ATOMIC PHYSICS AND FUNDAMENTAL PRINCIPLES

ATOMIC PHYSICS 10 H. Narumi, I. Shimamura (editors) © Elsevier Science Publishers B.V., 1987

1

ATOMIC PHYSICS AND FUNDAMENTAL PRINCIPLES

Vernon W. HUGHES Physics Dept., Gibbs Laboratory, Yale University, New Haven, Ct. 06520

1.

INTRODUCTION I am honored to give the opening talk at this joint session of the

International Conferences on Atomic Physics and on Few Body Systems in Particle and Nuclear Physics.

My subject, Atomic Physics and Fundamental

Principles, in the program of ICAP is a very broad one - indeed clearly an overambitious one - and it will be possible only to touch briefly on selected topics.

At this tenth meeting of ICAP - about 20 years after a

small group of us started this Conference in the New York City-New Haven area - it may be useful to focus on this subject. emphasized the fundamental aspects

ICAP has always

of atomic physics and their

ships to fundamental principles in physics.

relation­

Indeed one of the

most

exciting and significant things about atomic physics has been that it has led to fundamental theories and principles such as quantum mechanics, quantum electrodynamics and conservation laws.

Its study is still central

for modern basic physics. The table of contents from the first ICAP meeting1 in 1968 is shown in Table 1.

Some of the topics such as Invariance principles, the atomic

constants, and quantum electrodynamics fall within the present talk. Table 2 lists some broad fields of fundamental physical principles where atomic physics is currently making important contributions.

I will

make some brief remarks about each

of these

be discussed in much greater depth

by otherspeakers on our ICAP program.

2.

topics, several of which will

FUNDAMENTAL CONSTANTS

2.1 Introduction Table 3 will remind you of some of our present information on the fundamental constants.2»3 With the precision techniques of atomic physics we continue to improve quite dramatically the precision with which these constants are known. We know that quantum mechanics describes properly the dynamics of an atom, but relevant constants such as the masses of the electron and proton,

2

TABLE 1:

Doubly Excited States of Atoms U. Fano

ATOMIC PHYSICS

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

209

..........

227

Double Resonance and Level-Crossing Spectroscopy Gisbert zu Putlitz

Proceedings of the First International C onference on A to m ic Physics, June 3 - 7 , 1 9 68 , N ew Y o rk C it y

Conference Chairman

Theory of Electron Atom Collisions P.G. Burke

VERNON W. HUGHES

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

265

Yale University

Electron Collisions with Positive Ions .................. M.J. Seaton

Editors BENJAMIN BEDERSON N e w York University

Resonances in Eleetron-Atoin Collisions G.J. Schulz

VICTOR W. COHEN

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

295

321

Brookha ven N ational Laboratory

Rearrangement Collisions Kenneth M. Watson

and

FRANCIS M.J. PICHANICK

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

333

Yale University

353

Invariance and Symmetry Principles G. Feinberg

Collisions of Light with Atoms P.A. Franken

377

Quantum Electrodynamics: Experiment Vernon W. Hughes Quantum Electrodynamics: Theory S.D. Drell

Polarized Electrons Wilhelm Raith

..........

389

Colliding Beams .............. Gordon H. Dunn

417

Laser Sources ................................................. W.R. Bennett, Jr.

435

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

475

1

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

15

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

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

Precise Schrödinger Wave Functions for Two Electron Atoms Charles Schwartz

.

53

71

Coherence ..................................................... Marian 0. Scully

81

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

103

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

1 11

The Variability of Atomic Constants K.H. Dicke Many Body Theory of Atomic Structure Keith A. Brueckner

Low Density Astrophysics: George B. Field

Atomic Structure, Transition Probabilities, and Theory of Electron Correlation in Ground and Excited States ..... Oktay Sinanoglu Radiative Transitions A. Dalgarno

rf-Spectroscopy of Stored Ions H.G. Dehmelt

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

Symmetry Properties of Atomic Structure B.R. Judd

HI Regions

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

487

Low Density Astrophysics: H M.J. Seaton

Regions and the Solar Corona

501

131

Magnetic Hyperfine Anomalies H.M. Foley

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

509

161

Hyperfine Structure H.H. Stroke

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

523

199

Mesic Atoms ................................................... V.L. Telegdi

551

V.W. Hughes

....

Heavy Particle Collisions Felix T. Smith

A to m ic Physics and Fundam ental Principles

TABLE 2:

ATOMIC PHYSICS AND FUNDAMENTAL PRINCIPLES

Fundamental Constants Electron-Proton Charge Difference Variation with Time Quantum Mechanics EPR Paradox and Bell's Inequality Quantum Electrodynamics Discovery and Verification Quantum Optics Cavity Quantum Electrodynamics Laser Cooling and Trapping of Atoms Electroweak Theory Parity Violation Modern Standard Theory of Particle Physics Muon-Electron Puzzle Symmetries and Conservation Laws C Invariance T Invariance and Electric Dipole Moments General Relativity Mass Anisotropy TABLE 3: FUNDAMENTAL CONSTANTS BASIC ATOMIC CONSTANTS CHARGE (e) MASS (m ,m ,m ) e* U P MAGNETIC MOMENT (μ ,μ ,μ ) e ’ y’ p PLANCKfS CONSTANT (h) VELOCITY OF LIGHT (c) DERIVED ATOMIC CONSTANTS π

o π me 2

2

b

eft 2mc MEASURED VALUES c R„

= 2.997 - 1.097

924 58 x 10 10 cm/sec 373 156 9(6) x 10 5 cm- 1 (0.5 ppb)

a- 1

= 137.035 981 5 (123) (0.090 ppm)

μρ /μ^

= 1.521 032 209(16) (0.01 ppm)

μ6 /μρ

= 658.210 688 0(66) (0.01 ppm)

μμ/μρ

= 3.183

mp/me

= 1 836.152 701(37) (20 ppb)

345 47(95) (0.3 ppm)

iWme

= 206.768 259(62) (0.3 ppm)

m -f/m _ = 1 ± 4 x 10" ® eT e ae = ( S e ~ 2 ) / 2 = 1 159 652 193(4) x 10“ 12 (3.4 ppb)

3

4

V.W. Hughes

their charges, and the fine structure constant a are simply inserted into the theory as experimentally determined constants with no theoretical basis for their values.

We might hope, however, that a deeper theory would

predict the values of dimensionless quantities such as m^/n^- 1836, q^/q^ = 1, and a- 1

- 137.

More generally in the modern standard theory

of particle physics, which comprehends atomic, nuclear and particle physics, this same situation applies so that quark and lepton masses and charges and many coupling parameters are arbitrary constants in the theory to be determined by experiment. 2.2 Electron-Proton Charge Ratio I*

From the viewpoint of atomic physics

the ratio of the magnitudes of

the electron and proton charges as well as the neutron charge are arbitrary constants in the theory.

