic helium atom [11] based on the proposal by Morita et al. [12]. This success opened a wide field and as of 1995 seven resonance transitions have been found [13, 14, 15, 16, 17]. Parallel to these experiments, theoretical treatments of this atom advanced [18, 19, 20]. In this way the initial curiosity-oriented research of the PS205 group is turning toward high-precision frontier of fundamental physics.

2

Antiprotonic

Helium

Atomcules

The metastability of the antiprotonic helium atom is well understood by now. In the metastable ~He + atom the electron stays in the ls orbit while the antiproton with large-(n,l) undergoes a nearly classical orbital motion (see Fig. 1). The slowly-moving p polarizes the electron in the opposite direction, which helps retard the electric dipole transition. This effect was interpreted as being similar to the nuclear core polarization effects in terms of ls-np configuration mixing [18]. Another approach is to regard the ~ and He 2+ as the two centers of a molecule [19]. The large-(n,l) states of ~He + can be metastable because the Auger transitions to ionized states are suppressed due to the large ionization potential. As shown in Fig. 1, the whole levels are well divided into the radiation-dominated metastable zone and the Augerdominated short-lived zone. Each metastable state is expected to proceed as (n,/) --+ (n - 1 , / - 1) with a radiative lifetime of about 1.5 #s. The typical level spacing (transition energy) is around 2 eV, which is in the range of visible light. The metastable states are hardly destroyed via Stark mixing in collisions with surrounding helium atoms because the degeneracy in I is removed (about 0.3 eV energy difference between (n,l) and (n,l - 1)). Since this atom is neutral and has one electron, characterized as a kind of hydrogenic atom, it does neither stick to nor penetrate into surrounding He atoms. Since this atom possesses a dual character as an atom and a molecule in itself, it is often called "atomcule". Each state (n, l) is interpreted as a member of vibrational states with a vibrational quantum number v. A unique correspondence between (n,l) and (v, J) holds: J = l and v = n - l - 1. It is interesting that this behavior and correspondence result as the n and l become large in a two-body atom. Whether such large-/states can be formed in the p capture by a He atom or not is essential. Yamazaki and Ohtsuki [18] considered the non-statistical distribution of angular momenta brought in by the ~ in a naive way to understand the delayed fraction of 3 %. Korenman [21] made a more realistic calculation. It seems to be interesting that the maximum angular m o m e n t u m

Laser Spectroscopy of Metastable Antiprotonic HeLium Atomcules

97

H e+ A t o m c u l e

:p

E n e r g y (a.u.) He+

-2.0

Ionized ~He++ .... Io = 0.90 a.u. (24.6 eV)

1

He°

.................... ................

- - - :": - ~ ~

::: ::: - - - _

........ :.'.'.":-': - - - ~ . . . .

---==!

._. ; - ; : : : ::: ~ _ ~

_

~ "--" ~ " _

_

~

39

~

~ , 0

~;

42

=~/~-38

...::: .... - _ . H , -3.0

outra, P-H+o 30 Fig. 1. (Upper) The p and e - orbital distributions in a typical pile + atomcule state. (Lower) Level scheme of the ~He + atomcule. The bold, broken and dotted Lines represent metastable, short-lived and ionized states, respectively. From [18].

b r o u g h t in the capture process roughly corresponds to the m a x i m u m I ~ 37 when the ~ is b o u n d m o s t likely to a state with n ,~ ( M * / m ¢ ) 1/2 "~ 38. T h e appearance of metastability in antiprotonic a t o m s is a c c o m m o d a t e d by the above independent reasons jointly. There is no possibility in other elements. So, the antiprotonic helium a t o m c u l e is a miraculous existence of an antiparticle coupled to n o r m a l particles. Thus, the a t o m c u l e serves as a unique interface between m a t t e r and a n t i m a t t e r domains.

98

Toshimitsu Yamazaki 1993 v=3 ( 3 9 , 3 5 ) - > ( 3 8 , 3 4 ) r

•

•

i

.

.

.

1994 v=2 (37,34)->(36,33)

.

i

0.010

. . . .

i

•

•

0.010

o cl

o.ooi

0.001 I 1

. . . . Time

v

2.5

I . . . . 2 (,us)

o

1.5

v.

1.0

1 Time

597.259(2)3

2.0

"~

<

~ 470.724(2)~

?

-

~

21

LI 1 0.008

.

0.5 0

0.0 597.25 Vacuum Wavelength

597.30 (nm)

2 (p,s)

A A '^ 470.70 Vacuum

.

.

.

.

.

.

.

^~^^ 470.75 Wavelength (nm)

Fig. 2. The first two laser resonances observed in 1993 [11] and 1994 [14].

3

Laser

Spectroscopy

Morita et al. [12] proposed a laser resonance method to identify individual states. Since all the states are deeply bound with ionization energy of 25 eV, the laser ionization technique does not work. Instead, we can induce stimulated transitions from a metastable state to a short-lived state and detect the resonance from the response in the annihilation rate. Specifically, one can apply a pulsed laser and detect a spike in DATS. In 1993 and 1994 they succeeded in observing laser resonances in the (39, 35) --+ (38, 34) [11, 13] and (37,34) --~ (36, 33) [14] transitions, respectively. The resonance spikes and resonance profiles observed are shown in Fig. 2. Hayano et al. [13] succeeded in using two successive laser pulses to obtain information on the lifetime and population of the resonating state. They determined the decay rate of the (39,35) state to be 0.72 + 0.02 #s -1, which turned out to be nearly equal to the predicted one. In other words, this experiment confirmed the predicted retardation effect due to the e - - ~ (anti)correlation [18, 19]. The above method applies only to a pair of metastable and short-lived states. Hayano et al. [16] created a double resonance method in which a metastable --+ metastable --+ short-lived sequence can be studied. They identified the (38, 35) --+ (37, 34) up on the (37,34) 3tate. In 1995 the PS205 group succeeded in observing the laser resonances in Av = 2 "unfavoured transitions", (n, l) -+ (n + l, l - 1) [17], which have very small transition probabilities. The experiment was performed in a strong

Laser Spectroscopy of Metastable Antiprotonic Helium Atomcules -0.5

i .... (a)

-1

i ....

i ....

99

i",

k=726.096 nm (37,35) -~ (38,34)

,5

i (c)),=713.588 nm i (37,34) --> (38,33)

i-5 °~

"2.5

[l,,,l,.,,l 0.9

1

....

-6 ~=~lj,,ll

1,

1,1

1

'

I

'

I

'

I ....

I.

1.1

1.2

time ()as)

time (~ts) 300

....

0.9

12

I

'

~1

'

I

'

I

'

I

20

"~ 100

E

I

~

I

,

i

,

0.085 0.09 0.095 0.1 0.105 wavelength - 7 2 6 (nm)

0.5 0.55 0.6 0.65 wavelength - 7 1 3 (rim)

Fig. 3. The 726 nm and 714 n m " unfavoured" resonance spikes in analog-DATS and their resonance profiles, a) Analog DATS showing a resonance spike at 726.096 nm. b) Resonance profile of the 726 nm transition. The vertical bars indicate variances of ADATS peak intensities after repeated measurements and a single Gaussian function is used to determine the central wavelength, c) Analog DATS showing a resonance spike at 713.588 nm. d) Resonance profile of the 714 nm transition.

pulsed ~ b e a m by employing the analogue counting method. The resonance spikes revealed in "analogue" DATS and the resonance profiles obtained are shown in Fig. 3.

4

Comparison between Experiment and Theory

The search for laser resonance transitions was very much helped by theoretical predictions of the wavelengths. Without such theoretical guides it would have been impossible to find resonances. As of 1993-94 two or three different theoretical values were available [18, 19, 22, 23], but they are distributed as much as 1000 ppm, none of the theories at that time claimed they had precision better than 1000 ppm. In 1995 a theoretical breakthrough emerged; Korobov [20] calculated the energies of the atomcule by the molecular-expansion variational method and showed that they succeeded in reproducing the experimental values then available within 50 ppm. This triggered extensive experimental searches for unknown transitions. The successes in experiments after 1995 mentioned above were all guided by this theory. In Fig. 4 we summarize the present state of art in the comparison between

100

Toshimitsu Yamazaki L= 33

34

35 n = 39

....... ~ , , ~ 5 9 7 . 2 5 g

~470.724

-150

36

(kth- ;%xp) / ~'exp (ppm) -100 -50

5O i

t,v=O

i

I

v=3

I

I ,

v--3 7

IA (39,35)-* (38,34)J

• Korobov(1995) non-relativistic • Korobov (1996)

relativistic

-

• •

-

AV=2

v=2 v=21 (:38,35)--*(37,34)14He v=2 v=21 (37,34)--)(36,33)l v=3 v--3 7 (38,34)-~(37,33)J v=2 v=21 3He (36,33)-~(35.32)_J V=2 V=4 7 I-- --I (37,34)-~(38'33)1 )t=l v--31'He I- ~(37,35)-*(38,34)~

Fig.4. (Upper) Partial level scheme established by the present laser resonance spectroscopy. The observed resonance wavelengths are shown. (Lower) Comparison of the experimental wavelengths of various transitions with Korobov predictions (closed squares without [20] and closed triangles with [24] relativistic corrections). The upper part is for Av = A(n -- l -- 1) = 0 intraband transitions and the lower part is for Av = 2 interband transitions. The error bars are the experimental ones.

experiment and theory. The experimental wavelengths have high precisions ( ~ 2 ppm). The theoretical values of Korobov [20] are all close to the experimental ones, but with a close look we observe that the theoretical values are systematically longer than the experimental ones. Korobov further took into account possible missing effects; the most important m a y be the relativistic correction for the motion of the bound electron. Since the electron binding is correlated with the antiproton q u a n t u m numbers, the relativistic correction is state dependent and brings a sizable correction on the transition energy. The theoretical values including the relativistic effect by Korobov [24] are surprisingly close to the experimental

Laser Spectroscopy of Metastable Antiprotonic Helium Atomcules

101

values, as shown in Fig. 4. The remaining discrepancies are now only within several ppm. From this agreement we can say that the antiprotonic Rydberg constant is equal to the proton Rydberg constant to the precision of several ppm.

5

Hyperfine

Structure

The hyperfine structure associated with the interaction of the electron spin with the ~ magnetic moment (/,(~) = [9, (p)s + 9, (~)l]/.tN) will provide unique information on the e l e c t r o m a g n e t i c property of the 13. This is a new type of hyperfine structure, but similar to those of hydrogen and muonium and thus is expected to have a splitting of the order of GHz. On the other hand, the "fine structure" splitting (j = l + 1/2) associated with the one-body 1-s interaction is much smaller and thus is neglected at the present stage. Therefore, each state (n, l) is split into doublet states with F + = l + 1/2 and F - = l - 1/2. The unique feature of this hyperfine structure is that the "nucleus" here is not a proton, but an antiproton which has a negative charge. So, we expect that the F + state lies lower than the F - state. We also expect that because of the large 1 the parent doublet states with F + = l + 1/2 and F - = I - 1/2 proceed (without crossing) to daughter doublet states with F '+ = l ' + 1/2 and F ' - = l' - 1/2, respectively (see Fig. 5). This means that when the hyperfine splitting is nearly the same for the parent and daughter states the splitting in the laser resonance profile must be too small to be observed. So, we have to choose a good candidate transition which has sufficiently different hfs values between the parent and the daughter state. In 1995 this new type of hyperfine splitting was evaluated theoretically by Kartavtsev [25], Bakalov et hi. [26] and Korobov [27]. From these studies we learned that the best candidate for observing a doublet structure is the unfavoured transition (37, 35) --+ (38, 34), whose 1-2 GHz separation can be marginally observed by a high resolution laser with a band width of about 1 GHz. Fortunately, this transition is what was observed in 1995 (see Fig. 3). This will be one of the experimental programs to be carried out soon. As the splitting can only just be optically resolved by our present lasers, the resolution for the hyperfine energy (.~ several GHz) is poor (.-. 1 GHz). Therefore, our aim is to determine the hfs energy of the (37,35) state directly via microwave resonance with ~ 1 MHz resolution. However, how can we detect the microwave resonance without having polarization/asymmetric decay as in muonium spectroscopy? We propose first to induce an asymmetric population of the doublet states by a laser pulse tuned to the F + = l + 1/2 --~ F '+ = l' + 1/2 transition, then to turn the electron spin (i.e. invert the population asymmetry) by applying the microwave source for a suitable period, and finally to detect the inverted population with a second laser pulse, as illustrated in Fig. 5.

