Nuclear Physics AS22 (1991) 1670184~ North-notanda Amsterdam

167~

PERSPECTIVES IN ELECTRON SCATTERING AND NUCLEAR STRUCTURE

Bernard Frois DPhN/SEPN, CEN Saclay, 91191 Gif SW Yvette, France.

Foreword I woutd like first to give my warmest thanks to the organizers of this meeting a.nd all

those who have helped them to organize this celebmtion of Akito Arima 60th birthday. I

really appreciate their kind invitation to contribute to this celebration. Akito Arima is a

great humanist a,nd I am most? pleased to be here to pay tribute to his accomplishments in

physics. II&s group has played a central role in the field of electron scattering and nuclear

structure, by exploring the limits of the shell-model and the role of non nucleanic degrees of

freedom [1,2,3]. The work of Akito Arima and his cohaborators has been an important guide

for experimental research on the electromagnetic structure of nuclei. It is almost impossible

in the field of electron scattering to find any work without reference to Akito Arima or his

students and collaborators.

1 INTRODUCTION

The spa.tial resolution of high energy electrons is ideal to study nucleon, meson and quark

distributions. This has been extensively used to study nuclear structure. In order to map

out the detailed structure of the nuclear interior, one needs a probe that interacts without

significant ~ert~irbation of the nucleus. This requires a.n interaction su~c~~ntly weak to

avoid absorption at the nuclear surface and multiple scattering effects that are difficult to

disentangle. It is clear that the reaction mechanism must be well known. For a good spatial

accura.cy it is preferable to have point particles as a, probe. Leptons and photons have all

these qualities. Muons, neutrinos and phatnns can be produced only as secondary beams that are much less intense than electron beams. Electron beams are superior in terms of

luminosity and beam quality. This explains the accuracy of electron data and why electron

sca.ttering experiments have produced a. continuous stream of a,ccurate, precise, quantitative

and interpretable results [4].

The resolving power of electron scattering Ar is related to the momentum transfer q by

the relation: 7r

ars -- P

Incident electron energies of the order of 500 p\/IeV result in resolution of the order of 0.8

fm, which is ideally suited to the study of nucleon distributions in nuclei. At much higher

energies, E 2 10 GeV, electrons have a spatial resolution suflicient to probe quark distribu-

tions.

Elsevier Science Publishers B.V. (North-Holland)

168c B. Fmis f Elech‘on scattering and nuclear sttuctm

For an unpolarized incident electron beam, the inclusive electron-nucleus cross section

is a sum of two terms, the longitudinal and transverse response functions RL(q,w) and

&(P,LJ). By selecting the kinematic conditions one can vary the polarization of the virtual

photons and can separate the longitudinal and transverse response functions. One performs

a combination of forward and backward measurements, keeping the value of the momentum

transfer q fixed by varying the incident electron energy. The response functions Rt(n,w)

and RTfq,wf contain the information on the structure of charge and current distributions

in the nucleus.

The precision of electron scattering allows 11s to define accurately the limits of present

theoretical descriptions. The most stringent tests of the description of the nuclear ground-

state are the charge and magnetization densities measured by elastic electron scattering.

2.1 ~~g~etizati~n distributions

In the shell-model, nuclear ma.gnetization is due to the current of an unpaired valence

nucleon, either a proton or neutron. For protons there are contributions from orbital and

spin currents. There is only a spin current contribution in the case of neutrons. For nuclei

that have a single nucleon in a stretched configuration j = I+ l/Z outside a doubly-closed

shell core, the shape of the highest magnetic multipole is determined by the wave function

of the unpaired nucleon. This simplification is due to the high m~~lt~polarit~ and the parity

of the transition. In order to contribute to the highest multipole, a configuration other than the valence one must be at least Zfiw in energy. Only the spin current of the valence nucleon

contributes to the highest multipole. As a consequence of this simplicity, elastic magnetic

scattering provides the most precise measurements of the sizes of va.lence nucleon orbits [6,5].