Present evidence indicates that q = q and e Mp qn = 0 so that atoms are electrically neutral. Furthermore, standard particle theory assigns values for lepton and quark charges so that this is the case.

However, there is no fundamental principle which requires these

charge relationships.

Experimentally the question of the electrical

neutrality of matter is closely connected to searches for free quarks . 5 Even a slight difference in the positron and proton charges would have the major implication that proton decay could not occur without violation of charge conservation. 6 astrophysics.

There would also be important implications for

7 Q

Various measurements on the electrical neutrality of atoms are listed in Table 4.

The classical Millikan oil drop experiment established

directly that electronic and ionic charges are equal to about 1 part in 1,000.

Furthermore, from the electrical neutrality of an oil drop composed

of some 1 0 13 electron-proton pairs it could be concluded that |<5q| < 10” 16 qg where 6q = q - qg .

From other bulk matter experiments and in

particular from current searches for free quarks with magnetically levitated balls5 it is established that |
For example, the

= 10” 18 by an electric field E = 200 kV/cm

«e in the apparatus used in the latest such experiment (Fig. 1) is _ η

s

= 2 x 10 cm for source temperature T = 530 K, in which s is the a a deflection of an atom with the most probable velocity from the source. Deflections arising from the polarizability of the atom and the inhomogeneity of E can be subtracted by measuring also the deflection of

Atom ic Physics and Fundamental Principles

5

equal magnitude but opposite sign obtained with the opposite direction of ί.

The ultimate sensitivity10 was importantly limited by asymmetry in the

patch effect between the two electric field plates so that reversal of the sign of the potential difference between the two plates did not lead to an exact reversal of E.

The use of atoms cooled by a laser should allow use

of a much shorter apparatus and a substantially increased sensitivity in this measurement.

We note that a similar type of deflection experiment on

a neutron beam11 established that q

^n

TABLE 4:

< 4 x 10“ 20 q · ne

MEASUREMENT OF ELECTRICAL NEUTRALITY OF ATOMS Molecule

Upper limit3 for ε

oil drop

Millikan Stover, Moran and Trischka

Lron sphere

Piccard and Kessler

CO 2

Hillas and Cranshaw

Ar n 2

King

h 2 He sf6

±2x10" 19 (4 ±4)xl0"20 (6±6)xlO-20 (1.8±5.4)xl0-21 (-0.7 ±4.7)xl0-21 (0±4.3)xl0-21 4x10“ 13

Upper limit'3 for ε/Μ

Date

± 10 “ 16

1935

±0.8x10" 19

1967

±5x10"21

1925

(1+I)xl0"21 (2 ±2)xl0" 21 +(0.9±2.7)xl0-21 (-0.2 ±1.2)xl0"21 (0±3.0)xl0-23

1959

unpub

2x10" 15

1957

(1.0±4.2)xl0" 19 (-1.0±3.0)xl0" 18 ±1x10" 15 ±7x10" 16

1963

Hughes

Csl

Zorn, Chamberlain, and Hughes

Cs K h 2 d 2

Fraser, Carlson and Hughes 10

Cs K

Shapiro and Estulin

n

6x10" 12

6x10" 12

1956

Shull, Billman and Wedgwood

n

(-1.9±3.7)xl0-18

(-1.9±3.7)xl0" 18

1967

Gähler, Kalus and Mampe

n

(-1.5±2.2)xl0"2°

(-1.5±2.2)xl0"20

1982

(0.8±0.8)xl0” 21

1984

Marinelli and Morpurgo

steel ball

(1.3±5.6)xl0"17 (-3.8±11.8)xl0-17 +2x10" 15 ±2.8x10" 15 ±1.7x10" 18 ±1.3x10" 18

+1.3x10"20 ±3.3x10"20

Measured charge per molecule in units of the electronic charge. ^Measured charge per molecule divided by the total number of nucleons.

1968

6

V. W. Hughes

x

Fig. la:

Molecular beam measurement of atomic or molecular charge.

C O L L IM A T O R

DETECTOR

SOURCE

FIELD

ELECTRODES

(

)

Fig. lb: Geometry of atomic beam apparatus for latest deflection experiment 1 2.3 Time Variation A possible time variation of the fundamental constants is an old question.

12

Very generally we might expect that a unified theory of

everything (TOE) including the universe and atomic phenomena should involve a time variation of the fundamental constants because the universe is changing with time.

Atom ic Physics and Fundamental Principles

7

The large dimensionless number coincidences noted by Dirac

1 3 have

provided a focus for considering the time variation of the fundamental constants.

One of these is the approximate equality of the ratio of the

electrical to the gravitational forces between two particles, for example an electron and a proton, and the age of the universe T expressed in an atomic time unit, e.g. t^ =1i/mc2

G m m e p

t~ 0

1 0 39.

Furthermore the number of particles N in the universe given by N _ mass of universe = m P

. 2 . 1078 0

is the square of the above dimensionless number.

Dirac proposed that

these equalities have always been true, which would require that some constants vary with time, e.g. G decreases, with G/G ~ -10“ 10 per year. Modern Kaluza-Klein theories li+ seek to unify gravity with the other fundamental forces and introduce a radius associated with extra space dimensions.

Expansion of the universe in Kaluza-Klein cosmologies

could be associated with time variation of the fundamental constants. 15 These theories provide a modern framework for discussion of the time variation of constants. A third viewpoint which might involve time variation relates to the time or space evolution of vacuum expectation values. 16 Table 5 indicates some present sensitive limits on time variation of fundamental constants.

They rule out the variations required by Dirac’s

suggestion and show as yet no evidence for time variation.

Indeed they

establish the spatial and temporal homogeneity to 100 ppm over the observable universe for most of its history.

TABLE 5: Quantity

EXPERIMENTAL BOUNDS ON TIME VARIATION OF CONSTANTS 15 Bound on • nijQ/Q|

Method

(yr~ G a a a a g m /m 2 P e P a gp me /mp

< 1 χ

11

ί ο1-- 1 1

17 17

< 1 χ Ι Ο "1 5 ,-15 < 5 χ ίο-

112 2

< 4 χ ΙΟ" 1— 112 2 < 4 χ ΙΟ" -

< 8 χ ΙΟ"

112 2

1

< χ ί10 < 2 x ο -- !*♦ "

Astrophysics Geochemical Geochemical Astrophysics Laboratory Astrophysics Astrophysics

V.N. Hughes

8

3.

QUANTUM MECHANICS Perhaps the most important advance in quantum mechanics since its

discovery has been the resolution of the Einstein-Podolsky-Rosen (EPR) 17paradox in favor of quantum mechanics through Bell’s inequalities and their experimental tests.

The EPR paradox suggests that quantum

mechanics with its probabilistic interpretation is incomplete and that there are additional hidden or supplementary variables needed to make it a deterministic theory.