102

Toshimitsu Yamazaki

unfavoured transition (37,35)-+(38,34) •,'~,-

F_ = L- 1/2

LmewKI1h= 1.2GHz

" ~ h v =L,1t2 F

A

B

V

V_

.jay.,, :

F.' = k' + 1/2

..=_ ¢~ 0.04 ,.~ 0.03

t

~ ~

i

i

~ v

<

i

t2

J

>

2rdf~o

• O

0.02 O

L°"(v I / "-,,'.

0.01

.

.

.

.

"

$cn "~

."/ -,,. . . . . . . .,,.,~.... . . . . .--.,.,,...~,.-..~ . .

~ 01

.5

r 2

I;"(v ) , 2.5

i 3 t

i 3.5

4

(~)

Fig. 5. Hyperfme structure and the laser transitions involving the hyperfine doublets. The 1st laser tuned to u_ causes asymmetric populations of the F + and F states, which can be detected by the 2rid laser. Modulation of the 2rid resonance intensities occurs on the microwave resonance of the parent state with a Rabi period of about 1/~s (principle of 2-laser-microwave triple resonance).

6

Future

Scope

We started this series of studies from very strong curiosity. Gradually, our understanding about the structure of this atomcule advanced, but we hardly believe these would contribute to fundamental physics. With the advent of laser spectroscopy, however, we now hope that high precision spectroscopy of this unique three-body system will yield fruitful information on the basic aspects of the antiparticle, if theory develops as well. The laser resonance method has also played an important role as a microscopic probe of the interactions of the atomcule with neighbouring helium atoms or foreign atoms/molecules. The atomcule is a hydrogen like atom involving many metastable states which can be tagged by laser resonances and thus is expected to serve as a unique probe to study various chemical reactions microscopically [28, 29].

Laser Spectroscopy of Metastable Antiprotonic Helium Atomcu]es

7

103

Acknowledgement

I would like to thank Professor Gisbert zu Putlitz for his continuous interest and stimulation in exotic atom spectroscopy for many years. The present work is based on the collaborative experiments of the PS205 group at CERN. I would like to thank all the members. This work is supported by Grant-inAid for Specially Promoted Research of the Japanese Ministry of Education, Science and Culture.

References [1] [2] [3] [4] [5]

M. Iwasaki et al., Phys. Rev. Lett. 67 (1991) 1246. T. Yamazaki et at., Phys. Rev. Lett. 63 (1989) 1590. R.S. Hayano et at., Phys. Lett. B231 (1989) 355. G.T. Condo, Phys. Lett. 9 (1964) 65. J.E. Russell, Phys. Rev. Lett. 23 (1969) 63; Phys. Rev. 188 (1969) 187; Phys. Rev. A1 (1970) 721, 735, 742. [6] T. Yamazaki et at., Nature 361 (1993) 238. [7] S.N. Nakamttra et al., Phys. Rev. A49 (1994) 4457. [8] E. Widmann et al., Phys. Rev. A51 (1995) 2870. [9] E. Widmarm et al., Phys. Rev. A53 (1996) 3129. [10] B. Ketzer et al., Phys. Rev. A53 (1966) 2108. [11] N. Morita et at., Phys. Rev. Left. 72 (1994) 1180. [12] N. Morita, K. Ohtsuki and T. Yamazaki, Nucl. Instr. Meth. A330 (1993) 439. [13] R.S. Hayano et al., Phys. Rev. Lett. 73 (1994) 1485; 73 (1994) 3181(E). [14] F.E. Maas et at., Phys. Rev. A52 (1995) 4266. [15] H.A. Torii et at., Phys. Rev. A53 (1996) R1931. [16] R.S. Hayano et al., Phys. Rev. A55 (1997) 1. [17] T. Yamazaki et at., Phys. Rev. A, in press [18] T. Yamazaki and K. Ohtsuki, Phys. Rev. A45 (1992) 7782. [19] I. Shimamura, Phys. Rev. A46 (1992) 3776. [20] V.I. Korobov, Phys. Rev. A54 (1996) R1749. [21] G.Y. Korenman, Hyperfine Interactions 101/102 (1996) 463. [22] O. Kartavtsev, private comm. (1994). [23] Y. Kino, private comm. (1994). [24] V.I. Norobov, to be published. [25] O. Kartavtsev, Hyperfine Interactions 103 (1996) 369. [26] D. Bakalov et at., Phys. Lett. A211 (1996) 223. [27] V.I. Korobov, to be published. [28] T. Yamazaki et al., Chem. Phys. Lett. 265 (1997) 137. [29] B. Ketzer et al., Phys. Rev. Lett. 78 (1997) 1671.

Polarized, Compressed 3He-Gas and its Applications E. Otten Institut fiir Physik, Johannes Gutenberg-Universit/it Mainz, Germany

1

Introduction

The history of polarizing 3He gas traces back to the early sixties, when two different pumping techniques were developed almost simultaneously to tackle the problem. Colegrove, Schearer and Waiters [1] started from a gas discharge at low pressure (,-~ 1 mbar) in which the metastable 3S1 state is populated with a relative concentration of 10-6. This state can be efficiently pumped by the infrared circularly polarized resonance lines (~ = 1.0832 pm) to the u p states. The nuclear polarization built up in the 3S 1 state by hyperfine coupling is then transferred to ground state atoms by metastability exchange collisions which occur with a very large cross section of the order of 10-15 cm 2. In these early experiments in Houston most of the interesting physics of this polarization technique was carefully investigated and understood. Relaxation studies showed that surface collisions and surface diffusion at glass walls are the dominant processes, limiting relaxation times to a couple of hours depending on the particular glass or metal surface in question. Also first nuclear reaction experiments on this low density polarized target were performed already in these years. The alternative method is due to Bouchiat and Carver [2]. They investigated spin exchange of 3I-te with optically pumped rubidium vapour which occurs with a much smaller cross section of the order of 10 - 2 4 c m 2 by hyperfine coupling of the SHe nuclear spin to the polarized rubidium valence electron during collisions. Although this method is disfavoured from the side of the exchange cross section, most of this disadvantage can be compensated by much higher densities of the exchange partners. The advantage of the latter method lies, indeed, with the fact that it works almost independently of the 3He pressure: It takes the same time (~ 10 h) to polarize a sample at a few mbar as at a few bar of pressure. The method has been developed to its present perfection and successes by the efforts of the groups of Happer in Princeton [3] and Chupp [4] in recent years. When scattering experiments of polarized electron beams at the Mainz microtron (MAMI) came into sight by the end of the eighties my colleague W. Heil and myself decided to build a polarized 3He target in collaboration with the group of Mich~le Leduc at the l~cole Normale Sup6rieure (ENS),

106

E. Otten

Paris, following the Houston technique which is also called the direct pumping method. The main obstacles which had prevented up to then the polarization of large quantities of 3He were the lack of sufficient laser power at the desired wave length and the difficulty of compressing the polarized gas to reasonable density. The first problem was solved in these years at the ENS by developing a series of different laser types which culminated finally in the arc-lamp pumped LNA laser which delivers more than 5 Watt of laser power at reasonable cost [5]. The compression of polarized 3He was pioneered much earlier already by the work of Daniels and Timsit [6] in Toronto. They demonstrated that a Toepler pump driven with liquid mercury offers in principle a viable solution to the problem. In fact, they observed a few percent polarization in the compressed phase limited by the weak pumping power of the spectral lamps which were still in use at that time. This and other technical difficulties stopped this target project in the pilot phase before being used at accelerators, unfortunately. We decided to take up again Daniels' idea of the Toepler pump, but to develop in parallel also a piston compressor for its larger versatility. The target based on the Toepler compressor has reached now a steady state polarization of 50 % in a volume of about 100 cm 3 at a pressure of 1 bar [7]. It was exposed for many 100 hours to the 870 MeV electron beam of MAMI at a current of 5 to 10 #A. This experiment served for a measurement of the neutron electric form factor as described in section 3.

2 2.1

Polarizing

and

Compressing

aHe

Basic of Direct 3He Pumping

After recalling the basics of 3He pumping I will confine myself to the compression technique by pistons. Figure 1 shows the basic set-up and parameters of direct 3He pumping. The before mentioned laser delivers more than 5 Watt circularly polarized laser light which corresponds to a photon flux of the order of 1020 quanta/sec. The light is passed through an absorption cell containing about 1020 3He atoms, excited to a fraction of about 10 -6 to the metastable 3S1 state by a weak discharge. The cell has a volume of about 31. It is important to provide a long absorption length to make maximum use of the available light. Therefore, we use cells of 1 m length with a dichroic mirror at the end which reflects the laser light back into the cell but transmits red fluorescence light of the 1D2 -4 1P1 transition. The circular polarization of this fluorescence serves to determine the nuclear polarization of the sample, since it is transferred to the electron angular m o m e n t u m through hyperfine coupling after excitation [8]. To this end, the degree of circular polarization of the fluorescence light is analyzed. Figure 2 shows details of the optical pumping scheme. The laser is usually tuned to one of the two hyperfine components ( F --- 3/2 -4 F ' = 1/2)

Polarized, Compressed 3He-Gas and its Applications dichroic mirror

cell, l= ,m,,ID'=6 cm /a~ ~ ~3mbarl ~ ~

=

102_.°a

-T'-

l

orfo

o

--T-

Laser 1.08 jim 5 Watt =10z° hv/s circularly pol.

1 m

Pol. filter

X/4 / I.F. s

~

~

rlv' ~ q L°c~''' ,

~ \

IDz ~

107

v

,

z

IPI fluorescence Pol. monitor

Fig. 1. Principal design and parameters of direct aHe pumping via the aSx state in a low pressure discharge. On the right: Polarization monitoring through measuring the degree of circular polarization of the i D1 1 P1 fluorescence light.

and (F = 1/2 --+ F' = 1/2) of the 3S 1 -+3p0 transition, which are traditionally called C9- and Cs-transition, respectively. Choosing e.g. righthanded C9-pumping light, absorption takes place from the Zeeman sublevels ( m e = - 3 / 2 ) and (mR = - 1 / 2 ) with relative transition probabilities 3:1. Due to its orbital angular momentum the 3p0 state suffers almost complete relaxation by collisions not only between its own two Zeeman levels but within all states of the 3p multiplet. Consequently, the fluorescence repopulates each sublevel of the 3S1 state with equal probability. Setting up rate equations it turns out that an initially unpolarized sample gains in this pumping scheme 5/4h of angular momentum for each absorbed c~+-photon on the average. In this starting phase about 25% of the light is absorbed resulting in a gain of more than 1019 polarized spins/sec. With increasing polarization, however, the efficiency of the pumping process drops dramatically since the absorbing states are getting depopulated and the sample will no longer interact with the pumping light. 2.2

P u m p i n g D y n a m i c s a n d Spin E x c h a n g e

Very important is the fast exchange of the 3S1 excitation energy from one atom to the next by collisions which occur at a rate of typically 106/sec under the given conditions. These collisions conserve the total angular momentum of the colliding system and its projection, since spherical atomic S-states are involved only; but they will exchange electronic and nuclear spin polarization due to hyperfine coupling in the initial and final excited states. Under usual conditions this spin exchange rate is the fastest process in the rate equations. Hence, it leads to a spin exchange equilibrium, characterized by population numbers

N(mF) N(mD

-

exp(

(mr-

=

(1)

108

E. Otten

Is2p ~Po

F=i/2

P~

T

°/l _

n,-

(3) a' a (1)

uz

exitation transfer collisions Isz ISo

collisional mixing '~ isotropic °/lreemission

-3/2

F=I= 112

-1/2

Z2..au

+ I/2

i .... l -I/2 +i/2

+ 3/2

m F

my= ml

Fig. 2. Level diagram of the pumping scheme indicating also the principal processes. The height of the columns represent the relative population of Zeeman levels in spin exchange equilibrium at P1 = 33 %.