This is shown in particular by the measurement of the 4’Ca magnetic elastic form factor

at the MIT-Bates accelerator [8] and at Saclay 191. The experimental data are shown in

Figure 1 together with the best fit with a Woods-Saxon radial wave function. The amplitude

of the different multipoles and the radius of the Woods-Saxon potential were fitted to the

data. There is a significant quenching of the M3 and XII5 multipoles as observed already for 170 data [11,12]. At high momentum transfer the M? multipole is dominant. Figure 2 is a

comparison between the experimentai data and mean field predictions. One observes that

the contributions of the individual multipoles have their maxima for different values of q.

This is due to the nature of the electromagnetic operator which strongly depends on the

multipoiarity of the transition, The position of the m~imum corresponding to a multipol~

A is located at a q value which increases with the multipolarity. Each multipolarity has in

general a damped oscillatory behavior. Thus in a given q-range, one probes the contribution

of & specific multipole. At high q, above 2 fm-” the highest muIt~pole M7 is almost pure. In this q range, the data are very sensitive to the radial shape of the fri2 neutron wave function.

A 50 % variation in the cross section correspond to a 1 % difference in the rms radius of

the f7f2 neutron orbit. Core polarization and meson-exchange currents do not appreciably

change the shape of the Mir multipole, but they strongly modify the other multipoles. This permits the determination of the radius of the f 7i2 valence neutron orbit with an

experimental uncertainty of 1.5 70. The size of the valence orbit in 41Ca is important to

understand the binding energy difference between *lCa and 41Sc. The Coulomb energy

B. Froir / Electron scattering and nuclear structure 169~

l Bates 1 0 Saclay ,

1 2 3 L 5

q Ifm-‘1

Figure 1: The 41Ca magnetic form factor. The solid curve is the result of a

fit using a Woods-Saxon wave function. The other curves show the individual

multipoles. 181.

10-3 , , , 1 ’ 1 1 I 1 1 ’ 0 ’

~-_. "Ca (e, e) 0 Bates 1

10-L ‘-\ . I- cy

I: 10-s LL -

i

q (fm-4

Figure 2: The 41Ca magnetic form factor. The different curves are theoretical

predictions of Dechargk and Goggng (solid curve) [13/, Negele and Vautherin

(dashed) 1141 a.nd Kim (dotted) 1151.

17oc B. Froth / Electron scattering and nuclear structure

_ EXPERIMENT

---- MEAN FIB.0 Tt+ZORI

0 2 4 6 8 10

r (fm)

Figure 3: Charge density distributions of doubly closed shell-nuclei [4]. The thick-

ness of the solid curve depicts the experimental uncertainty. The dashed curves are

microscopic calculations in the framework of the rn~an-~e~d theory [13].

difference between these nuclei is predicted to be significantly smaller than the value exper-

imentally determined (16,171. The binding energy difference between mirror nuclei with the

sa.me doubly-closed core is expected to be determined to a large extent by the electromag-

netic interactions of the valence nucleons. A possible explanation of this discrepancy would

be that the radius of the fr,s neutron orbit in 41Ca is 3.5 fm, a value about 15% lower than

given by mean-field calculations. The recent data from magnetic elastic scattering reject

this explanation. The experimental value of the rms radius of the f7,2 neutron orbit in

*rCa is 3.99 $ 0.06fm, in good agreement with mean field predictions. The shape of the

&I7 multipole is in good agreement with the prediction of Decharge and Gogny [13]. This

confirms that the measurements of proton and neutron valence radii in the fris shell are

well described by the most complete mean-field calculations. This demonstrates that the

explanation of the Coulomb energy differences cannot be found in a reduction of the valence

orbit radius.

2.2 Charge distributions

In the shell-model the charge density distribution is just the sum of the squares of the

proton single particle wave functions folded with the finite size of the proton. Thus the charge distribution of a nucleus gives direct information on its ground state wave function.