Bell's inequalities, which were formulated in 1964

and are based on a locality condition as a consequence of Einstein's causality preventing faster-than-light interactions, provide a quantitative criterion for testing supplementary parameters theories versus quantum mechanics.

18

Local supplementary parameters theories are constrained by

Bell's inequalities and certain predictions of quantum mechanics sometimes violate Bell's inequalities. The test of Bell's inequalities has focussed on the two photon polarization correlation experiment indicated in Figure 2.

Detectorl

Q

Anolyzerl

Atomic Transitions: J = 0 > 1 Two photon state:

A nalyzerU

Measurements

DetectorXH

+0

J = 1, P = 1

Quantum Mechanicjs Ψ0 (polarization) =

i

[|x, x > + |y, y>]

/2

Probabilities of various single and joint detections after the polarization analyzers can be evaluated. Thus P+(a) = P-(a) = i , where + or - refers to linear polarization being parallel or perpendicular to a. P++(a,t)) = P— (a,£) =

j

cos2 (a,£)

Several combinations of quantities involving polarization correlation are useful. E(a,tf) = P++(a,£) + P— (a,i) - P+_(a,b*) - P_+(a,1?)

EQM(*’^ = cos2(^ ^ ); S = E(a,i) -

E(a,P)

+

E(a' ,£) + E(a',f')

S_., = 2 / 2 for a particular set of orientations of (a,if) and (a',?'). QM

Theories with supplementary^ parameters A parameter λ characterizes each emitted pair and there is a probability distribution p(λ) Bell's Inequality requires - 2 < S < 2 This conflicts with S ^ for a particular set of orientations. Fig. 2:

Two-Photon Correlation Experiment.

Atom ic Physics and Fundamental Principles

9

are made of the linear polarizations of two photons emitted in a radiative atomic cascade.

Bell’s inequalities require that the quantity S involving

polarization correlations satisfy the relationship shown for any theory involving supplementary parameters.

Experimental conditions can be found

for which the value of S predicted by quantum mechanics violates Bell’s inequality. Many experiments have been done to test Bell’s inequalities and all the published results have clearly confirmed quantum mechanics.

19 20

»

The pioneering experiment of Freedman and Clauser21 is indicated in Fig. 3 and the most recent experiment by Aspect et al.,

22

in Fig. 4.

The last

experiment added the important feature of an optical switch which operated in a time small compared to the photon transit time and hence provided for time-varying polarization analyzers. A new EPR experiment involving the hydrogen 2S+1S two photon transition is reported by H. Kleinpoppen in this volume. The results of all these experiments confirm quantum mechanics unambiguously and are in conflict with supplementary parameters theories. Thus an important clarification has been achieved on the foundations and interpretation of quantum mechanics.

.==7-------3d4p

'f>

V so

4s2lS0

Fig. 3a: Level scheme of calcium. Dashed lines show the route for excitation to the initial state 4p21S Q.

o 0

22 I

45

67j

90

ANGLE Φ IN DEGREES

Fig. 3b: Schematic diagram of apparatus and associated electronics.

Fig. 3c: Coincidence rate with angle φ between the polarizers, divided by the rate with both polarizers removed, plotted versus the angle φ. The solid line is the prediction by quantum mechanics, calculated using the measured efficiencies of the polarizers and solid angles of the experiment.

V.M. Hughes

10

C:,

Ih b )

iV II'(b

)

FOURFOLD COINCIDENCE MONITORING

Fig. 4a: Timing experiment with optical switches. Each switching device (C^., Cj j ) is followed by two polarizers in two different orientations. Each combination is equivalent to a polarizer switched fast beween two orientations.

Fig. 4b: Optical switch operated at 50 MHz by diffraction at the Bragg angle on an ultrasonic standing wave.

4.

Fig. 4c: Average normalized coindence rate as a function of the relative orientation of the pola­ rizers. The dashed curve is the quantum mechanical prediction.

QUANTUM ELECTRODYNAMICS 4.1 Introduction Atomic physics has played a central, even dominant role in the

discovery and verification of modern relativistic quantum field theory of quantum electrodynamics (QED).

Quantum electrodynamics is our most

advanced and successful fundamental theory and is the model from which the unified electroweak theory and indeed the present standard theory of Table 6 gives some general features of

particle physics has developed. QED and lists some QED processes.

The state of QED in 1944 is indicated in the quotation from Heitler's important book 23 and makes clear that the theory was plagued by infinities. "THE QUANTUM THEORY OF RADIATION" W. Heitler Second Edition, 1944 Looking back at the present quantum

th e

contents of this book and asking to what extent

th e o ry

of radiation is consistent and correct, we must

Atom ic Physics and Fundamental Principles

11

arrive at the following two conclusions: (i)

If the interaction between the radiation field and particles

is

considered as small and the solution only worked out to the first non-vanishing approximation in this interaction,

the theory always gives

correct results which agree with the experiments

up to the highest

energies known. (ii) On the other hand, if the present formalism is applied to approximations higher than the first, the result always diverges and the higher approximations are therefore meaningless.

Strictly speaking, the

present theory has no exact solutions at all and cannot therefore be regarded as an exact theory. TABLE 6:

QUANTUM ELECTRODYNAMICS

Quantized Field Theory of Photons, Electrons, and Muons

^

Σ

=<^Free,e

ε

Σχ

+

Ή

Free,y

(N+ (r > ( q V N _(r)(a))

+1

+ ^

(aW

Interaction

(k+ ) , a * a ) (k+ )! + J ^

A state is defined by the number of photons and electrons (muons) together with their momenta and spins. Interactions between the particles and the electromagnetic field is generally treated by perturbation theory with the fine structure constant ot=e /'fie as the perturbation parameter. The principles of relativity, quantum mechanics, P,C and T invariance, unitarity, and analyticity are satisfied. QED PROCESSES OR APPLICATIONS Particle properties Electron and muon g-values Hydrogenic atom energy levels Fine structure, Lamb shift, hyperfine structure, decay rates Positronium, muonium, muonic atoms High energy processes Electron-Electron (Positron) Scattering Pair production Bremssrahlung The well-known discoveries at Columbia in 1947-48 by radiofrequency atomic beam spectroscopy of the anomalous hyperfine structure interval in hydrogen,24 the Lamb shift in hydrogen,25 and the anomalous g-value of the electron2^ and their theoretical explanation by renormalization theory (Table 7) changed the situation in QED dramatically so that only 14 years 28 the

later we find in Källen’s authoritative Encyclopedia article following quotation:

V.W. Hughes

12

TABLE 7:

QED DISCOVERIES IN 1947-48

IIyperfine Structure Interval Δν in H, l^S^/2 (June, 1947) Δνe x p t = 1 420.410(6) .1Hz

Avtheor(FERMl) = (]| a 2c r J ^ ) (1 ♦ £ r ) ’3 = 1 416.97(54) MHz

PB

Lamb shift in H (August , 1947) 2^si /2 " ^Pi/2 interval C^-1000 MHz ) Dirac theory predicted

^ 1/2 degeneracy

Electron g-vALuc (December , 1947) g = 2.002 29(8) = 2(1 + 0.001 15(4)) 9D irac

= 2

RENORMALIZATION THEORY Δν = Δνρ (i + Q) = i 420.26 MHz

= 1 040 MHz g = 2(1 + 2%·) = 2(1 + 0.001 16)

Ex t .