The case x = 2, which is plotted in Fig. 2 by the height of the columns on each m F sublevel, corresponds to a nuclear polarization Ps = (N(]') - N ( $ ) ) ( N ( $ ) + N($)) = 33% .

(2)

At Ps = 85 % (about the m a x i m u m which has been achieved, so far) z has risen to 12.3 . At that point the absorbing levels are depopulated so much already, that the pumping efficiency has dropped to about 1% of its initial value. These features of the pumping dynamics are illustrated in Fig. 3 which is an on-line recording of the built-up of polarization in the pumping cell in the first 200see, followed by the relaxation in the plasma after the laser has been turned off. Within the first 25see the polarization rises already to 65 %. The pumping efficiency at that point is indicated by the tangent to the slope; it corresponds to a gain of about 3 × 10 is polarized spins/see. The final rise to the saturation level of Ps = 85 % takes 10 times longer. Hence, this saturation point is not economic anymore under conditions where one has to maximize a quality factor defined as the number of atoms times the polarization squared. From the right half of Fig. 3 we read a relaxation time of the gas of Ta ~ 5 rain. It is caused by exciting the atoms to higher levels in the plasma where the nuclear polarization couples to orbital angular m o m e n t u m which is then dissipated by fluorescence and gas kinetic collisions. The stronger the plasma, the faster the relaxation! On the other hand, one needs a m i n i m u m discharge level in order to maintain a sufficient density of metastable atoms. The o p t i m u m is usually found for a very soft, homogenous radio-frequency discharge.

Polarized, Compressed 3He-Gas and its Applications

90

~

g

......

_P: :85~o

laser

beam

109

"o1"["

70

so

"~

30

~

20

running

~ = 5.6cm I = 100 cm

3He :I m bar

~0

0 t 0

,

I

SO

,

I 100

'

I

1~

I

,

200

*

,I

I

2~

300

350

Time lsecl Fig. 3. Built-up and decay of 3He polarization in the optical pumping cell. After 200 sec of pumping the laser was shut off. The tangent to the curve at P = 65 % -4 corresponds to a polarization rate of 3.1018 3He/s.

2.3

Relaxation by Molecular Ions and Questions of Gas Purity

Another source of relaxation is the formation of 3He+ molecules which are formed in the discharge bY 3-body collisions. They are paramagnetic and have a strong hyperfine coupling of the nuclear spin to the electronic one. The latter is again weakly coupled to the orbital angular momentum of the molecule which relaxes very fast in gas kinetic collisions. As their formation rate rises with the square of the gas pressure it starts to dominate relaxation above 1 mbar and causes the equilibrium polarization to drop. The relaxing power of these molecular ions is enhanced furthermore by a kind of catalytic process which consists in exchanging atoms during collisions. This process is particular dangerous in high pressure targets under irradiation of an accelerator beam. Under these conditions a single molecular ion may cause a thousands of relaxations until it is quenched by neutralization [9]. Therefore, it is important to spike the helium with some quenching gas. An admixture of 0 . 1 % of N2, e.g., suffices already for that purpose. Therefore, in our system spiking of the compressed, polarized 3He gas is provided by a needle valve. On the other hand, any kind of impurity of the helium gas in the optical pumping cell is fatal because it also quenches the essential metastable 3He atoms and, moreover, lowers the electron temperature in the plasma to a level which prohibits the excitation of helium completely. Therefore, spectral purity of the 3He (corresponding to about 1 ppm impurity level) is mandatory in this region. For that purpose the helium is passed through a NEC-getter and a LN2-trap before it enters the pumping cell (see Fig. 4). Also the connection between the pumping cell and the compressor is secured by a LN2-trap in order to suppress back diffusion of rest gas from the compressor into the pumping region.

110

E. Otten

;H-'e-Filling-Station ,,it. 3He-Reservoir , SI.... 4 optical

~LN:

Pumping-cells [ ~

4.J W !~/I = 1083nm

i -,-.4,,

OpL

Pol.-Detek'tion

t%

,Fie.Container

HelmhoRzguiding'field

2.4

Design and Performance

Fig. 4. Schematic design of the 3He polarizer and compressor.

of the Piston Compressor

Our latest version of the piston compressor has two stages with a buffer cell in between (Fig.4) [10,11]. They are made of titanium for the excellent mechanical and vacuum properties of this material. Note that any ferromagnetic material has to be avoided for reasons of relaxation through magnetic field gradients. Even austhenetic stainless steel cannot be tolerated. The stroke of the pistons is bridged by a titanium bellows in order to guarantee tightness to the outside. The pistons are sealed with respect to the cylinders by special Quad-rings and fluorinated grease. After the second stage a pressure of up to l o b a r is reached in the target cell. The cell can be detached from the apparatus by the help of a glass cock and a flange. It may then be transferred for use in some remote experiment. During transport a pair of Helmholtz coils guarantees a sufficiently homogenous guiding field of a few Gauss. After use the cell is reconnected to the system and evacuated, whereas the depolarized 3He gas is sluiced back through the aforementioned getter into the optical pumping cell. In the optical p u m p i n g region which actually consists of a battery of four 1 m long cells we reach at present a polarization between 60 and 70 %, distinctly smaller than in sealed off cells. The spectrum of the discharge shows that the latter seem to be cleaner. The best result obtained in the compressed phase so far is PI = 52 % at p = 6 bar. The system polarizes up to 10 m b a r l / m i n . The reasons for polarization loss during compression are in principal clear and more or less under control. Since relaxation occurs predominantly at

Polarized, Compressed 3He-Gas and its Applications

1] ]

surfaces, the relaxation time is proportional to the ratio of the volume to the surface. This ratio is getting very unfavourable during the last phase of compression. Moreover, the dead volume in the transfer region between the compressor and the storage cell which includes in particular the valve is very dangerous. There, the gas is stored for at least one compression cycle which is 10seconds for the first and a couple of minutes for the second compressor. Also in this region the volume to surface ratio is unfavourable. In the original version of the piston compressor [12] these transfer losses were much more serious than at present after we have redesigned the valves and the transfer region. There are reasons to expect that also the residual transfer losses will be overcome in the course of further development work.

2.5

Relaxation Studies with Glasses and Surface Coating

For a volume to surface ratio of (V/S) = 1 cm, corresponding to a spherical cell with ~ ~ 6 cm one measures a relaxation rate of about 1 hour for Pyrex glass and roughly 10 hours for an alumino-silicate glass, like Corning 1720 or the Supremax glass from Schott. These latter glasses are supposed to have a tighter surface which is less penetrated by diffusion. Moreover, the paramagnetic purity of the glass is decisive. First experiments with iron free Supremax glass show substantial improvement with T1 ranging from 20h to 60h. The numbers given apply to carefully cleaned, baked and highly evacuated vessels. T1 may drop to several minutes for an untreated vessel which has just been pumped down to rough vacuum. Using a detached cell in a remote experiment asks for particularly long relaxation times. A great variety of materials had been tested already in early experiments, e.g. by Timsit et al [6]. They inserted bulk samples into glass vessels which were then sealed off. None of the materials tested reached relaxation times longer than those obtained by the best glasses. Therefore, we decided to evaporate in situ very pure, volatile metals onto the inner surface of Supremax vessels. Our primary choices were bismuth and caesium for the following reasons: Bismuth is known to be a diamagnetic metal, having only minimal pockets of paramagnetic band structure. Caesium on the other hand shows the usual paramagnetism of a conduction band. But it is known, that it practically does not bind any helium to its surface (in fact, it is the only surface which is not wetted by superfiuid helium) [13]. The suspicion that an alkali metal might be good arose also from the observation that groups using rubidium exchange pumping reported consistently longer relaxation times than obtained by direct pumping in a clean 3He atmosphere. Both our expectations were fulfilled. With bismuth we reached relaxation times of 50 hours in Supremax vessels, for caesium up to 117 hours were observed, (Fig.5), [14]. Detachable ceils coated with bismuth or caesium showed no evidence for increased relaxation after several refillings [14], [10]. Still, one has to add the caveat that these very long relaxation times were not reproduced

112

E. Otten

50

z.O

ci

p=2.17bar I10cm3

~

r30 o 'K. 20 o

.o

-5

a_

10

T~" 117h = 30rain

:12 oJ

- " ~

i

0

100

200

300

~0

Time [hi

Fig. 5. Relaxation of compressed 3He in a detached Cs coated cell with 0 ~ 6cm.

in every of these experiments; but they seem to correlate positively to the effort invested in the preparation of the surfaces. 3 Determination of the Electric Form Factor of the Neutron i n D o u b l y P o l a r i z e d a H e ( 7 , e' n ) - S c a t t e r i n g The internal structure of hadrons has always been a central issue in particle physics since R. Hoffstadter discovered in the fifties that charge and magnetism of the proton are spread over a certain volume. Nowadays the form factors of the nucleons are cornerstones for checking effective quark models and QCD-calculations. In this respect the electric form factor of the neutron is particularly interesting, since it should vanish identically in any first order quark model where the quarks occupy the same spatial wave function. Indeed, it is so small that it escaped precise measurements so far, except for its mean squared charge radius which - surprisingly enough - could be measured with high accuracy in thermal neutron scattering to be [15] 2 ( r ch}n = - 0 . 1 1 6 e fm 2 .

(3)

Charge distribution and magnetization of a neutron enter the elastic cross section of electron scattering through their Fourier-transforms, the elastic form factors G~ (Q2), G ~ (Q:) which are functions of the square of the four momentum transfer Q2. They modify the M O T T cross section of a point-like charge by do-(Q ~) dX?

=

(d~(Q~)) • [a G ~ ( Q 2) + b G~u(Q2)] \ dc~ MOTT

(4)

where a and b are kinematical factors known from the Rosenbluth formula. At Q2 = 0 the two form factors yield the total charge (i.e. zero for the neutron)

Polarized, Compressed 3He-Gas and its Applications

] 13

and magnetic moment, respectively. The neutron problem is characterized by the fact that for all Q

GE,~(Q2) _< 10-2G2

/O2~1

(5)

holds. Thus, it is extremely difficult to extract its electric form factor from a measurement of (4) reliably with the experimental and systematic errors of such experiments given. The problem can only be solved if one manages to enhance the effect of electric scattering by interference with the magnetic one. This situation occurs in spin polarized scattering, since the electric scattering amplitude is insensitive to the relative orientation of spins whereas the magnetic one is. Thus, one searches for an asymmetry of the scattering cross section with respect to positive and negative helicity of the electron beam given by A --

cr+--cr-

-- Pe

Pn±CGE,nGM,n+PlnldG2Mn = A± +All '

.

(6)

Pe is the polarization of the electron beam. Thanks to the efforts of E. Reichert and his group [16], we dispose now at MAMI of an excellent polarized electron (~+) - source, delivering 10 to 15 pA at a polarization of 80 % to 50%. PnJ- and pie are the components of the neutron polarization parallel and perpendicular to the momentum transfer which it got by the electron. The coefficients c and d are two more known kinematical factors. We see that the asymmetry measured for perpendicular neutron polarization A ± is indeed proportional to the interference term between electric and magnetic scattering whereas A II is of purely magnetic origin. Measuring the ratio of these two asymmetries gives directly the electric form factor in terms of the known magnetic one:

GE,n (O2) = (c Al /d AII) GM,n(Q ~) .