The precision of the experimental results for the charge density distributions of magic

nuclei are shown in Figure 3 together the predictions of a microscopic self-consistent cal-

culation in the framework of the mean-field theory [13]. These calculations use the finite

range force Dl of Gogny and include pairing self-consistently in the Hartre-Fock-Bogoliubov formalism. It is the same force which is used for all nucIei.

A remarkable achievement of mean field theory is to be able to accurately describe the

phase of shell-fluctuations of charge density distributions in the nuclear interior. The success

of the mean-field theory in such dense system as nuclei is understood as a consequence of

the Pauli principle. Short range interactions between nucleons are sign~~cantly suppressed

beca.use nucleons cannot scatter into occupied states. The size of charge density fluctuations

in the nuclear interior has been for a long time difficult to understand. This discrepancy is

today understood as arising largely from correlations whose effects cannot be incorporated

into the mean-field approach to the nuclear many-body problem. The effects of short-

range correlations are partly accounted for by the introduction of density dependence in the

effective NN force.

2.3 Occupation of Single Particle Orbits

Mean field calculations predict different density fluctuations in the nuclear interior. Some

calculations using either the Hartree-Fock method with a. Skyrme force [I91 or the Finite

Fermi System theory of the Moscow group [20,21,22,23] g ive a reasonable description of

nuciear ground state distributions and in particular of the difference between the “*Pi and ao5Z’l charge densities. One of the most interesting observations is to note that the shape of

the single-particle wave functions does not significantly depend on the effective MN force.

In particular the 3s shape predicted by the SkM and Dl forces are essentially identical.

Nevertherless one observes that, in the calculation of ref.[l9] using the SkM force, charge

densities are we11 described by mean-field theory while the predictions of ref.[l3] using the Dl force are compatible with a 30 % depletion of the 3s orbit. This can be understood by

examining the contribution to the charge density arising from nuclear polarization. Nuclear

polarization corresponds to the rearrangement of the nucleus when a nucleon is added or

subtracted. It depends on nucleon-nucleon correlations whose effects are described by a

density dependence of the effective NN force. The two effective forces have a different density

dependence. The SkM force induces a large nuclear polarization effect which depletes the

3s orbit by about 30 %.

Exact calculations have been studied in the context of atomic droplets [24]. The com-

parison between exact calculations and the mean-field approximation shows that in fact it is

equivalent to explain ground state charge density distributions either in terms of partial oc-

cupancy of nucleon orbits or in terms of polarization of the nucleus. Therefore it is possibie by taking effective forces with different density dependence to find apparently contradictory

results for the occupation of single particle orbits if the analysis of experimental data is

restricted to ground state charge distributions.

Charge distributions alone are not ~u~c~ent to provide a reEabEe estimate of obvolute

occupation of single particle orbits.

In order to determine the absolute occupation of single particle orbits, one must also take into account the wealth of data that exists on magnetization densities, single particle transitions and single nucleon knock-out reactions. Spectroscopic factors have been exten- sively measured by transfer reactions, in particular by high resolution (c$,~ Ile) experiments

[25]. The results of these experiments in terms of absolute occupation probabilities is not suficiently reliable without additional information. Furthermore there is always the possi-

172~ 3. Fro& j Electron scattering and nuclear structure

0.8

Figure 4: integrated strength mea5u~ed by the 20sPb(e, e’p) reaction

for various orbits mar the Fermi srrrface. [27,19].

bility of a contamination by two-step processes. strongly depends on a parameter which is

the radius of the nucleon orbit. Absolute occupation numbers ha.ve to be derived by anot,her

method. Recent analyses have shown tbat the (e, e’p) rea.ction produces reliable estima.tes

of single particle strengths in nuclei. Extensive nuclear structure studies using the (e, e’p)

reaction have been performed throughout the periodic table at the high resolution facility at

Amsterdam N~K~~~-K Labora.tory 1261. The spectroscopic strength found amounts only

to about 50 % of the naive single particle prediction. There seems “a priori” to be a puzzle

because this result seems to be in conflict with the 70-80 % found for the occupation number

of the 3s orbit by sum-rule analyses of the same da,ta. in the Pb region 128,271. This problem is understood by ta.king into account all the electron da.ta in the Pb region and performing

a detailed analysis using microscopic calculations with correlated wave functions [32,35,19].