■0 ; Va c u u m Po l a r i z a t i o n

"QUANTUM ELECTRODYNAMICS" G. K£llen 1958 In the last chapter we worked out various examples of radiative corrections·

We proved that the infinite quantities, appearing in the

lowest approximation, nay be interpreted physically by means of the renormalization of the charge and mass of the electron and so may be eliminated. The remaining finite terms can be compared with experimental measurements.

The calculated and measured values show

remarkably good agreement. The excellent agreement of theory and experiment in modern QED has prevailed over the past 30 years as experiments of ever greater precision and variety have been performed.

Periodically discrepancies of about 3

standard deviations have appeared but they have always been straightened out by the correction of some theoretical or experiment error.

Atom ic Physics and Fundamental Principles

13

It is well-recognized, of course, that there are other interactions than the electromagnetic one namely the strong interaction, the weak interaction and the relatively weaker gravitational interaction.

Real

systems-particles, atoms, etc. - experience all the interactions and the electromagnetic interaction can not be isolated even though it may be the dominant one.

Hence as tests of QED get more precise the effects of the

other interactions must be considered. We consider now briefly some of the simple systems in which QED is currently most sensitively tested. 4.2 The Lamb Shift The hydrogen Lamb shift is a classic testing ground for radiative corrections in QED.

The energy levels for the n=l and n=2 states of

hydrogen are shown in Figure 5 including the 2 2S shift interval.

2 t0 2 2P jy 2 Lamb

Table 8 gives the current theoretical value29 of Δν as

well as recent experimental values. agreement at the 10 ppm level.

30

Experiment and theory are in

Proton structure due to the strong

interaction contributes importantly to the Lamb shift, and its uncertainty limits the theoretical accuracy. In principle M (p+e“) is a more favorable atom than H for a test of the Lamb shift because μ+ like e“ but unlike the proton is a structureless lepton.

Figure 6 shows the energy level diagram for M and Table 9 shows

the theoretical and experimental values.

The experimental measurement is

very difficult and has been achieved only recently 3 3 2 at the 1% level, so considerable improvement is required for a sensitive test of QED.

X= 12I5Ä (!0.2eV)

Fig. 5:

Energy level diagram of , , ,

the n=l and n=2 states of hydrogen.

,s" 2 -

o

r

\i4 2 0 m h z

.

14

V.N. Hughes

TABLE 8:

THE LAMB SHIFT IN HYDROGEN

MHz

I r ^ '2

1 050.560

8 '■m

,427

3

(Za) L f . - j l n

, mR.

7.129

( Z a ) ~ 2 ♦ l n ( Z a ) ’ 2 [4 In 2 ♦ | | ]] ( 5 ) *

(Za) 2L[ 2 4 . 0 ± 1 . 2 ] («μ/ι» ) 3

-

e

-

. 3 2 3 ( a / i r ) L ( m R/me ) 3

.246 .173(9) .101

Z ( m e/mp) L ( a + b l n ( Z a ) * 2 )

.359

(ir/ 2a)m| ol
.127(3)

(*/2α)πξ < r \ a.nz

________. 1 4 5 ( 4 ) 1 057.875 MHz (using Malnz)

L = 1,10CZa)

6tt

1 3 5.6 43 891(44)

Experimental Values 1 057.845(9) 30

iexpt " A h e o r

1 057.862(20)a

1 057.77(6)c

1 057.90(6)b

1 057.851(2)d

= 1 057.845(9) - 1 057.875(10) = - 0.030(13) MHz

30See reference this paper; aD.A. Andrews and G. Newton, Phys. Rev. Lett. 37, 1254(1976); G. Newton, D.A. Andrews, and P.J. Unsworth, Phil. R.T. Robiscoe and T.W. Trans. Royl. Soc. London 290, 373 (1979). Shyn, Phys. Rev. Lett. 24_, 559 (1970). c S. Treibwasser, E.S. Dayhoff, and W.E. Lamb, Jr., Phys. Rev. 89^98 (1953). d . V.G. Palchikov, Yu. L. Sokolov, V. P. Yakovlev, Lett. Jour. Tech. Phys. 38, #7, 347 (1983).

4.3 Hydrogen Hyperfine Structure The hyperfine structure interval in the ground state of hydrogen was an early indicator of the anomalous magnetic moment of the electron.

It is now one of the most precisely determined intervals in atomic physics. 3 3

Table 10 gives the theoretical value for Δν.

It is determined primarily

by QED but the effects of proton structure and proton polarizability

A to m ic Physics and Fundam ental Principles

15

X- 1221Ä

Fig. 6 :

Energy level diagram of muonium. TABLE 9:

MUONIUM LAMB SHIFT

Theoretical Value

CORRECTION

ORDER (me)

α(Ζα)

Self energy Vacuum polarization

α(Ζα) 2

ι +

2

[ΐη(Ζα)" ,1,Ζα,...]

ι +

[ΐ,Ζα,...]

4

Fourth order

α (Ζα)

Reduced mass

α(Ζα)^m/Mp[1η(Ζα)~2,1]

Relativistic recoil

(Za)5m / M y [ln(ZcO” 2 ,l]

Total

VALUE (MHz)

1 085.812 -26.897 0 . 101

-14.626 +3.188 1 047.578(300)MHz

The estimated uncertainty in the theoretical value is due to uncalculated terms of higher order in m/My and in am/M^, that is the terms (m/Μμ) (reduced mass term) and a (reduced mass term). An estimate of the size of these terms is 0.3 MHz.

Experimental Value A

expt

= 1054 ± 22 MHz LAMPF ^31') 1070^ 5

MHz

TRIUMPF(32)

V. W. Hughes

16

TABLE 10:

HYPERFINE STRUCTURE IN n=l HYDROGEN MHz 1 418,.840 832

ef

1 .645 359

ae EF

! “2

0 .113 337

ef

- 0 .136 521

ε 1 Ef

- 0 ..010 471(53)

( ε 2 + £3 >e f "Static" proton structure

- 0 .,049 1(13) 1 420.403 4(13) MHz

Δν(expt) = 1 420 405 7 5 1 ’ 766 7^10) Hz <0 · 7 x 10“ 12) e e Δν, - Δν.,.. Λ = 0.002 3(13) MHz \r (expt) (th) ______ Some of data on spin-dependent proton p p structure function needed for proton Polarizability Contribution polarizability contribution is now available.

associated with the strong interaction contribute about 40 ppm to Δν. Proton polarizability depends on the proton’s spin-dependent structure function and limits the theoretical accuracy for Δν at the several ppm level.