(7)

How to get a target of free polarized neutrons of sufficient density? We can only dream of it. But a polarized 3He target is a realistic substitute since its spin and magnetic moment is ahnost entirely carried by the unpaired neutron (see Fig. 6). To make sure that it is the neutron and not the proton from which the electrons are scattered quasi-elastically one asks for coincidence between the scattered electron and the neutron. For the case of parallel neutron polarization Fig. 7 shows the electron spectrum for positive and negative electron helicity, respectively. In the quasielastic peak on the right hand one recognizes the large asymmetry of this scattering. After having analyzed 50 % of the total data, the decisive ratio of asymmetries in (7) could be determined to be A 1e x p Al!xp

=

0.146 (13)

(8)

114

E. Otten

,tire

t,, ~

~:~, n-defector

P°I

P

-detecfor

up dow n mognefisofion

C:J

Fig. 6. Principle of determining neutron form factors by exclusive doubly, polarized, 3 -4

quasi-elastic He ( e , e ' n ) scattering.

from which we determine an electric neutron form factor of GE,n (Q2 = 9 fro-2)

=

0.045 (±) 0.005

(preliminary) .

(9)

Figure 8 shows this value together with some earlier measurements which also dealt with polarization variables. The point at 8 fm -2 stems from our pilot experiment [17]. Note that this experiment was not performed with the offline target cells described above, but still used the on-line Toepler compressor which yielded in a target of 100 cm 3 a pressure of 1 bar at P t = 50 %. Figure 8 shows in addition a few theoretical curves for GE,n including the first recent QCD-prediction by O. Nachtmann [18] which seems to fit quite well. [ , i , , . i

6O0

A~xp=- ll' °/°

i:iii-- G-

ii =-16 oVo At.It

5OO

_

LO0 I/% ,.l,..

r-3OO o i,..J 20O

-1~ inelostiC quas'ci |mr evenl's

\

tO0 . ~ - i

0

2O

,

I

i

I

i

I

=

60 80 100 120 Energy (a. u. )

140

Fig. 7. Electron spectra of 3He ( e , e ' n ) scattering obtained by a Pb-glass detector array. The asymmetry with respect to negative (upper curve) and positive (lower curve) electron helicity shows up in the quasi-elastic peak. The 3He spin is oriented parallel to the momentum transfer.

Polarized, Compressed 3He-Gas and its Applications

115

0.12 Dl~,e'fi)

/ d

aK

f

c~

I Wetimir~ry }

1a-~ \ 3

"°°°°°°°°*'*'*°°. . . . . . . . . . . . . . . . .

He I~,e'nl

IJL 0

~

'

I(}

2O

(12 (fm-2l Fig. 8. Results of GE,n (Q2) measurements in doubly polarized electron scattering experiments together with various theoretical curves. The point at Q2 _ 8 fm -2 is the most recently pubfished value, obtained in the pilot phase of the experiment at Mainz [17]; the point at Q~ = 9fm -2 stems from a preliminary evaluation of 50% of the full data set obtained in that experiment. The curve with points and short dashes results from a recent QCD-calculation [18].

4

Neutron

Spin

Filter

A very promising application of samples of dense polarized 3He opens up for thermal and epithermal neutron beams. Neutrons with spin opposite to that of 3He are absorbed with a cross section of 6000barn; this enormous cross section applies for neutrons with a wavelength of 1 ~ and decreases in proportion to the wavelength. The parallel component, on the other hand, is hardly attenuated by elastic scattering with a cross section of a few barn only. Thus, polarized 3He can serve as a neutron spin filter for a broad band of energies and for any direction of the neutron m o m e n t u m . This is a great advantage over traditional neutron polarizers or analyzers which accept only a very limited phase space, like Bragg-reflexes or total reflection from magnetized materials. First successful a t t e m p t s to polarize a neutron b e a m by a 3He spin filter have been undertaken with a sample, polarized by the Rb spin exchange method [19]. Figure 9 shows polarization and transmission of a neutron spin filter as a function of its opacity which is proportional to the product of its pressure, its length and the wave length of the neutrons; it is given in practical units: bar ~ cm. The contrast of the filter rises of course with the SHe polarization. Two curves are plotted for PI = 20 % and 52 %, respectively. The lower value, 20 %, was achieved in our first test experiment at the Mainz T R I G A reactor in 1994 [10,11]. The second test with 52 % SHe polarization by the end of last year yielded a neutron polarization of 84 % at a total transmission

116

E. Otten

IOO 1995

80

F~

60. 40.

20-

1

•

~"

T m

00

I0

20

Pile * L

30 *

40

50

60

70

I [bar */~ * cm ]

Fig. 9. Polarization Pn and transmission Tn of a 3He neutron spin filter as a function of its opacity which is the product of pressure, absorption length and neutron wave length. Plots are given for two different 3He polarizations as indicated. The pilot data points result from an experiment, performed at the Mainz TRIGA reactor [10,11].

of 20 %. This is not too far anymore from the ideal values of PI = 100 % at 50 % transmission. For this experiment the target was polarized at the piston compressor in the Institut fiir Physik and then transferred to the broad band neutron b e a m from the T R I G A reactor on campus. The polarization was analyzed by the Bragg-reflex from a magnetized cobalt iron single crystal. At present we are building in our laboratory in collaboration with the Institut Laue-Langevin another two-piston 3He polarizer and compressor. Similar instruments are planned at the National Institute of Standards and Technology (NIST) in Washington, at the Hahn-Meitner Institut in Berlin and for the Research Reactor in Munich. 3He spin filters would be particularly useful as polarizers and analyzers for pulsed neutron beams from spallation sources (Fig. 10). T i m e of flight analysis and a large detector array would allow simultaneous measurement of doubly differential cross sections regarding scattering energy and angle. A 3He analyzer close to the scatterer could analyze the polarization of the scattered neutrons simultaneously at full solid angle of scattering. A single 3He cell would thus replace the extremely expensive arrangement of an array of super mirrors otherwise used for polarization analysis of scattered neutrons. 5

3He Tomography

of the

Human

Lung

Last year W. H a p p e r ' s group at Princeton demonstrated in cooperation with the magnetic resonance imaging group at Duke University in a seminal paper

Polarized, Compressed 3He-Gas and its Applications

1 17

-+

Fig. 10. Possible scheme of using 3He spin filters for polarizing a pulsed broad band neutron beam from a spauation source and analyzing the polarization of scat+ tered neutrons; a polarized 3He counter may integrate the analyzing and detection function.

the possibility of imaging lung tissue filled with hyperpolarized noble gas [20]. The term "hyperpolarized" indicat,es that the noble gas has been polarized (by means of optical pumping) to a degree far beyond the ordinary Boltzmann equilibrium P ~ o l t z m a n n= exP ( - p B / k T ) (lo) which is of order to under usual nuclear magnetic resonance (NMR) conditions. The first pilot experiments were performed with small samples of lZ9Xe and later 3He polarized by rubidium spin exchange. The gas was inserted into the lungs of small test animals and NMR-pictures taken. The enormous gain in polarization degree by 5 orders of magnitude as compared to conventional NMR outweighs not only the loss in spin density between tissue and gas which is of order 1000, it also has enough signal capacity in order to feed the many hundred consecutive NMR pulses which each pixel suffers in the process of imaging taking. For that purpose the magnetization is tilted only by a few degrees out of the field axis by each radio-frequency pulse, such that the longitudinal magnetization is effected marginally per pulse. The induction signal is still large enough! This procedure is enforced by the circumstance that the hyperpolarization can be used up only once during image taking, once destroyed it will recover only to the tiny value of the Boltzmann equilibrium (10) which is useless at these small densities. The large interest raised in the medical community by this method stems from the fact that porous tissue like the lungs is difficult to image by conventional magnetic resonance imaging (MRI). Also X-ray or nuclear radiation methods do not give truly satisfactory results for that task. With our technique of compressing polarized 3 ~ into e detachable and transportable cells we found ourselves well prepared for entering this new field

1~8

E. Otten

Fig. 11. Sagittal slice of a human thorax imaged with conventional MRI (left) and MRI on hyperpolarized 3He, inhaled in the lungs (right) [21].

of research. In collaboration with the Radiological Institute of the University of Mainz and with the Deutsche Krebsforschungszentrum in Heidelberg we made a first try to image the human lung in vivo by inhaling a liter of 3He polarized to a degree of 46 %. The result is shown in Fig. 11 which shows two sagittal slices of the volunteer's thorax, on the left taken with conventional proton MRI, on the right with 3He MRI. Where proton MRI leaves a large, black hole, indicating no structure, 3He gives a bright signal revealing the lung in any detail. The in-plane resolution of this picture is (1.2mm) 2 [21]. In parallel, also the Princeton-Duke-collaboration has produced an in vivo 3He picture of the human lung [22]. 6

Conclusions

Optical pumping of 3He has been subject of studies in atomic physics for very many years. With the advent of powerful pumping lasers it became possible and worthwhile to start a research and development program towards production of large quantities of spin polarized 3He. Polarization preserving compression techniques as well as storage cells with relaxation times exceeding several days were developed. Production rates of order I bar liter/h were achieved at a polarization of about 50 %. Such large amounts of spin polarized 3He gas are necessary and useful for interdisciplinary applications. To that end we have engaged ourselves into three very different topics: 1. In Particle Physics: Determination of the electric form factor of the neu---)-

__+

tron in 3He ( e , e n) - scattering. 2. In Neutron Physics: Establishing 3He spin filter for polarizing and analyzing thermal and epithermal neutron beams for scattering experiments. 3. In Clinical Research: 3He MR-tomography of the human lung.

Polarized, Compressed aHe-Gas and its Applications

119

References [1] [2] [3] [4]

[5] [6]

[7] [8] [9] [10] [11]

[12]

[13] [14] [15] [16]

[17] [18] [19] [20] [21]

[22]

F.D. Colegrove, L.D. Schearer and G.K. Waltes, Phys. Rev. 132 (1963) 2561 M. Bouchiat, T.-R. Carver and C.M. Varnum, Phys. Rev. Lett. 5, (1990) 463 W. Happer, this volume J.R. Johnson, A. K. Thompson, T.E. Chupp, T.B. Smith, G.D. Cates, B. Driehuys, H. Middleton, N.R. Newbury, E.W. Hughes and W. Meyer, Nucl. Instr. and Meth. in Phys. Research A 356 (1995) 148; also reviewed e.g. by T. Chupp in Proc. Int. Workshop on Polarized Beams and Polarized Gas Targets, Cologne, June 1995, eds. H. Paetz gen. Schieck and L. Sydow, World Scientific Co., Singapore, 1996, p. 49-62 C.G. Aminoff, C. Larat, M. Leduc, B. Viana and D. Vivien, J. Luminescence 50 (1991) 21. R.S. Timsit, J.M. Daniels, E.T. Denifing, A.K.C. Kiang and A.D. May, Can. J. Phys. 49 (1971) 508; R.S. Timsit, W. Hilger and J.M. Daniels, Rev. Sci. Instrum. 44 (1973) 1722 G. Eckert, W. Heil, M. Meyerhoff, E.W. Otten, R. Surkau, M. Werner, M. Leduc, P.J. Nacher and L.D. Schearer, Nucl. Instrum. Meth. A 320 (1992) 53 N.P. Bigelow, P.J. Nacher and M. Leduc, J. Phys. II,1 France, 2 (1992) 2159 K.D. Bonin, T.G. Walker and W. Happer, Phys. Rev. A 37 (1988) 3270 R. Surkau, Doctoral Thesis, MaJnz, 1995 J. Becker, M. Ebert, T. Grossmann, W. Heil, H. Humblot, M. Leduc, E.W. Otten, D. Rohe, M. SchMer, K. Siemensmeyer, M. Steiner, R. Surkau, F. Tasset and N. Trautmann, Journal of Neutron Research 5 (1996) 1 J. Becker W. Heil, B. Krug, M. Leduc, M. Meyerhoff, P.J. Nacher, E. W. Otten, Th. Prokscha, L.D. Schearer and R. Surkau, Nucl. Instrum. Meth. A ~46 (1994) 45 P.J. Nacher and J. Dupont-Roc, Phys. Rev. Lett. 67 (1991) 2966 W. Heil, H. Humblot, E.W. Otten, M. 8chMer, R. Surl~u and M. Leduc, Phys. Lett. A 201 (1995) 337 H. Leeb and C. Teichtmeister, Phys. Rev. C 48 (1993) 1719 E. Reichert in Proc. Int. Workshop on Polarized Beams and Polarized Gas Targets, Cologne, ~lune 1995, eds. H. Paetz gen. Sehieek and L. Sydow, World Scientic Co., Singapore, 1996, pp. 285 M. Meyerhoff et al., Phys. Letters B 327 (1994) 201 O. Nachtmann, Lectures given at the First ELFE Summer School, July 1995, Cambridge, UK, to be published K.P. Coulter, A.B. Mc Donald, W. Happer, T.E. Chupp and M. Wagshul, Nucl. Instr. and Meth. in Phys. Res. A 288 (1990) 463 M.S. Albert, C.D. Cates, B. Driehuys, W. Happer, B. Saam, C.S. Springer Jr. and A. Wishnia, Nature, Vol. 370 (1994) 199 M. Ebert, T. Groflmann, W. Heil, E.W. Often, R. Surkau, M. Ledue, P. Bachert, M.V. Knopp, L.R. Schad, and M. Thelen, LANCET 347 No. 9011, p. 1297 Reported in Laser Focus World, Nov. 1995.