Charge and magnetization distributions have been measured by elastic electron scattering

]18,29,30,31], Single particle transitions have been determined by (e,et) inelastic scatter-

ing. At ANT-fates laboratory 120 states have been recently isolated [33] in the 208Pb(e, e’)

reaction up to 7.3 MeV with an energy resolution between 10 and 20 keV. Momentum dis-

tributions have recently been measured [28,27\ in the Pb region using the (e,e’p) reaction

with a missing energy resolution of 80 keV. The comparison of theoretical predictions and

experimental data for the spectroscopic strengths[28,27] in the Pb region are shown in Fig-

ure 4. The theoretical curves are a. prediction of the occupa.tion number n(k) (solid curve)

and the single particle strength Z (d as e curve) [36]. The pr(~bability of finding a particle h d

with momentum k and energy E is split in two parts, the single particle component and

a multi particle component. The single particle component corresponds to the one-hole strength which is well localized in energy; it is t.his component which is measured by the

(e, e’p) reaction. The multi particle component turns out to be distributed over a very large energy range and cannot be measured by the (e, e’p) reaction. This explains the apparently

low value 50 % of the single particle strength observed by the (e, e’p) reaction if one com-

pa.res this value to n(k), while there is a good agreement with theoretical predictions for Z.

B. Frob / Electron scattering and nuclear structure 173c

Similar conclusions have been independently obtained using a. theoretical approach based

on dispersion relations [37].

The combined analysis of all the electron dota in the Pb region clearly demonstrate.9 that

single particle orbits are partially occupied due to nucleon-nucleon correlations.

The experimental values of the radius found by the (e,e’p) reaction and by magnetic

elastic electron scattering are in good agreement with each other and with mean field pre-

dictions [13]. If the values for the radii of valence orbits determined by electron scattering

[7] are used to analyze the data of (d,3He) and (e,e’p), one finds similar results for the

partial occupancy of shell-model orbits.

3 MESON-EXCHANGE CURRENTS

The calculation of properties of the trinucleon system, in terms of nucleons, is nowadays

reliable [42,X3]. A three-body force is needed to reproduce the correct binding energy of the

three-body system, but is not Sufficient to reconcile experiment and theory for the charge

form factors of 3He and 3H. One needs to take into account the presence of meSonS and

A’S.

The measured trinucleon charge and magnetic form fact,ors [48,49,50,51,52,53] differ sub-

stantially from theoretical predictions, based on a purely nucleonic description, of “He.

There is a considerable improvement when the contribution of meson-exchange currents is

taken into account. The most significant discrepancy between experiment and theory re-

mains in the region of the second diffraction maximum of the charge form factor of 3He.

A new experiment has been recently performed [53] to d e ermine with great accuracy the t

behavior of the 3He charge form factor in this region. A complete series of forward and back-

ward measurements has separated the charge and magnetic form factors up to 1 (GeV/c)‘.

The fit to the new magnetic data yield essentially the same result as the fit to previous

data, but the new charge data are 15 % lower than previous data in the region of the second

diffraction maximum. A complete reanalysis of the tritium data confirm the results of Juster

et al. [51] without significant changes. The trinucleon form factors are now sufficiently well

known to allow a reliable separation of their isospin components up to 1 (GeV/c)*.