Experiment and theory agree at the level of the theoretical error.

4.4 Electron and Muon g-Values The anomalous g-value of

theelectron

= (g^ - 2)/2

has been very

precisely measured by direct observation of a g- 2 transition for a single electron in a Penning trap at low temperature.

3

The theoretical

situation is very pure, since only QED contributes, the strong and weak interactions being negligible even at the ppb level.

Using the condensed

matter value for a from Table 3 we find excellent agreement between the a (theor )35 and a (expt). e e r

Alternatively a ’ e

can be used to determine the

most precise value for a. The muon anomalous g-value, a = (g - 2)/2, is fundamentally similar u u to a^ . However, technically its measurement'36 is done in a high energy experiment with a muon storage ring in which the g- 2 precession frequency for 3 GeV/c muons is measured in a magnetic field, using the parity nonconservation in the weak interactions to produce polarized muons and to detect their spin direction. in a^ is 7.3 ppm.

(Figure 7).

The present experimental

accuracy

Theory j7 and experiment are in good agreement

(Table 12). Although the experimental error in a^ is much larger than for ag, the larger mass scale for the muon makes a much more sensitive to other u interactions than QED so that the strong interaction contributes via hadron vacuum polarization and also the weak interaction contributes significantly

Atom ic Physics and Fundamental Principles

17

through a virtual radiative correction involving W and Z particles. t Thus a^ is not as good a test for pure QED as is ag, but the possibility of interesting new physics is present.

An important test of the standard

theory, in particular of the renormalizability of the electroweak theory, would be provided by themeasurement of the virtual to a^ shown in Figure 8.

a^ also provides a test

radiative contribution38

of new

speculative theories

beyond the standard model.

TABLE 11: EXPERIMENT a + = 1 159 e a _ = 1 159 e

ELECTRON g-2 [g-2(l + a)]

652 222(50) x 10-12 652 193

43 ppb)

(U.

Washington)

(4) x 10-12(3.4 ppb)

(U.

Washington)

THEORY QED

= 0.5 (-1-0.328 478 965 i-)2+ 1.176 5 (13) i-)3-0.8(2.5) (-)** J ν,ττJ

aQED (μ) ■ 2 ·8 X 10" 12 aQED a.

had

■ °·01 * 10" 12 .= 1.6(2) x 10"12

a

, - 0.05 x 10~12 weak

a , th

= 1 159 652 302(104)(44) x 10~12 (0.11 ppm) \

«j fa-1 L cm

^

TH

= 137.035 981 5(123) (0.090 ppm)]

SOURCES OF ERROR (1)

a“ 1 = 0.09 ppm

(2)

QED theory - 0.04 ppm ->■ 10 ppb

(3)

cavity wall effect - 10 ppb

COMPARISON OF THEORY AND EXPERIMENT a , - a = 1 1 1 (128) x 10"12 th exp _1

“g-2

_ (137.035 994(5)

(0.04 ppm)

i137.035 989 8(27) (0.020 ppm)

I/. W. Hughes

18

39

A proposal

has been inade to measure a

in a new experiment at the AGS

at Brookhaven National Laboratory to a precision of 0.35 ppm, which is a factor of 20 improvement over the CERN experiment.

This measurement would

test the electroweak radiative contribution and also predictions of more speculative theories.

TABLE 12:

MUON g-2[g=2 (1 +a)]

EXPERIMENT

ay+ = 1 165 911(11) x 10- 9 (9 ppm) a - = 1 165 937(12) x 10- 9 (10 ppm) 165 923(8.5) x 10" 9 (7.3 ppm)

=1 THEORY ay

~ aQED + ahadron + aweak

aQED = 0 - 5

tt" = 116 140 989(10) x 10 ” U

0.765 858 1 0 (1 0 )( ^ ) 2

+

+ 24.073(11)(^)3 140(6) ί^ · ) 4

+

= 413

219

x 10-1 1 (a.^ = 42 x ID-11)

=30 170(14) x 10-11 =

408(17) x 1 0 " 11

a ^ = 1 165 847.9(0.3) x 10~ 9 (0.25 ppm) QhiD [a" 1 = 137.035 981(12) (0.09 ppm) au . = had

(70.3 ± 1.9) x 10~ 9 (60.3 ± 1.6) ppm

aweak

= ( 1 *95 1 °*01) X 10” 9 ( 1 , 7

a , th

= (1 165 920.1 ±2.0)

x 10~ 9

Sources of error a - 1 = 0.09 ppm QED Theory = 0.23 ppm Hadron = 1.6 ppm COMPARISON OF THEORY AND EXPERIMENT aexp " ath = ( 3 , 9 4 8,7) x 10" 9 ( 3 · 3 4 7,5) ppm

1 ° ‘01) Ρ Ρ Π 1

(1.7 ppm)

A to m ic Physics and Fundam ental Principles

Fig. 7a: Plan view of the muon storage ring and a cross section through one of the forty magnets. For most of the data-taking 22 electron detectors were used. These were distributed around the ring at intervals which were as nearly uniform as possible. Low-voltoge

Fig. 7b: Cross section through the quadrupole electrodes and vacuum chamber.

----1----1----1--- 1 ----1 ----1----1----1 --- I ■■ r

I0 e

-

•

icr

'O

r

’■ '···■ '’V ' \ .

a

'C v ? V

^

·-' V

. v ··'·.

16-59/i.sec 59-102

] Ί

102-146

I

146-189

:

189-232

io4

232-275

I

275-318

;

318-362

io3

362-405

“

405-448

'■

\

* V '. '.V ! v

Α· Λ

icf

i

20

30 Time

V -

40 in

v

'V '

* i Ί ι-

50 microseconds

60

448-491 491-534

]

Fig. 7c: The decay electron count rate as a function of time. The distribution contains a total record of 1.4 x 10 8 electron counts.

19

20

V.N. Hughes

M D IA G R AM S C O N TR IB U T IN G TO TH E MUON g FACTOR MODEL.

i IN THE STA N D A R D A*p(w)» 5 * -*£3 = + 3.89 x I0 ' 9 e r 2y[2 ° F m^2

e*2^

* ±

CO·' i ( 3 -4 c o.20 )2 - 5 ] = -I.94X 10-9

3L

J

< 0.01 * 10”·

2

'y SIN^ Θ = 0.217 ± 0,014; m A > 7 GeV w

Q m( w e a k )

= (1,95 ± 0.01)

x

10'9

Fig. 8 : Weak interaction contribution to a^. 4.5 Muonium Hyperfine Structure The hyperfine structure interval Δν of muonium (M) provides an important test of QED and of the behavior of the muon as a heavy structureless lepton.l+0» 1+1

The Breit-Rabi energy level diagam for the ground state of M

in a magnetic field is shown in Fig. 9.

Precise measurements have been made

in microwave magnetic resonance experiments of the transitions indicated. Parity nonconservation in the

decay chain provides polarized muons and

the means for detecting the muon spin direction.