Medical N M R Sensing with Laser-Polarized aHe and 129Xe William Happer Department of Physics, Princeton University, Princeton, NJ 08544, USA I want to review how some interesting new applications of atomic physics to medical imaging have been influenced by work clone at Heidelberg by Professor Gisbert zu Putlitz and his predecessors over the past two centuries. I will begin my story in the year 1860 when two Heidelberg scientists Robert Bunsen, then aged 50, and 36 year-old Gustav Kirchhoff aspirated the residue of forty tons of evaporated Diirkheim mineral water through a Bunsen burner and were the first persons to see the beautiful, sky-blue spectral line of a new alkali metal which they called "cesium" from the Latin adjective "blue-gray", a typical Latin usage being " c a e s i o s o c u l o s G e r m a n o r u m - the blue eyes of the Germans." A year later in 1861 Bunsen and Kirchhoff observed a dark red spectral line from a few grains of the mineral lepidolite, the first discovery of another new alkali metal, which they named "rubidium" from the Latin adjective r u b i d u s - red or blushing. Rubidium, especially, is going to play an important role in the medical applications that are the subject of this paper. In 1894, seven years after Kirchhoff's death, Lord Rayleigh and William Ramsay discovered the noble gas argon. A year later, in 1895, Ramsay discovered helium, fossil alpha particles as we know now, by outgassing the uranium mineral c l e v i t e . Four years later, in 1898 Ramsay and Travers discovered the other noble gases, neon, krypton and xenon. Bunsen died in 1899, living just long enough to see the discovery of all of the stable noble gases. Noble-gas atoms and alkali-metal atoms are very closely related. For example, a rubidium atom has a single valence electron bound to a krypton-like core. The single valence electron of the alkali-metal atom is extremely efficient in absorbing or emitting light, and that is one of the reasons Bunsen and Kirchhoff were so successful in their first application of spectroscopic analysis to the alkali-metal atoms, which make beautiful colors in the flame of a Bunsen burner, or in the fireworks displays that Rector zu Putlitz was so fond of arranging above the Heidelberg Castle. It remained for the scientists of this century to begin to work out the improbable physics that makes magnetic resonance imaging possible: the discovery of isotopes, the development of quantum mechanics and its spectacularly successful application to atoms and nuclei. I want to mention a major contribution of Heidelberg during this period, the studies of atomic hyperfine structure by Professor Hans Kopfermann [1] and his research group. Of the many outstanding students trained by Kopfermann, Gisbert zu Putlitz was not the least distinguished. Much of what we know today about atomic hy-

122

William Happer

Fig. 1. One of the first images of a human lung [2], that of Dr. Cecil Charles of Duke University, taken with laser-polarized 3He gas. perfine structure was discovered in Heidelberg. The hyperfine interactions of nuclear moments with their surrounding electrons play a crucial role in the applications of spin polarized 3He and 129Xe to medical imaging. The first application of physics to medical imaging was made in Germany 100 years ago in the fall of 1895 by Wilhelm RSntgen with his discovery of x-rays. Many other applications of physics to medical imaging have occurred since RSntgen's discovery, for example, the use of radioactive isotopes, positron emission tomography, ultrasound, etc. Nevertheless, RSntgen's xrays have remained the most widespread imaging method in medicine. However, a fairly recent entry into the medical imaging field, magnetic resonance imaging or MRI, is giving x-rays serious competition for the first time. Probably most of you know a little bit about MRI already, but a recent, novel variant of MRI is displayed in Fig. 1, which shows the first MRI picture of a human lung, obtained with laser-polarized 3He gas in a collaboration of our Princeton group with researchers at Duke University [2]. The very first images with laser polarized gas, a crude image of the excised lungs of a mouse [3], were obtained in a collaboration between our Princeton group, led by Gordon Cates, and a group at the State University led by Arnold Wishnia. Unlike x-rays, which scatter preferentially from the higher-Z elements of the body - the calcium of bones for example, conventional magnetic resonance images are of the protons in the watery and fatty tissues of the body. For this

Medical NMR Sensing with Laser-Polarized aHe and 12°Xe

123

reason the soft tissue, which is full of protons, shows up very clearly with lots of structure, while the same tissue would be almost featureless when observed with x-rays. Until recently, the lung, has stubbornly resisted all attempts to produce good images - with MRI, x-rays or any other modality. The reason is that the lung is designed to be filled with air. Consequently, it has a very low proton density and a complicated three dimensional structure of tissue and gas spaces, with magnetic susceptibility gradients that produce artifacts in conventional MRI images. There is little to scatter x-rays in a healthy lung, but well-advanced pathologies like the calcified lesions of tuberculosis do show up clearly. So the ability to make detailed lung images like those of Fig. 1 has been a welcome innovation, and I want to review some of the curiosity-driven basic research that has made it possible. Nuclear magnetic resonance (NMR), which was discovered in 1946 by E. M. Purcell, H. C. Torrey and R. V. Pound [4], and independently by F. Bloch, W. W. Hansen and M. Packard [5], makes use of the small voltages induced in a pickup coil by the changing magnetic flux from nuclear spins, which are precessing about a magnetic field. In NMR experiments, the signal voltage is proportionM to the static magnetization density of the nuclei, which can be written as M = NpIP , (1) where N is the number density (spins/cma), P l is the magnetic moment of a nucleus of spin I, and the polarization P measures how nearly the spins are lined up with the magnetic field. For simple spin-l/2 nuclei like those of ordinary hydrogen atoms, 3He or 129Xe atoms, the thermal-equilibrium polarization P at a temperature T and in a magnetic field B is P=tanh(~T

B)

(2)

Because the nuclear moment # I is so small, the nuclear polarization (2) is very small at room temperature, even in very large magnetic fields. For example, for a proton in a magnetic field of 1 T, the polarization is P = 3.4 x 10 -6. However, the number density N of (1) is often so large (for example N = 6.7 x 1022 c m - 3 in water) that this weak thermal polarization is adequate to produce good signals. The lung images of Fig. 1 were made possible by using lasers to increase the small thermal polarization described by (2) by some five orders of magnitude, to values on the order of P ~ 0.3. Therefore, the signal per aHe nucleus in the lung of the volunteer of Fig. 1 was 100,000 times stronger than the signal per proton, and this enormous signal enhancement m o r e than made up for ~, 2,000 times smaller density of 3He nuclei in the lung compared to the density of protons in human tissue like muscle or the brain. Among the many applications of NMR, magnetic resonance imaging (MRI) is perhaps the most striking to the average person. In 1973 Paul Lauterbur

124

William Happer

1 Slowly processing

proton spin

Distance

Rapidly pre~ essing proton spin

RF signal

intensity

Fig. 2. Basic idea of magnetic resonance imaging [6]. The patient is placed in an inhomogeneous magnetic field and the protons in the body are tipped with appropriate radiofrequency pulses. As the protons precess about the field, the more slowly precessing protons in the patient's foot produce lower-frequency radio waves, and the more rapidly precessing protons of the patients head produce higher-frequency radio waves. In practice, very elegant pulse sequences are used to make the best images for diagnostic purposes. [6] pointed out that it should be possible to use magnetic resonance in an inhomogeneous magnetic field to produce images of the distribution of nuclei in a three-dimensional object. Rather than struggling to eliminate all magnetic field inhomogeneities, one applies carefully controlled inhomogeneities to map spatial information onto the free induction decay transients and spin echos of classical NMR. The essence of Lauterbur's idea is sketched in Fig. 2. The high polarization of the 3He nuclei used to make the image of Fig. 1 has its origins in photons of light and spin-exchange collisions. In 1948, Albert Kastler [7] showed that it is possible to transfer much of the spin polarization of circularly polarized photons to the electron and nuclear spins of atoms. Kastler called this process optical pumping. The great majority of optical pumping work is done with the alkali-metal vapors, mercury vapor or metastable helium atoms [8]. Although the polarized 3He gas used to make the image of Fig. 1 was produced by spin exchange with optically pumped rubidium vapor, I should mention that the research team of Professor Ernst OLten [9], a classmate of Gisbert zu Putlitz, has developed such fantastic equipment for pumping metastable 3He, that they make equally good images of human lungs [10] with this alternate method. Fittingly enough, the first images of the Otten

Medical NMR Sensing with Laser-Polarized 3He and 129Xe

]25

group were obtained in Heidelberg, in collaboration with the a group led by Mich~le Leduc and Pierre-Jean Nacher of the Ecole Normale Sup~rieure in Paris. Atoms that can be efficiently optically pumped have several features in common. The polarized atoms have spherically symmetric pumped states, 2S states for the alkali-metal atoms, a 1S state for mercury atoms, and a 3S state for metastable helium atoms. Such electronic states are exceptionally resistant to electron or nuclear spin depolarization during collisions because their electric charge distributions are nearly perfectly round. Furthermore, all of these systems can be pumped with near-visible light, and they have appropriate atomic number densities to absorb most of the pumping light at convenient temperatures. Containing the gases and vapors presents manageable materials problems. In our group at Princeton, we have mostly made use of the rubidium atoms discovered at Heidelberg by Bunsen and Kirchhoff. A typical arrangement for optically pumping rubidium vapor is sketched in Fig. 3. Not shown is the source of the static magnetic field H, which is often only a few Gauss produced by Helmholtz coils and designed to prevent spin depolarization by stray 60 Hz fields or the ambient field of the earth. A simple oven is used to keep the cell, containing a few droplets of rubidium metal, at a constant temperature, usually greater than 80 °C and less than 150°C. This ensures that the density of Rb atoms in the cell is adequate to absorb the light and to collide frequently enough with 3He or 129Xe atoms to efficiently transfer spin to their nuclei. The number density of Rb atoms is typically 1011 to 1014 atoms cm -3. More intense pumping light is needed to handle the higher number densities. The sample cell also contains the noble gas which is to be polarized by spin-exchange and a chemically inert quenching gas, normally nitrogen, to prevent reradiation of light from the excited atoms. Since the reradiated light would be nearly unpolarized and can be absorbed by the Rb atoms, it would optically depump the atoms. The damage done by the reradiated photons becomes more severe at high Rb vapor densities where the reradiated photon can be scattered several times and depolarize several atoms before escaping from the cell. The detailed atomic physics of optical pumping for the arrangement of Fig. 3 is shown in Fig. 4. We consider an imaginary alkali-metal atom for which the nuclear spin is zero. All real alkali-metal atoms have non-zero nuclear spins, but the basic mechanisms of optical pumping and spin exchange are qualitatively similar. Circularly polarized D~ resonance light is incident on the atoms. The light can excite the atoms from the 2S1/2 ground state into the 2P!/2 first excited state. In both the ground state and the excited state, the electronic angular momentum of the atom can point up or down. This is represented by two Zeeman sublevels, which are split by their respective Larmor frequencies when the atom is in an external magnetic field. Since the atom must absorb both the energy and the spin angular momentum of the photon, transitions are only possible from the spin-down ground-state sub-

126

WilliamHapper n

Illuminated

Dark Volume

Magnetic Field

Volume ~ .................