Figure 5 is a comparison of the experimental results for the isoscalar and isovector mag-

netic form factors with the result of a calculation [43] b ased on the Paris nucleon-nucleon

potential 1661 including the contributions of meson-exchange currents and isobar degrees of

freedom. It is important to note that nucleonic, pionic and A isobar degrees of freedom are

included in a consistent manner. The meson exchange currents dominate the isovector mag-

netic form factor because the nucleonic contribution is very small a.~ a result of a destructive

interference. For Q2 < 15 fmm2, the pion exchange current contribution dominates and ex-

plains the substantial shift observed for the diffraction minimum. The sum of the nucleonic

and mesonic prediction is very close to the data. The isovector magnetic meson-exchange

currents are identical to those used to calculate the electrodisintegration of the deuteron at

threshold [39,41,40]. The data for th e t wo and three-body systems are shown in Figure 15.

Complete calculations [45,46]which include both nucleonic and mesonic degrees of freedom

are in excellent agreement with experiment. These results are now considered a.s the cla.ssic

example of the presence of meson-exchange current.s in nuclei.

We clearly see that nuclear physics cannot be restricted to thr study of protons a.nd nru-

trons in interaction. The interpretation of fexv-nuclron da.ta requires the explicit treatment

174c B. F&v / Electron scattering and nuclear structure

\ DEUTERON

‘y, ELECTRODISINTEGRATION

‘C. \* :%

- ‘, L, \ t 1 c ‘1 0.

Nucleons

I

0.1

0.01

0.001

Q?GeV/c 1’

0

MAGNETIC FORM FACTOR

:

\

A = 3 ISOVECTOR : : : : :

\ i \ Exp.

:

I I

0.5 I Q2(GeV/d2

Figure 5: Isovector magnetic form factors of the deuteron and of the

three-nucleon system.

of non-nucleonic degrees of freedom. Meson degrees of freedom are sufficient to account

for most of the observed data. The data for the isovector magnetic form factors of the

deuteron and of the three-nucleon systems demonstrate that the amplitudes for charged photopionproduction on the proton at threshold are well described by low-energy theorems.

A similar agreement should be expected for the neutral photopionproduction y + p + x0 + p

at threshold. An experiment performed at Saclay [55] used tagged monochromatic photons

produced by positron annihilation. The low flux of photons (104/s) was compensated by

using a 47r detector. Angular distributions were determined by reconstruction of the events

produced in an active target. Experimental da.ta are shown in Figure 6 The value of the

Eo+ multipole determined by this experiment is -0.5 f 0.3 x 103/m, while theory predicts -2.4 x 103/m,. This result is confirmed by a recent experiment at Mainz [56,57] using the

continuous (100% duty cycle) electron beam of MAMI A. The Maina preliminary result is

-0.3 f 0.1 x 103/m,. This large discrepancy between theory and experiment is not yet

understood.

The Maina experiment was performed in about 48 hours with a high intensity flux of

tagged monochromatic photons E lO’/s while the Saclay experiment which is the state of

the art for a 1% duty cycle accelerator took several weeks of bea.mtime. This demonstrates

the power of continuous beams for coincidence experiments.

The comparison between the data measured at Maint and Saclay is at present one of the

best illustration of the new frontiers opened by continuow beam accelerators.

B. Frob / Electron scattering and nuclear struchu-e 175c

I I I I I I

0 - x+p--n +P

++

. Saclay 1986 - 0 Main2 IPreliminaryl b Q 9Q

I

b

3%

JF __~esmnocodao406aoocf)---___-

I I I I I I 135 1LO 115 150 155 160

ET (MeV)

1.5

2 I0 c)

05

0.0

Figure 6: Total cross section for the reaction 7 + p + no t p. The

data. are represented as a function of the photon energy in the threshold

region

4 THE NEW FRONTIERS

A fully consistent description of nuclear charge and current distributions in terms of mesons,

nucleons and A-excitations has been achieved up to momentum transfers Q2 N 1 (GeV/c)2.