The experimental

arrangement and two resonance lines are shown in Fig. 10.

The line width is

determined by the lifetime of the muon and by microwave power broadening. The experiment1+2 determines Δν to 36 ppb and the magnetic moment of the muon, or y /y , to 0.36 ppm.

V P

The theoretical value29» 1+3 for Δν is given in Table 13, based on the QED treatment of the relativistic two-body problem.

There is a small but

adequately well-known strong interaction contribution to Δν.

Uncertainty in

the theoretical value arises from uncertainties in our knowledge of the fundamental constants cc and y /y (1.4 kHz or 0.31 ppm), from the estimate in y p the accuracy with which the calculated terms have been evaluated (0.2 kHz or 0.04 ppm) and from an estimate in the size of uncalculated terms (1.0 kHz or 0.22 ppm).

The weak interaction contribution^ to Δν arising from the axial

vector-axial vector interaction is + 0.07 kHz or 16 ppb.

A to m ic Physics and Fundam ental Principles

HUG)

I

2

3

4

5

6

7

8

9

10

X

K* o5„.J ♦ μ ΐ ijJ'H - Me x

' ^ j h -S

ιπ/ιλδκ)

o / h » Δ * » 4 4 6 3 MHz

Fig. 9:

Energy levels in ground n=l state of y+e” .

Fig. 10a: Schematic diagram of the experimental setup. S, scintillation counters.

Fig. 10b: Typical resonance line with theoretical line shapes (solid lines) fitted to the data points.

Agreement of theory and experiment for Δν is excellent and provides one of the best tests of QED.

A proposal has been made at LAMPF for a new

measurement of Δν and μ /u which would increase the precision in these μ P quantities by a factor of 5 to 10.

21

V.W. Hughes

22

Table 13:

THEORETICAL VALUE FOR MUONIUM Δν AND COMPARISON WITH EXPERIMENT.

" ["3"®

)]

+ € qed]

€ q £ q * 3/2CX2 + Qj + € I -♦* € 2 +

- %μ

a e · (9e - 2 ) / 2 ; €, - a 2 (ln 2 - 5 / 2 ) βα3

2θΐ

€z = - |^ - ln a (ln a - ln

a3

^ "*“ ΑΘΟ); € 3β π

S’U · ^ m /mg a* “+ a ^ 7Γ πι^,-m® In mu

( ,5,|Ο ί 0,29) m *pm R

■ 2 l n a + 8 l n 2 - 3 - 18-* ~ m^+meL

Γ

11Ί

+ ( a / 7 T ) 2 m , / m /i X [ 2 l n 2 (m/l4/ m e ) - ^ - l n ( m M / m e ) + ( ^ + ^ - l . 9 - Q , ) ] where

m R = m e rry / (m e + nry)

Ol = 7.21 i 0.19

______________________________

R e = 1 . 0 9 7 3 7 3 152 I (II) X

I 0 5 c m ' ' ( 0 . 0 0 1 pp m)

C = 2 . 9 9 7 9 2 4 5 8 0 ( I 2 ) X I O ,0 cm /se c ( 0 . 0 0 4 p p m ) a ' 1»

1 3 7 . 0 3 5 981

ae *

I 15 9 6 5 2 2 0 0 ( 4 0 ) X I0 - 1 2 ( 0 . 0 3 5 p p m )

(12) ( 0 , 0 9 ppm )

μμ/μ%■ (μμ/μρ) {μρ/μ%)·,μρ/μ\ ■

1.521 0 3 2 2 0 9 (16 ) (0 .0 1 p p m )

nry/m# · 2 0 6 . 76Θ 2 5 9 ( 6 2 ) (0.3ppm)

μμ / / u p *

3 .1 8 3 3 4 5 4 7 ( 9 5 ) ( 0 .3 ppm )[

μμ/μ^ 3 .1 8 3

3 4 6 1(11) ( 0 . 3 6 p pm )]

A l / t h * 4 4 6 3 3 0 3 . 3 ( 1 . 4 ) ( 0 . 2 ) ( l . 0 ) k H z ( 0 .3 9 p p m ) Δ ζ / βχ ρ * 4 4 6 3 3 0 2 .8 8 ( 0 .1 6 ) k H z ( 0 . 0 3 6 p p m ) A l / t h - A l / e x p * 0 . 4 + 1.8 h H z D E T E R M IN A T IO N O F a : a * 1 * 13 7.0 3 5 988 (2 0 )(0 .Ι5 ρ ρ ιη )μ *β 4.6 Positronium For positronium Ps (e+e~) several energy intervals have been measured1* 5» 1+6> 1+7» 1+8 by microwave and laser spectroscopy as indicated in Table 14. scale.

Positronium is a quite pure QED system because of its low mass

However, precise theoretical calculations of its energy intervals

are difficult because it is a fully two-body relativistic problem so that at present the theoretical values 29 are less accurately known than the experimental values.

Agreement of theory and experiment is good within the

theoretical errors. 4.7 Fine Structure Constant a Determinations of the fine structure constant a from several approaches

A to m ic Physics and Fundam ental Principles

are given in Table 15.

23

The most precise one is based on the electron

anomalous g value with an uncertainty of 38 ppb due principally to the theoretical error given at present for the QED calculation. The condensed kq matter value based on both the ac Josephson effect and quantized Hall effect is usually taken as the standard value.

The value from muonium Δν is

Those from helium fine structure50 and from

also of significant accuracy.

hydrogen hyperfine and fine structure51 are of lesser precision. these determinations are in agreement within their errors.

All of

This agreement

in effect confirms to high precision our understanding of a number of different QED systems as well as condensed matter. TABLE 14:

POSITRONIUM.

Gross S tr u c tu r e

F in e Structure 3s . — J 9G H

n -2

f"

^

\

1

3p . *0

2430 (5.1

2

3p* .p X p i ------P, — —

I

'S0

eV)

ί

X T 1 3S

-

Ai/

n ■ 1 ------------^---------------

'So

.

m nuif

r

THEflR.

£X£T.

{203-389 1 0 ( 7 4 ) GHz ( 3 - 6 ppm)

Ai/

* 203GHz *

203 4 0 0 .3 * 10 NHz (50 ppm )

I 1

y

3 3 (2 S - 2 P ) (8 628.<1 ± 2 . 8 ) KHz 1 2

V

(2S-1S)

1 233 607 185

TABLE 15:

±15

8 6 2 5 .1 4 NHz

HHz ( 1 2 ppb) 1 233 607 198

MHz ( 1 6 ppb )

VALUES FOR THE FINE STRUCTURE CONSTANT. a" 1 VALUE

METHOD Hydrogen Fine Structure, 2 2P 3/ 2-2 2P Helium Fine Structure,

±20

2 3P q- 2 3P 1

2

137.036 47(26) (1.9 ppm) 137.036 13(11) (0.8 ppm)

Hydrogen Hyperfine Structure

137.035 97(22) (1.6 ppm)

Muonium Hyperfine Structure

137.035 988(20)(0.15 ppm)

Electron g Value

137.035 994(5) (0.038 ppm)

Condensed Matter

137.035 981 5(123)(0.090 ppm)

Josephson, Quantized Hall

V. W. Hughes

24

5.