~ "- .

~-~

(•)Rb @ Xe

sI

JJ

C3N

2

Pumping Light Sample Cell Fig. 3. Optical pumping of an optically thick vapor of rubidium atoms (see text).

level to the spin-up excited-state sublevel. The noble gas and the quenching gas collisionally transfer atoms between the sublevels of the excited state. When a quenching collision finally deexcites the atom, both ground state sublevels will be repopulated with nearly equal probability. Since the atom had - 1 / 2 units of spin angular momentum before absorbing the photon and 0 units of spin angular momentum after being quenched from the excited state, each absorbed photon deposits 1/2 a unit of spin angular momentum in the vapor. The precise frequency of the pumping light is not important, so lasers or lamps with very broad spectral bandwidths can be used for pumping. Even though the alkali-metal vapor is often many optical depths thick, intense circularly polarized laser light can still illuminate most of the cell [11], as indicated in Fig. 3. In the illuminated part of the cell most of the alkali-metal atoms are pumped into the non-absorbing +1/2 sublevel of the ground state and the spin polarization is nearly 100%. In the dark volume where no light penetrates, the alkali-metal spin polarization is nearly zero, but some small spin polarization may be maintained by spin exchange with the polarized nuclei of the noble gas. Because of its long relaxation time, the spin polarization of the noble gas is nearly the same throughout the cell. The boundary between the illuminated and dark volumes of the cell is about one optical depth thick. In a well-designed system, the gas composition, the cell temperature and the laser intensity are matched to ensure that most of the cell is illuminated.

Medical NMR Sensing with Laser-Polarized 3He and 120Xe

]27

Collisional Mixing

-1/2~

1/2

50%

2p1/2

50%

Quenching by N 2

/ [_ -1/2

2S112

1/2

Fig. 4. Optical and collisiona] transitions involved in the optical pumping of an alkali-metal atom with D1 fight at high gas pressure (see text).

A key step forward was the discovery by T. R. Carver, M. A. Bouchiat and C. M. Varnum [12] in 1963 that a substantial fraction of the electron spin angular m o m e n t u m of optically pumped alkali-metal atoms could be transferred to the nucleus of 3He by spin exchange collisions. In 1978 B. C. Grover [13] and his colleagues at Litton Industries reported the extension of the spin exchange method from 3He to isotopes of xenon and krypton. Extensive studies of the physics of spin exchange between the electrons of alkali-metal atoms and noble-gas nuclei were subsequently carried out by our group at Princeton University [14]. As indicated in Fig. 5, spin exchange from the alkali-metal atomic electron to the nucleus of the noble gas can occur either in a three-body collision (Fig. 5A), for which a third body carries away the binding energy of the van der Waals molecule which is formed, or in a simple binary collision (Fig. 5B). The main observable difference between the two types of collisions is that the relaxation and spin transfer caused by the van der Waals molecules, while extremely efficient, can be suppressed with external magnetic fields of a few hundred to a few thousand Gauss. The relaxation due to binary collisions is hardly affected by magnetic fields which are readily available in the laboratory [14]. The relaxation due to van der Waal molecules also depends nonlinearly on the gas pressures in the cell [14]. The three-body collisions can account for much of the spin exchange for the heavier noble gases, Kr, Xe or Rn,

128

Wilfiam Happer B

Fig. 5. Polarization by spin-exchange collisions of optically pumped Rb atoms with the nuclei of noble gases. Three-body collisions (A), leading to the formation of weakly-bound van der Waals molecules, are very important for spin-exchange polarization of 129Xe. Binary collisions (B) are the sole polarization mechanism for 3He, and they are also very important at high gas pressures for 129Xe.

but binary collisions are the dominant spin exchange mechanism for the light gases He and Ne, which have particularly weak van der Waals attraction for alkali-metal atoms. The transfer of angular m o m e n t u m from the electron spin S of the alkalimetal a t o m to the nuclear spin I of a noble-gas a t o m during a collision is mediated by the Fermi contact interaction [15] aS-I

.

(3)

Bernheim [16] first pointed out that a large fraction of the spin angular m o m e n t u m S of the alkali-metal atoms is lost to the rotational angular mom e n t u m N of the alkali-metal a t o m and its collisional partner through the spin-rotation interaction 7S-N

.

(4)

The fraction [14] e of angular m o m e n t u m which is collisionally transferred to the nucleus of the noble gas is ot2 _

(5) +

Medical NMR Sensing with Laser-Polarized aHe and 12~Xe

129

For example [14], for the pair 129Xe Rb, the root mean squared values of the coupling coefficients are a / h = 38 MHz and "/N/h = 121 MHz so the efficiency of spin exchange would be about 4%, that is, 1/7/= 25 photons are needed to produce each fully polarized t29Xe nuclear spin. Especially for the lighter noble gases 3He and 21Ne, the spin-exchange probability per collision is relatively small, and it is advantageous to operate with as high a number density of alkali-metal atoms as possible to speed the growth of polarization in the noble-gas nuclei. At high densities, there are frequent spin exchange collisions between alkali-metal atoms A and B A(I") + B(J,) -+ A($) + B ( t ) .

(6)

The up and down arrows indicate the orientations of the electron spins. The cross section for electron-electron spin exchange collisions [17] are on the order of 10 -14 cm -2, so the exchange rates can be on the order of 104 s -1 at alkalimetal atomic number densities of 1014 cm -3. Electron-electron exchange is much faster than any other spin relaxation rate, but since such collisions conserve the total spin of the vapor they do not interfere with the polarization of noble-gas nuclei. Unfortunately, a small fraction of the collisions between alkali-metal atoms transfer spin angular to the translational angular momentum of the vapor [18] in spin-dependent collisions of the form A(~) + B($) --+ A($) + B($) .

(7)

The angular m o m e n t u m losses are most pronounced for vapors of the heavy alkali metal cesium, less for rubidium, and still less for potassium [19]. For the important case of aHe gas, in which the electron-nucleus spin exchange interaction (3) and the spin-rotation interaction (4) are both very small, it is spin-destroying collisions between alkali-metal atoms like those of (7) that set the practical upper limit on the alkali-metal vapor pressure and on the speed with which the 3He can be polarized. To date, the basic physics of the loss mechanism (7) has remained a mystery, with current theories predicting much smaller loss rates than those that are experimentally measured. Although Kastler and his contemporaries did the first optical pumping experiments with a few hundred microwatts of useful resonance light from lamps, it is now straightforward to get watts of useful laser light for optical pumping experiments. A watt of 7947 A Rb resonance radiation is 4 x l0 Is photons per second. Since one unit of angular m o m e n t u m h is added to the electron spin of the vapor of alkali-metal atoms for every two photons absorbed, 4 x 1018 fully polarized electron spins can be produced per second. In favorable cases, about 10% of the electron spin polarization can be transferred by spin exchange t o nuclear spin polarization of noble gases in the same container with the alkali-metal vapor. The spin can be accumulated for a time period on the order of T1, the longitudinal spin relaxation time of the noble gases. 2"1 can be hours or longer for spin-l/2 species like 129Xe or 3He,

130

William Happer

so some 10 ~1 highly polarized spins can be produced. The exceptionally long values of T1 for these gases are essential to the success of gas imaging, but they are the least understood part of the physics and most in need of further basic research. With more powerful tunable lasers, for example, diode arrays with tens or even hundreds of watts of power, it would be possible to produce many grams of solid 129Xe with nearly complete nuclear polarization. Like so many other useful new technologies, magnetic resonance imaging of lungs resulted from years of curiosity-driven, basic research, much of it done or inspired by zu Putlitz and his talented colleagues at Heidelberg. As we are about to move into the twenty-first century, let us hope that society will continue to find ways to support basic research for all the benefits it brings, intellectual, moral and practical.

References [1] H. Kopfermann, Nuclear Moments, Academic Press, New York (1958). [2] James R. MacFall et al., Radiology 200, 553 (1996). [3] M.S. Albert, G.D. Cates, B. Driehuys, W. Happer, B. Saam, C.S. Springer, Jr. and A. Wishnia, Nature 370, 199 (1994). [4] E.M. Purcell, H.C. Torrey and R.V. Pound, Phys. Rev. 69, 37 (1946). [5] F. Bloch, W.W. Hansen and M. Packard, Phys. Rev. 70, 474 (1946). [6] P.C. Lauterbur, Nature 242, 190 (1973). [7] A. Kastler, J. Phys. Radium 11, 225 (1950). [8] G.K. Walters, F.D. Colgrove and L.D. Schearer, Phys. Rev. Lett.8,439 (1962). [9] J. Becker et al. Nuclear Instruments and Methods in Physics Research A 346, 45 (1994). [10] P. Bachert et al., Magnetic Resonance in Medicine 36, 192 (1996). [11] A.C. Tam and W. Happer, Phys. Rev. Lett. 43, 519 (1979). [12] M.A. Bouchiat, T.R. Carver and C.M. Varnum, Phys. Rev. Lett. 5, 373 (1960). [13] B.C. Grover, Phys. Rev. Lett. 40, 391 (1978). C.H. Volk, T.M. Kwon, and J.G. Mark, Phys. Rev. A 21, 1549 (1980). [14] N.D. Bhaskar, W. Happer and T. McClelland, Phys. Rev. 49, 25 (1982); N.D. Bhaskar, W. Happer, M. Larsson and X. Zeng, Phys. Rev. Lett. 50, 105 (1983); W. Happer, E. Miron, S. Schaefer, D. Schreiber, W. A. van Wijngaarden and X. Zeng, Phys. Rev. 29, 3092 (1984); X. Zeng, Z. Wu, T. Call, E. Miron, D. Schreiber and W. Happer, Phys. Rev. 31, 260 (1985); S.R. Schaefer, G.D. Cates, Ting-Ray Chien, D. Gonatas, W. Happer and T.G. Walker, Phys. Rev. 39, 5613 (1989). [15] E. Fermi and E. Segrr, Z. Physik 82, 729 (1933). [16] R.A. Bernheim, J. Chem. Phys. 36, 135 (1962). [17] W. Happer, Rev. Mod. Phys. 44, 169 (1972). [18] N.D. Bhaskar, J. Pietras, J. Camparo and W. Happer, Phys. Rev. Lett. 44, 930 (1980). [19] R.L. Knize, Phys. Rev. A 40, 6219 (1989).

Test of Special Storage Ring

Relativity

in a Heavy

Ion

G. Huber 1 , R. Grieser l, P. Merz 1 , V. Sebastian 1, P. Seelig 1, M. Grieser 2, R. Grimm 2, D. Habs 2, D. Schwalm 2, T. K/ihl 3 1 Institut fiir Physik, Universit~it Mainz, D-55099 Mainz, Fed. Rep. Germany 2 Max Planck Institut ffir Kernphysik Heidelberg, D-69029 Heidelberg, Fed. Rep. Germany 3 Gesellschaft fiir Schwerionenforschung, D-64220 Darmstadt, Fed. Rep. Germany

1

Introduction

Experiments can be described in any inertial frame using the space time transformation of the special theory of relativity (SRT) as far as gravitational effects can be neglected. The existence of a preferred cosmological frame of reference [1] would violate the underlying symmetries of the theory. The natural candidate for such a preferred frame would be the the 3 K cosmic background radiation horizon with a relative velocity to the solar system of v' = 3 0 0 k m / s [2, 3]. All known experiments are in agreement with the special theory of relativity. Local deviations due to the general theory of relativity are beyond the the limitations of present experiments. Nevertheless, it is an experimental challenge to establish new upper limits for any deviation from the special theory of relativity. In a historical key experiment in 1938 Ires and Stilwell [4] have determined the Doppler shifted spectrum of a fast hydrogen beam as a function of its kinetic energy. In this experiment the time dilation factor

sRT = (1 -

,

(1)

where ~ = v/c is the atoms' velocity v measured in units of the speed of light c, was tested for any additional terms which could be present as a result of a hypothetical deviation from the Lorentz transformation between two inertial reference frames. Mansouri and Sexl [5] have developed a test theory for deviations induced by the presence of any preferential frame with relative velocity/3~ with respect to the laboratory and a moving clock with relative velocity/3 in the laboratory frame. These small and hypothetical deviations can be expressed in general as a function f(/3,/3') which modifies the time dilation factor to 7 = (1 - j32) - 1 / 2 . (1 + a - f ( / 3 , / 3 ' ) ) where a is a parameter measuring this deviation ( a = 0 for SRT).