Interactions are well understood for internucleon distances larger than 0.8 fm, but at smaller

dista.nces very little is known. Th is is the new domain that must be explored with higher

energy electron accelerators and continuous beams. The central question is now to determine

what are the relevant degrees of freedom. The magnetic form factor of the deuteron B(Q2) is

known up to 65fme2. Recent SLAC measurements [58] h s own in Figure 7 have considerably

increased the momentum transfer range of previous measurements of B(Q2), providing a very

discriminating test of theoretical predictions. In contrast to the predictions of the parton

model, a diffraction minimum is clearly observed in the region of 50fmm2. The existence

of this minimum shows that asymptotic behavior has not been reached. Frankfurt, Grach, Kondratyuk and Strikman [59] have shown that this result indicat,es that nucleonic degrees

of freedom play a dominant role in the ground state description of the deuteron even at such

high momentum transfers. Recent data on the two-body phodisintegration of the deuteron

taken at SLAC for photon energies between 0.8 and 1.6 GeV appear to obey a simple scaling

law in agreement with the parton model [60]. In th is experiment the energy transfer is large

while there it is very small in the measurement of the deuteron magnetic form factor. These

data illustrate that the central issue of nuclear physics is now to determine what are the

appropriate degrees of freedom.

In order to uhderstand higher momentum transfer data, a description of the nucleon-

nucleon interaction consistent with the nucleon substructure is needed. This will require

an understanding of the structure of the nucleon and the development of a theoretical framework based on QCD valid for both non-perturbative, long-wavelength interactions

and perturbative, short-wavelength interactions. This is now one of the most interesting

challenges with which Nuclear Physics is confronted. The long-term goal of nuclear physics is to understand hadron interactions and the

176~ B. Froir / Electron scattering and nuclear structure

Figure 7: The magnetic form factor of the deuteron.

dynamics of quark confinement in nuclei. The specific role of high energy electrons is to

provide quantitative data on the following topics :

l Structure of the nucleon (spin structure, resonances, etc...).

. Role of non nucleonic components in nuclei.

a Nature of short-range nuclear interactions.

l Effects of the nuclear medium on quark distributions.

The present electron accelerators for nuclear physics are pulsed and have a low duty factor

: electrons are accelerated on target nuclei only 1 % of the time. One uses very high peak

currents to have a reasonable luminosity which is a cause of high background for coinci-

dence experiments. The energy of these accelerators is typically below 1 GeV, though a

few experiments have been performed at significantly larger energies using particle physics

accelerators. These machines have been sufficient to establish the limits of present theoret- ical descriptions of nuclear phenomena. However they are no longer sufficient to extend the

exploration of nuclear structure significantly beyond the frontiers tha.t have been already reached [61]. Many new electron scattering facilities are now under construction all over the

world. By 1992 experimental facilities will have powerful features : continuous beams, high

incident energy, high energy resolution, polarized beams and targets, high flux of monochro-

matic photons by tagging scattered electrons. Continuous beams will open a virgin territory

in coincidence experiments. Several experimental techniques will also be developed and used

extensively :

l Polarized beams

B. Froth / Electron scattering and nuclear structure 177c

l Polarized targets

l Recoil polarization detection

l Internal targets

. Out-of-plane detection

. Large solid angle detectors

There are very few data from polarization experiments. Such experiments have been diffi-

cult up to now because of the limitations of the present generation of experimental facilities.

Polarization experiments will play a central role which is illustrated in the following sec-

tions. I have chosen three examples where polarization brings important new information.

These examples are the measurement of the tensor analyzing power tzs in electron-deuteron

scattering, the neutron charge form factor and parity violating asymmetries.

4.1 Tensor analyzing power in elastic e-D scattering

The electromagnetic structure of the deuteron can be determined by elastic electron scatter-

ing. The elastic electron scattering cross section is a combination of two structure functions A(Q’) and B(Q’). The A(Q’) structure function is known up to 150 fm-’ [64]. A(Q’) is

a combination of monopole and quadrupole charge form factors and a magnetic form fac-

tor. The experimental results do not show any diffraction structure. One only observes a

smooth fall-off of the data as a function of Q”. The magnetic form factor has been isolated

by measurements at backward scattering angles. The only way to separate the monopole

and quadrupole charge form factors of the deuteron is to measure the tensor analyzing power

tzs in electron-deuteron elastic scattering. An experiment has been recently performed at