QUANTUM OPTICS

5.1.

Cavity Quantum Electrodynamics Important modifications in the properties of a free particle or atom

take place when it is in a cavity where the vacuum modes of the electromagnetic field are altered. The first example 5 2 is the inhibition of the spontaneous emission by a Rydberg atom in a microwave cavity due to the suppression of the mode at the transition frequency because of the boundary conditions imposed by the conducting cavity.

Time-of-flight curves for atoms in a Rydberg state can

be calculated as a function of their spontaneous emission rate in a cavity. When emission is inhibited by changing the spacing of conducting parallel plates to inhibit some possible decay modes, the dramatic increase in overall transmission shown in Fig. 11 was observed.

X/2d Fig. 11: The sharp increase is due to the inhibition of spontaneous emission; the decrease is due to field ionization. For the interpretation of the precise measurements

of ag animportant

question is whether the cavity affects the intrinsica v a l u e . 53 been much recent discussion of this question.

There

has

It appears that the cyclotron

frequency of the electron can be significantly modified (10 “ n ) in a cavity due to the classical effect of the image charge but that the spin precession frequency is effected much less.

The order of the shift in ag value is

10 ppb (which is smaller than the theoretical error in ae ), but it depends

importantly on the resonant frequencies of the cavity and it should be possible to make it negligible. 5^ (Fig. 12) 5.2.

Laser Cooling and Trapping of Atoms Laser cooling and trapping of atoms may be considered an application of

quantum optics and will surely eventually be of great importance for some

Atom ic Physics and Fundamental Principles

25

ζ =u)L/irc * 2 L / X

Fig. 12: (a) The decay constant for a charged particle moving in the midplane between two perfect conducting planes (spacing 2L). ay=particle freqeuncy; γ = free-space damping constant, (b) Cyclotron frequency shift for 6/L = 2 x 10"3 (δ = skin depth). fundamental experiments in high precision atomic spectroscopy or perhaps on collective phenomena at high densities. Deceleration and velocity-bunching of Na atoms in an atomic beam has been achieved by absorption of counter-propagating resonant laser light, and, furthermore, cooled and stopped Na atoms have been confined in a magnetic quadrupole trap with a density of 103/cm3 and a trapping time constant of about 0.9 sec limited by gas collisions (Fig. 13.)55 Three-dimensional viscous cooling and confinement of atoms by the resonance radiation pressure of six counter-propagating laser beams is shown in Fig. 14.

A Na atom density of 106/cm3 and a temperature of 240 yK has been

achieved.56

Chu reports on this important development at our Conference. COLLECTION OPTICS

f

MECHANICAL TAPERED SHUTTER SOLENOID

/

MECHANICAL SHUTTERS

\

N

up stream d o w n s tre a m c o il c o il

------------- TRAP

I \ COOLING ' \ LASER BEAM NEARLY \ MERGED MECHANICAL LASER BEAMS CHOPPER

Fig. 13: Schematic of the apparatus. The solenoid is 1.1 m long and the trap is 40 cm from the end of the solenoid. The combination of shutters and chopping wheel allows the cooling and probe laser beams to be turned on and off rapidly and independently.

V.W. Hughes

26

Fig. 14: Schematic of the vacuum chamber and intersecting laser beams. 6.

UNIFIED ELECTROWEAK INTERACTION Quantum electrodynamics has been extended or joined with the weak

interactions within the past 15 years into a unified electroweak theory. ±

The new heavy particles Z, W discovered.

which transmit the weak interaction have been

The neutral Z transmits the weak force in atoms between

electrons and nucleons or quarks.(Fig. 15)

Although much weaker than the

electromagnetic force transmitted by photons, the weak force transmitted by Z can be observed because it is a parity-violating force.

Fig. 15: Neutral current PNC interactions in an atom. constants characterizing the interactions.

The C ’s are

Although searches for PNC effects in atoms started early (-1974), stimulated by an important paper by the Bouchiats, 57 difficulties and disagreements between different experimental results and to a lesser extent

A to m ic Physics and Fundam ental Principles

27

with theory delayed the decisive observation of the electroweak interference effect in atoms. The first definitive observation of electroweak interference was made instead in a high energy experiment at SLAC by a SLAC-Yale group in 1978.58 High energy longitudinally polarized electrons were scattered from unpolarized deuterons and the asymmetry or normalized difference in the cross sections for the two cases of spin parallel and antiparallel to the momentum was measured.

This asymmetry which depends on the pseudoscalar

quantity σ·ρ^ is an explicitly parity violating quantity. The asymmetry AV AV determines the combination of electron-quark coupling constants 2 ε ^ ο

and a value for the electroweak parameter sin θ^. By now several atomic experiments have measured parity violating effects in high Z atoms through forbidden Mtransitions and optical rotation in allowed Mj transitions. 59 (Fig. 16) These experiments measure the combination AV AV of coupling constants ε , + ε . The most accurate results have been obtained r ° ed eu for CS and considering both theoretical and experimental errors attain an accuracy of about 15%.

A new experiment on Cs is reported by Wieman at this

Conference. 60 Hence through high Z atoms atomic physics is now contributing importantly to testing modern electroweak theory, particularly for low momentum transfer characteristic of atoms.

More precise experimental and theoretical work in

this field can be expected. Although several serious experiments have been undertaken to measure electroweak interference in hydrogen, 6

62> 63» 64 none as yet has

achieved adequate sensitivity to observe the effect.

7S>1/2-

5394A

6 P3 1* 6 P 1/2

6 Sv2-

Fig. 16a: Configuration of PV experiments in forbidden transitions. 59 P's electronic polarizations. 7.

Fig. 16b: First energy level of cesium.

STANDARD THEORY In particle physics we now have a so-called standard theory including

structureless leptons and quarks with the group structure SU(3) x SU(2) x U(l) encompassing the strong and electroweak interactions.

However, many

V.W. Hughes

28

fundamental questions remain completely unanswered and the general belief is that a more unified theory, probably including the gravitational interaction, is needed. One central question is what spectrum of leptons do we expect-their number and characteristics.

This question relates to the properties of the

muon (Table 16), many of which have been determined from atomic physics experiments on muonium. 65

They indicate that the muon behaves in all its

electromagnetic and weak interactions like a heavy electron.

Our standard

theory does not predict the existence of the muon (or tau particle).

When

the muon was discovered or identified in the late 1940*s, Professor Rabi, a central founder of modern atomic physics, asked the crucial question, as was his custom, "Who ordered that?"

This is still an unanswered question.