(2)

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G. Huber et al.

In the original experiment a could be determined to < 0.01. Modern modifications have used highly relativistic hydrogen beams. At the Los Alamos Meson Physics Facility (LAMPF) in New Mexico, USA, a limit of a < 1.9.10 -4 was found for/3 = 0.84 [6]. At the NASA Jet Propulsion Laboratory an upper limit of a < 1.8.10 -4 could be established with/3 = 0.0016 [7]. Among the most accurate tests, MSt3bauer rotor experiments using fast moving disks yielded a < 10 -5 [8]. The space born experiment "Gravity Probe A", employing highly stable hydrogen maser clocks, determines from the frequency residuals between experiment and theory an upper limit of 0" < 2.1.10 -6 [9]. It also produced today's most stringent test on gravitational red shift [1]. In a laser spectroscopy experiment using the 3s[~]2-4d 30 , [3]3 5 0 transition in 2°Ne atoms at/3 = 3.6-10 -3 the limit for the existence of any preferred frame of reference was set to 0" < 1.4.10 -6 [10]. An atomic two-photon transition is induced by two counter-propagating laser beams. This technique is considered "Doppler free" spectroscopy, since the first order terms (1 +/3) and (1 - / 3 ) cancel and the resonance condition is given through u0 = 2 7//LaserWith the realization of heavy ion storage rings like the Test Storage Ring (TSR) in Heidelberg a new generation of experiments became feasible. A relativistic 7Li+ ion beam with well defined velocity, i.e. small m o m e n t u m spread, can be used for high resolution laser spectroscopy at the TSR. These ions had been investigated before at many places with high accuracy as they are fundamental two electron systems, e.g. in the laboratory of G. zu Putlitz [11]. The 7Li+ ions are stored as fast moving clocks at 13.3MeV particle energy corresponding to/3 = 0.064 . Two transitionswith frequencies vl and v2 in the rest frame are used in the experiment, as explained in Sec. 2. The first one is observed with a laser beam parallel to the ion beam, the second one with an antiparallel laser beam. In the laboratory frame, the resonance frequencies are Doppler-shifted to Ua and ~v, respectively. They are compared with two clocks at rest, realized by single-mode lasers stabilized to calibrated transitions in molecular 12712, in order to determine the frequencies ua and u v on an absolute scale. According to SRT they are related to the resonance frequencies vl and v2 in the particle rest frame by .p = va3`(1 - / 3 ) va = v27(1 +/3)

(3)

In the special theory of relativity the relation between the clock rates in the moving system and the laboratory system is -avp = v1~'2

(4)

since 3,2(1-/3)(1 +/3) = 1, independent of the clock's velocity. Any deviation of the time dilation factor from Eq. (1) may be written as '~ = 3,SRT ( I -'1- 0"/3 2 "l- higher order corrections ) .

(5)

Test of Special Relativity in a Heavy Ion Storage Ring

133

This could be observed experimentally through a violation of Eq. (4) which can be extended to read [5]

(6)

v.vp = vlv2 (1 + 2~/3 2 + ...)

A detailed analysis in the framework of Mansouri's and Sexl's test theory taking into account the kinematic situation in the storage ring experiment has been worked out by Kretzschmar et al. [12], resulting in a modification of Eq. (4) (7)

vavp : vlv2 ( 1 + 2a(/3 2 q- 2/3~' cos(K2)) )

where/2 is the angle between the velocities/3 and/3~. Usually/3r is identified with the velocity relative to the 3 K background. Evidently, an increase in/3 (at the T S R / 3 = 0.064 corresponds to v ,-* 19000km/s) always increases the sensitivity to the parameter a according to Eq. (7).

2

Result

of a Doppler

Effect Experiment

at t h e T S R

The experimental procedure is based on saturation spectroscopy with 7Li+ ions in a collinear excitation [t3]. The 7Li+ ion has a helium like spectrum and, similar to helium, only the triplet system with its high lying metastable 3S1 state is suitable for optical laser spectroscopy. Due to the hyperfine interaction all states in the triplet system exhibit a large hyperfine splitting, as can be seen in Fig. 1 with the relevant l s 2 s 3S1 --+ 3 P 2 line. The transitions F = 5/2 ++ F r --- 5/2 ++ F --- 3/2 are used for saturation spectroscopy. With their common upper level they form a "A" system which shows strong fluorescence when both transitions are driven in the same velocity class of the ions. The 7Li+ ions are partially excited into the metastable 3S1 state in the stripper of the Heidelberg TANDEM accelerator. After injection into the T S R the ion beam is cooled by Coulomb interaction with an isochronously cooled electron beam. The 7Li+ ion beam exhibits a narrow, well defined velocity distribution and is overlapped with two co- and counterpropagating laser beams from a single mode argon ion laser at A = 515nm and a single mode dye laser at )~ = 585 nm to excite the A resonance. This laser beam passes through a single mode fiber into the experimental area. Special expansion optics is needed to direct the beam through the 10 m long experimental section of the T S R where it is back reflected to reenter the optical fiber. The laser frequencies are determined by two auxiliary saturation spectroscopy setups for recording precisely calibrated resonances in molecular 12712. The argon ion laser is tuned to a wavelength standard, where the optical frequency is given by [14] and the wavelengths of the 12712 resonances close to the frequency where the dye laser excites the A resonance together with the argon

134

G. Huber et al.

eV

Ionization Limit

v5.8 ~ " / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / F 7/2 6t,3

sD n43 s_~~ [11.7758(05)GHz "' I ~-',i 9"6087(;~0) ~-H; \I

;k=545.5 nm

5.2035(05) _CH_~

.....

I-

.....

/_

v=546466.91879 4.0) GHz /

_ .5/2 3/2

-

- i/2

/

59.0

~

\

11.890018(40)C n z

k____1~So

3/2 1/2 3/2

Fig. 1. Transitions in 7Li+ relevant for the experiments at TSR. The closed two level system F = 5/2 --+ F ' = 7/2 and the A-system transitions F : 5/2 -+ F ' : 5/2 and F = 3/2 --+ F' = 5/2 are indicated. Most of the data are given by [11].

ion laser have been calibrated at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig relative to the 12712 stabilized helium-neon laser to a---~-~= 1.3- 10 - l ° [15]. These reference signals are recorded simultaneously with the A resonance as shown in Fig. 2. The resonance position of the maximum was determined to ua = 512 667 592.4 (3.1) MHz

(8)

where the error reflects the uncertainty of systematic contributions. The observed linewidth of this resonance is twice the value resulting from various broadening effects present in the laser excitation. The further broadening seems to be mainly due to wave front distortions in the laser beams, as can be shown in a numerical solution of the optical Bloch equations for ions moving in the T S R at typical parameter settings of the ion beam optics. An uncertainty of 2.7 MHz for the position of the line center has to be taken into account. Sources for systematic uncertainties are possible light shifts and recoil-induced shifts, the method for determining the laser frequency and the uncertainty in the angular alignment between lasers and ion beam respectively. All these add up to a total uncertainty of Au = +3.1 MHz .

Test of Special Relativity in a Heavy Ion Storage Ring

I

,---~3000

I

I

I

I

135

i

N

2500-

~2000 I

1500 0

1000 500 0

0 -300

I

I

100 200 -200 -100 0 Detuning f r o m i - c o m p o n e n t

300 400 [MHz]

Fig. 2. Spectrum of the A-resonance with the simultaneously detected 12T12fines.

The measured frequency ua can be compared with the frequency b'a,SRT calculated according to Eq. (4) with the known frequencies. The value U~,SRT = 512 667 588.2(8) MHz

(9)

differs from the experimental value u~ by 4.3(3.2) MHz. Within two standard deviations the result is compatible with zero, and with Eq. (7) the corresponding limit of a < 8 - 10 -7 is deduced. 3

Laser Cooling

and Bunching

for Precision

Experiments

So far, the test of special theory of relativity at the TSR has been performed with an electron cooled ion beam with a longitudinal momentum spread of Ap/p = 5.10 -5 and a beam of diameter 1 mm consisting of ions in both singlet and triplet states of 7Li+. With additional laser cooling, the longitudinal momentum spread of the stored lithium beam has been reduced significantly to Alp/p = 1- 10 -6 at the TSR [16, 17]. The applied cooling scheme using an Ar + laser and an induction accelerator allows in a natural way for a separation of the singlet and triplet ions in phasespace. Moreover, it is possible to cool a radio frequency (RF) bunched ion beam with a laser [18]. In this case, the particle velocity and phase are known with high precision, which leads to the expectation of a significant increase in sensitivity for the test experiment.

136

G. Huber et al.

0.00020

,

I

I

I

I

I

I

I

I

I

-'2

-'1

(3 A¢

I

2

0.0001,5 0.00010

-

0.00005 0.00000 -0.00005

-

-0.00010 -0.00015 -0.00020

-3 22 -'i

-3

&¢

3

Fig. 3. Phasespace trajectories for RF-bunched ion beams. On the left a hot beam is bunched resulting in synchrotron oscillations. On the right additional laser cooling is applied, leading to a damping of the ion's motion. Ap and A¢ correspond to the momentum- and phase deviation of the particle's trajectory relative to the RF phase. The calculation has been carried out with a RF amplitude corresponding to the maximum laser cooling force.

The principle of laser cooling of a bunched ion beam is shown in Fig. 3. Without laser the particles are subjected to the voltage U of the RF cavity resulting in a net force which depends on the particle's phase relative to the phase of the RF frequency :

dp = eU sin(A¢)/2~:ns dt

(10)

with the radius Rs of the 'sollbahn' and the particle's phase difference A¢ relative to the phase of the oscillating voltage. The corresponding trajectories in phasespace can be calculated [19] and the result is shown on the left side of Fig. 3. The influence of an additional collinearly aligned laser is illustrated on the right of Fig. 3. The additional force of the cooling laser is [20] dp _ hk r

dt

s

(11)

2 I+S

with the absolute value of the wave vector k =J k J, the natural decay rate F of the optical transition and the velocity dependent saturation parameter

S

=

n2/2 (n~ + (r12)~)

(12)

Test of Special Relativity in a Heavy Ion Storage Ring

137

where $2 denotes the Rabi frequency of the optical transition and z~ ~- w0 --WLaserT(1 -- t3) Due to the velocity dependence of the laser cooling force (Eq. (11)) a damping of the longitudinal synchrotron oscillation in the ion b e a m occurs. In this simplified picture, the bunch length is strictly related to the longitudinal temperature. In a more sophisticated approach space charge forces of the b e a m that are limiting the bunch length significantly have to be taken into account [18]. At the T S R this bunched laser cooling has been observed with 7Li+ by time resolved detection of the fluorescence light. The spatial resolution of the ion position inside the bunched ion b e a m is achieved with a time resolved signal registration. The fluorescence of the laser cooled and bunched ions is detected. With this scheme, which is phase synchronized to the RF frequency, a time resolved spatial resolution of 0.17m in the moving ion b e a m is obtained. Moreover, the demultiplexing of the fluorescence light allows for additional background suppression by a factor of more than 5. With this device the integration time necessary for the detection of one single ion reduces to a fraction of a second.

800 ..~ 600

4oo

~oo

~_.~..%.~

~

.

~

z

~

~

Fig. 4. Recorded longitudinal phase space distribution function of laser cooled and bunched 7Li+ ions at the TSR. The position AS in the confining RF potential is measured by a time resolved and synchronous signal detection relative to the RF phase. The momentum deviation is calibrated during the scan of an additional dye laser using the Doppler effect. At AS = 0 a constant count rate for every value of Ap/p is visible. These photons are produced by the fixed frequency cooling laser.