MIT-Bates Laboratory [62] to measure t 2. by a coincidence experiment between the electron

and the recoil deuteron. Scattered electrons were detected in a magnetic spectrometer while

recoil deuterons were transported to a polarimeter using a specially designed transport sys-

tem that included two dipole magnets bending in opposite directions. The results of the

measurements are shown in Figure 8 together with a theoretical prediction based on the

Paris nucleon-nucleon potential. Systematic errors are not included and are estimated to be of the order of 0.12. One can conclude that there is no really significant disagreement

between experiment and theory. Another experiment, based on a different technique, has

been performed by an Argonne-Novosibirsk collaboration [63] using a.n internal target of po-

larized deuteron in the VEPP-3 electron stora.ge ring at Novosibirsk. Polarized deuterium

atoms from an atomic-beam source were confined within a storage cell to achieve a target

thickness 15 times greater than that of the atomic beam alone. Electrons of 2 GeV and up

to 0.2 A in average intensity were passed through the cell. Scattered electrons were detected

in coincidence with recoil deuterons using four detectors with large solid angles. Several

improvements of this experimental set-up are already planned in order to reduce experi-

mental uncertainties. It is clear from the Bates and Novosibirsk results that one has now

demonstrated that precise measurements are within our reach, but one needs continuous electron beams to perform these experiments.

178c B. Froir / Electron scattering and nuclear structure

0 Bates

0.5 o Novosibirsk

-1.0

-1.5

q (fm-‘1 Figure 8: The tensor analyzing power tzo of the deuteron. The solid

curve is a theoretical prediction based on the Paris potential.

4.2 The Neutron Electric Form Factor GE(@)

An accurate measurement of the neutron electric form factor small model dependent uncer-

tainty requires polarization measurements in both the leptonic and the hadronic channels.

Such measurements require a continuous electron beam tha.t will be accessible only with the new generation of electron accelerators after 1992. The progress a.chieved in the under-

standing of the two-nucleon system up to 1 (GeV/c)’ o ff ers an alternative method based on the measurement of the electromagnetic structure of the deuteron. Theoretical uncertainties

have become sufficiently small to improve considerably the determination of Gs(Q’). Below

25 fm- 2 the theoretical description of relativistic effects and isoscalar meson-exchange cur-

rents is reasonably well understood and a quantitative interpretation of the data is possible.

This is of considerable interest to determine the neutron electric form factor of the neutron

GE(Q’). Up to now experimental data were not sufficiently accurate to provide a reason-

able estimate of the behavior of Gi(Q’). R ecent measurements have accurately determined

A(Q’) up to 20fm- ’ [65]. Given the present knowledge on the nucleon-nucleon interaction it is possible to deduce from these measurements a reasonably accurate estimate of Gi(Q’). These new data are shown in Fig. 9. The model dependence of this analysis is related to

the choice of nucleon-nucleon potential. However there exists a strong constraint due to very precise low q2 data on Gz(Q’) f rom neutron scattering on atomic electrons. One finds

that only the Paris potential [66] . IS compatible with this constraint. This potential is in good agreement with two- and three-body data. and therefore this new estimate of Gg(Q*)

seems reliable. The results are now much more sensitive to the models of the neutron charge distribution. In particular they are compatible with the model of Hoehler et al. [67], but

not with the model of Gari and Krumpelma.nn [68]. The chiral soliton model [69] gives a

B. Frois / Electron scattering and nuclear structure 179c

Figure 9: The neutron electric form fxtor GE(&‘)

reasonable description of the nucleon form factors up to Q” = 1 G~V/C)~ but the slope of

the neutron form factor at the origin is not compatible with experimental data. It is very

important to extend these measurements beyond 25 _fm~~‘, but at such large momentum

transfers, the estimates for relativistic effects and meson-exchange currents are no longer

reliable. Polarization experiments are the only experimental approa.ch possible.