(Parenthetically, Professor Rabi has come to almost all our ICAP Conferences and has been a major supporter of ICAP in many ways.

He expresses his

regrets that he could not come to Japan for our Tenth Anniversary Conference.)

TABLE 16:

MUON PROPERTIES

M A SS - f — Λ 206.768 259(62 )(0.3ppm)

me m^

- 2 0 6 .7 6 5 ( 10 ) ( 50 pp m )

SPIN 1 ^ * 1/2 MAGNETIC M O M E N T Η'μ*

* 3.183 3 4 5 47 (9 5) (0.3ppm)

Mp Mu- f - * 3.183 4 ( 9 ) ( 3 0 0 p p m ) Η- P

G-VALUE ( $μ+ - 2) / 2 ■ I 165 9 1 1( II) X IO"9(IOppm)

(g/x- - 2 ) / 2 - I 165 937(12) XIO‘ 9(IOppm) ELECTRIC DIPOLE MOMENT fjie < 7 X 1 0 '19 e-cm (95 % confidence level) S T A T IS T IC S Fermi - Dirac

L IF E T IM E Ύμ+ · 2 19 7 .0 9 3 (5 2 ) ° s ( 2 4 ppm)

MUON NEUTRINO MASS 0.52 MeV

Wh o

Ordered

That?

A to m ic Physics and Fundam ental Principles

8.

29

DISCRETE SYMMETRIES AND CONSERVATION LAWS 8.1. C Invariance The discrete symmetries of P, C and T are of great importance.

all conserved in QED but not in the electroweak theory.

They are

In a system

dominated by the electromagnetic interaction some of the most sensitive tests of C invariance come from the study of positronium annihilation. Experimental limits have been established to the C violating decay modes of 3 I C C ground state parapositronium ( S 0) into 3γ and of orthopositronium ( Sj) into 4γ67. 8.2. T Invariance In the weak decays of the neutral kaon system the important phenomenon of CP violation has been observed, of course, although its explanation is not yet understood.

From the assumption of CPT invariance T violation must

follow, but as yet T violation has not been observed.

The existence of an

electric dipole moment (EDM) of an elementary particle would violate T (and also P) invariance and extensive searches for an EDM of the neutron and other particles have been made by atomic spectroscopy.

The most recent experiment

on the neutron involves the storage of cold neutrons in a bottle and is shown in Fig. 17. 68

It has established the limit n ^ ^ = eD with D < 6 x 10“ 25 cm.

Very recently experiments on the EDM of atoms and associated theoretical calculations have advanced to the extent that information of comparable sensitivity on the EDM of the proton is being obtained from NMR studies of xenon polarized by spin exchange with optically pumped Rb. (Fig. 18).

69

Fortson discusses this research in his contribution to our Conference.

Fig. 17a: Schematic diagram of apparatus for measuring at the ILL the neutron electric-dipole moment with bottled neutrons.

30

V.W. Hughes

0.022 Hz

Fig. 17b: neutrons.

Neutron magnetic resonance obtained experimentally with bottled

ognefic shield*

100

150

20C

time (seconds)

Fig. 18a: Schematic diagram of experimental apparatus for optical pumping and NMR resonance studies.

Fig. 18b: along B.

Xenon magnetization

A to m ic Physics and Fundam ental Principles

31

c e nte r o f galaxy Mo

Fig. 19a: Body of inertial mass m accelerated relative to a bit of distant matter of mass ΔΜ.

T

Fig. 19b: Principal axes for inertial mass tensor for model of mass distri­ bution.

"

Fig. 20a: Spatial distribution of a p electron (£=1 ) in different magnetic substates m^ relative to z axis in the direction of an external field Hg·

Fig. 20b: Zeeman energy levels and resonance lines for a P 3/ 2 electron as perturbed by mass anisotropy.

(M,. Mj) (-3/2, 1/2)

(-1/2, 1/2) F=1

(1/2,

1/2)

(3/2, 1/2)

F=2 (3/2, -1/2)

0/2, -1/2) (-1/2, - 1/2) (-3/2, -1/2)

Fig. 21a: Hyperfine structure of the 9Be+ 2 s 1/2 ground state as a function of magnetic field, v is a first-order magnetic field-independent transition at 0.819 T.

S ID E R E A L T IM E

Fig. 21b: Variation of the ^Be* clock transition frequency referenced to a passive hydrogen maser plotted against sidereal time. Tick marks on the vertical scale are 100 μΗζ apart.

V.W. Hughes

32

9.

GRAVITATION The general question of whether the Inertial mass of a body may be a

tensor quantity so that the mass of a body is anisotropic is a natural one in the framework of Mach’s principle, which proposes that the mass of a body is determined by the total mass distribution in the universe and hence might have a directional aspect. (Fig. 19).70»71 If mass were anisotropic then, for example, the mass and hence binding energy of a P electron in an atom would depend of its magnetic substate M^ and similarly for a P nucleon in a nucleus.

Hence the Zeeman energy levels

would not be equally spaced and the energy level pattern would vary with time as the axis of a magnetic field fixed on earth varies with the earth’s rotation. (Fig. 20). The first such search for mass anisotropy72 was made at Yale in an NMR measurement on 7Li with spin I = 3/2 and subsequently on 85Rb with I = 5/2. A very sensitive limit for the anisotropic component of mass An was established,namely, Am/m < 5 x 10“ 23 with a P 2(cos9) angular dependence using 7Li, and Am/m < 3 x 10” 20 with a P l+(cos0) angular dependence using 85Rb.

Recently impressive new limits have set with NMR experiments using an ion trap for 9Be+ (Am/m < 4 x 10“ 25) 73 and optically pumped

199Hg and 201Hg

with (Am/m < 2 x 10 “ 28) 7l+. The absence of mass anisotropy has been established with great sensitivity.

This result is a convincing test of local Lorentz invariance

and a cornerstone of gravitation theory.

10.

CONCLUSION This brief review of some basic topics to which atomic physics has made

and is now making important contributions surely justifies pride in the field and hope for its future impact on fundamental problems.

ACKNOWLEDGEMENTS Research supported in part by the U.S. Department of Energy under contract DE AC02-76ER03075. G.

I am happy to acknowledge helpful discussions with

Feinberg, E.N. Fortson, S. Haroche, W. Marciano, and B. Taylor.

REFERENCES 1. 2.

Atomic Physics, ed. by V.W. Hughes, B. Bederson, V.W. Cohen and F.M.J. Pichanick (Plenum, New York, 1969). The Fundamental Constants and Quantum Electrodynamics, ed. by B.N. Taylor, W.H. Parker and D.N. Langenberg (Academic Press, New York, 1969); E.R. Cohen and B.N. Taylor, The 1986 Adjustment of the

A to m ic Physics and Fundam ental Principles

3. 4. 5. 6.

7. 8.

9. 10. 11. 12. 13. 14. 15. 16.

17. 18.

19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

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