138

G. Huber et al.

The velocity distribution function is determined with the optical Doppler effect. With an additional scanning laser the m o m e n t u m distribution Ap/p can be estimated from the detuning of the scanning laser. Since the optical transition frequency in the 7Li+ rest system is known with sufficient accuracy, the mean velocity can be calibrated with a precision of Av/v < 10 -7. A typical spectrum recorded with a 7Li+ beam at the T S R is shown in Fig. 4.

4

Outlook

A bunched and cooled ion beam represents an ensemble of clocks moving at fixed velocity and phase, which can be used to probe the structure of local space time. Similar to the quality of the ion beam the interacting laser beams will have to meet highest phase front performances. The precision of the frequency measurement will be increased with a new laser spectrometer which is presently being developed at the Universit/it Mainz. Due to the preparation of the laser cooled and bunched ion beam, the AC stark shift and the photon recoil can be precisely controlled and a sensitivity of a _< 1.5 10 -7 can be expected. Of course, a dramatic increase in sensitivity to the value of a can be expected by performing this experiment at the Experimental Storage Ring (ESR) at the Gesellschaft fiir Schwerionenforschung (GSI) in Darmstadt. With an ion velocity of/3 = 1/3, va is shifted to va = vo/v/2 (,.~ 776 nm) and up = 2va. In this case one single frequency standard can be used. Its fundamental frequency can serve as reference for the antiparallel excitation and for parallel excitation the frequency can be compared to a frequency doubled beam generated from the light of the same reference source. Using the velocity dependence of the correction term in Eq. (7), the overall sensitivity to violations of special theory of relativity can be increased by a factor of about 30. -

References [1] C.M. Will, 'Theory and experiment in gravitational physics', Cambridge University Press (1993) [2] A.A. Penzias, R.H. Wilson, Astrophys. Journ. 142, 419 (1965) [3] G.F. Smoot, M.V. Gorenstein, Phys. Rev. Lett. 39, 898 (1977) [4] H.E. Ires and G.R. Stilwell, J. Opt. Soc. Am. 28, 215 (1938) [5] R. Mansouri und R. Sexl, Gen. Rel. and Grav. 8(7), 497, 515, 809 (1977) [6] D.W. MacArthur, K.B. Butterfield, D.A. Clark, J.B. Donahue, P.A.M. Gram, H.C. Bryant, C.J. Harvey, W.W. Smith, G. Comtet, Phys. Rev. Lett. 56, 282

(1986) [7] T.P. Krisher, L. Maleki, G.F. Lutes, L.E. Prima.s, R.T. Logan, J.D. Anderson, C.M. Will, Phys. Rev. D. 42, 731 (1990) [8] D.C. Champeney, G.R. Isaac, A.M. Khan, Phys. Lett. 7, 241 (1963)

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[9] R.F.C. Vessot, M.W. Levine, E.M. Mattison, E.L. Blomberg, T.E. Hoffman, G.U. Nystrom, B.F. Farrel, R. Decher, P.B. Eby, C.R. Baugher, J.W. Watts, D.L. Teuber, F.D. Wills, Phys. Rev. Lett. 45, 2081 (1980) [10] E. Riis, L.-U. A. Andersen, Nis Bjerre, Ove Poulsen, S. A. Lee, J. L. Hall, Phys. Rev. Lett. 60, 81 (1988) [11] J. Kowalski, R. Neumann, S. Noethe, K. Scheffzek, H. Suhr, G. zu Putlitz, Hyperf. Interact. 15/16, 159 (1983) 70, 251 (1993) [12] M. Kretzschmar, Z Phys. A 342,463 (1992) [13] R. Grieser, R. Klein, G. Huber, S. Dickopf, I. Klaft, P. Knobloch, P. Merz, F. Albrecht, M. Grieser, D. Habs, D. Schwalm, T. Kiihl, Appl. Phys. B 59, 127 (1994) [14] Documents concerning the New Definition of the Metre, Metro/ogia 19, 163 (1984) Comit~ International des Poids et M6sures (CIPM), 8U session (1992), Recommendation 3 [15] R. Grieser, G. BSnsch, S. Dickopf, G. Huber, R. Klein, P. Merz, A. Nicolaus, H. Schnatz, Z. Phys. A 348, 147 (1994) [16] S. SchrSder, R. Klein, N. Boos, M. Gerhard, R. Grieser, G. Huber, A. Karafilfidis, M. Krieg, N. Schmitt, T. Kiihl, R. Neumann, V. Balykin, M. Grieser, D. Habs, E. Jaeschke, D. Kr~imer, M. Kristensen, M. Music, W. Petrich, D. Schwalm, P. Sigray, M. Steck, B. Warmer, A. Woff, Phys. Rev. Lett. 64, 2901

(1990) [17] W. Petrich, M. Grieser, R. Grimm, A. Gruber, D. Habs, H.-J. Miesner, D. Schwalm, B. Wanner, H. Wernoe, A. Wolf, R. Grieser, G. Huber, R. Klein, T. Kiihl, R. Neumann, S. SchrSder, Phys. Rev. A. 48, 2127 (1993) [18] J.S. Hangst, J.S. Nielsen, O. Poulsen, P. Shi, J.P. Schiffer, Phys. Rev. Lett. 74, 4432 (1995) [19] J. LeDuff, in CERN 94-01 (1994) [20] C. Cohen-Tannoudji, 'Atomic motion in laser light', in 'Fundamental systems in quantum optics', J. Dalibard et al. (eds.), North Holland (1992)

R e s o n a n c e F l u o r e s c e n c e of a Single Ion J. T. HSffges, H.W. Baldauf, T. Eichler, S.R. Helmfrid and H. Walther Max-Planck-lnstitut f/it Quantenoptik and Sektion Physik der Universitiit Miinchen 85748 Garching, Fed. Rep. of Germany Resonance fluorescence of atoms is a basic process in radiation-atom interactions, and has therefore always generated considerable interest. The methods of experimental investigation have changed continuously due to the availability of new experimental tools. A considerable step forward occurred when tunable and narrow band dye laser radiation became available. These laser sources are sufficiently intense to easily saturate an atomic transition. In addition, the lasers provide highly monochromatic light with coherence times much longer than typical natural lifetimes of excited atomic states. The laser light, when scattered off atoms from a well collimated atomic beam, leads to an absorption width being practically the natural width of the resonance transition, and it became possible to investigate the frequency spectrum of the fluorescence radiation with high resolution. However, the spectrograph used to analyze the reemitted radiation was a Fabry-Perot interferometer, the resolution of which did reach the natural width of the atoms, but was insufficient to reach the laser linewidth, see e.g. Hartig et al. (1976) and Cresset et al. (1982). More recently, ion traps have allowed the study of the fluorescence from a single laser cooled particle which is practically at rest, thus providing the ideal case for spectroscopic investigation. The other essential ingredient for achievement of high resolution is the measurement of the frequency spectrum by heterodyning the scattered radiation with laser light. Such an optimal experiment with a single trapped Mg+ ion is described in this paper. The measurement of the spectrum of the fluorescent radiation at low excitation intensities is presented. Furthermore, the photon correlation of the fluorescent light has been investigated under practically identical excitation conditions. The comparison of the two results shows a very interesting aspect of complementarity since the heterodyne measurement corresponds to a "wave" detection of the radiation whereas the measurement of the photon correlation is a "particle" detection scheme. It will be shown that under the same excitation conditions the wave detection provides the properties of a classical atom, i.e. a driven oscillator, whereas the particle or photon detection displays the quantum properties of the atom. Whether the atom displays classical or quantum properties thus depends on the method of observation. The spectrum of the fluorescence radiation is given by the Fourier transform of the first order correlation function of the field operators, whereas

142

J . T . HSffges, H.W. Baldauf, T. Eichler, S.R. Helmfrid and H. Walther

the photon statistics and photon correlation is obtained from the second order correlation function. The corresponding operators do not commute, thus the respective observations are complementary. Present theory on the spectra of fluorescent radiation following monochromatic laser excitation can be summarized as follows: fluorescence radiation obtained with low incident intensity is also monochromatic owing to energy conservation. In this case, elastic scattering dominates the spectrum and thus one should measure a monochromatic line at the same frequency as the driving laser field. The atom stays in the ground state most of the time and absorption and emission must be considered as one process with the atom in principle behaving as a classical oscillator. This case was treated on the basis of a quantized field many years ago by Heitler (1954). With increasing intensity upper and lower states become more strongly coupled leading to inelastic components, which increase with the square of the intensity. At low intensities, the elastic part dominates since it depends linearly on the intensity. As the intensity of the exciting light increases, the atom spends more time in the upper state and the effect of the vacuum fluctuations comes into play through spontaneous emission. An inelastic component is added to the spectrum, and the elastic component goes through a maximum where the Rabi flopping frequency 12 -- Fly/'2 (F is the natural linewidth) and then disappears with growing 12. The inelastic part of the spectrum gradually broadens a s / 2 increases and for 12 > F/2 sidebands begin to appear. For a saturated atom, the form of the spectrum shows three well-separated Lorentzian peaks. The central peak has width F and the sidebands which are each displaced from the central peak by the Rabi frequency are broadened to 3F/2. The ratio of the height of the central peak to the sidebands is 3:1. This spectrum was first calculated by Mollow (1969). For other relevant papers see the review of Cresser et al. (1982). The experimental study of the problem requires, as mentioned above, a Doppler-free observation. In order to measure the frequency distribution, the fluorescent light has to be investigated by means of a high resolution spectrometer. The first experiments of this type were performed by Schuda et al. (1974) and later by Walther et al. (1975), nartig et al. (1976) and Ezekiel et al. (1977). In all these experiments, the excitation was performed by singlemode dye laser radiation, with the scattered radiation from a well collimated atomic beam observed and analyzed by Fabry-Perot interferometers. Experiments to investigate the elastic part of the resonance fluorescence giving a resolution better than the natural linewidth have been performed by Gibbs et al. (1976) and Cresset et al (1982). The first experiments which investigated antibunching in resonance fluorescence were also performed by means of laser-excited collimated atomic beams. The initial results obtained by Kimble, Dagenais, and Mandel (1977) showed that the second-order correlation function g(2)(t) had a positive slope

Resonance Fluorescence of a Single Ion

143

which is characteristic of photon antibunching. However, g(2)(0) was larger than g(2)(t) for t ~ ~ due to number fluctuations in the atomic beam and to the finite interaction time of the atoms (Jakeman et al. 1977; Kimble et al. 1978). Further refinement of the analysis of the experiment was provided by Dagenais and Mandel (1978). Rateike et al. used a longer interaction time for an experiment in which they measured the photon correlation at very low laser intensities (see Cresset et al. 1982 for a review). Later, photon antibunching was measured using a single trapped ion in an experiment which avoids the disadvantages of atom number statistics and finite interaction time between atom and laser field (Diedrich and Walther 1987). As pointed out in many papers photon antibunching is a purely quantum phenomenon (see e.g. Cresser et al. 1982 and Walls 1979). The fluorescence of a single ion displays the additional nonclassical property that the variance of the photon number is smaller than its mean value (i.e. it is sub-Poissonian). This is because the single ion can emit only a single photon and has to be re-excited before it can emit the next one which leads to photon emissions at almost equal time intervals. The sub-Poissonian statistics of the fluorescence of a single ion has been measured in a previous experiment (Diedrich and Walther 1987 and also Short and Mandel 1983 for comparison). The trap used for the present experiment was a modified Paul-trap, called an endcap-trap (Schrama et al. 1993) (see Fig. 1) which produces strong confinement of the trapped ion. Therefore, the number of sidebands, caused by the oscillatory motion of the laser cooled ion in the pseudopotential of the trap, is reduced. The trap consists of two solid copper-beryllium cylinders (diameter 0.5 mm) arranged co-linearly with a separation of 0.56 mm. These correspond to the cap electrodes of a traditional Paul trap, whereas the ring electrode is replaced by two hollow cylinders, one of whic