4.3 Parity Violating Electron Scattering

The standard model of Weinberg and Salam for the weak and electromagnetic interactions

assumes the existence of four massive vector bosons. Three of the vector bosons are in a

SU(2) triplet (W’, W’, W-) and the fourth is a singlet, B”. The W bosons couple only to the weak charge while the B” couples to the weak and the electromagnetic charges. The

B” and the W” are not physical particles. The physical particles a.re the photon and the

Z” which correspond to orthogonal combinations. The photon is massless and has vector

couplings:

y = cos 0~ B” ~ sin&v W”

The 2’ is massive and is the mediator of a new force, the weak neutral current:

2’ = sin tiw B” + costiw W”

The mixing parameter sin 0~ is not specified by the standard model, but ma.ss relations are

predicted:

mw = 37.4 GeV/ sin 6’1~

rnzn = rnw/ cos Bw = 75 GeV/ sin 26’w

18Oc B. Frois / Electron scattering and nuclear structure

Figure 10: Parity violatingresults in scatteringpolarized electrons from

‘Be /70]. The shaded area represents the allowed region for the quark

coupling constants at a 90 % confidence level. The result from SLAC is

also represented [71].

The standard model introduces an asymmetry between left and right-handed particles

and predicts a parity violating asymmetry interference between the weak and electromag- netic forces. Parity violation in electron scattering is thus a. direct test of the validity of the

standard model. These interferences effects are small but have been clearly seen at SLAC

[71] and Maim [70]. The most precise result has been recently obtained at Maim [70] for

scattering polarized electrons from ‘Be at an energy of 300 MeV. A parity violating asym-

metry of A,, = (-9.4 i 1.8 l O.5).1O-6 has been found in t,his experiment which has taken

ten years of fight against experimental errors. The result is shown in Figure 10 together

with the result of a previous experiment [71] at SLAC. The coordinates represent quark

coupling constants C2d and Czu. The Maim experiment was much more sensitive to the

axial vector coupling constants, but at the expense of an experimental asymmetry ten times smaller than observed at SLAC. This h as required the development of very elaborate tech-

niques to sufficiently decrease systematic errors. This experiment has improved the previous

error limits in the sector of quark coupling constants by a factor of three. One should note that even with a 300 MeV electron beam, one clearly observes the exchange of a massive

2” by its interference with the exchange of a virtual photon. This explains the impact of

the SLAC experiment which was performed before the observation of the W and 2 bosons

at CERN in high energy pp collisions at CERN. Th e va.lue of sin’& determined by the

Mainz experiment is 0.221 i O.O14(s~nt.) i 0.004 (cyst.) . Th is is compa.tible with the best,

determination of sin’ Ow which is 0.223 & 0.004. The parity violation result is interesting

not because it is more precise but because it it, provides an independent test of the standard

B. Frois / Electron scattering and nuclear structure 181c

model in a different energy regime.

Parity violation in electron scattering is also of interest because the proton weak anoma-

lous magnetic moment is sensitive to the presence of as pairs. McKeown (721 and Beck

[73] have recently proposed to measure this observable by parity violating elastic electron

scattering with a polarized electron beam at an incident energy of 200 MeV. The expected

asymmetry is 8.10e6 which appears experimentally feasible.

5 CONCLUSIONS

Major upgrades at Amsterdam, Bonn, and Mainz a.nd Bates-MIT will considerably expand

the possibilities of present accelerators for Nuclear physics. Similar projects exist also in the

USSR. The developments of stretcher rings will allow for the first time the use of internal

targets. At present CEBAF the most ambitious of these new facilities is being built in the

United States, This machine is a high intensity superconducting accelerator designed for

three simultaneous beams of variable energies up to 4 GeV. There are also some plans to use

the Mark II detector with the PEP ring at SLAG f or nuclear physics experiments. These

experimental facilities will bring the study of nuclei with high energy electrons to a new era.

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