Electromagnetic interactions

Iruclear Physics Á335(19a0)17-26 . ONOSÜl-Sollend Publishing Co ., .ueterder Not to be reproduced by photoprint or nicrofiln rithout vrittan permission fron the publisher .

ELECTROMAGNETIC INTERACTIONS D . DRECHSEL Institut fOr Kernphysik, Universität Mainz D-6500 Mainz, West Germany i . Introduction Electron scattering is an extremely precise tool to investigate nuclear and nucleon structure . Over the past years it has been applied on a large scale to problems of intermediate energy physics . There has been an increasing awareness that it is extremely useful, if not necessary, to study nuclei and nucleons with complementary tools such as electrons, pions and other high energy probes, in order to understand the commón physical phenomena of interest . With the advent of high duty-cycle accelerators the potential of electromagnetic studies will increase even more . Present and future investigations with electromagnetic interactions have been the togi~ of the recent Mainz conference, the Proceedings of which will appear shortly ~ ) . Perhaps as a consequence of hat conference the papers that I have the honour to review are not too numerous3~ . Four papers will be presented orally, contributions by Zamick4) on the puzzle of the suppres~~d M3 transitions, by Sato et a1 .5) on two-boson exchange currents, py Day et al . on inclusive electron scattering from 3He and by Barreau et al .~ on (e, e'p) in heavier nuclei . Since you will hear about these investigations later in this session, I shall mention them only very briefly . Ther~ are two more papers which I should like to discuss only briefly . Resnick et al . ) report that they have found a prescription, which relates radiative and non-radiative decay of charged relativistic bound states, conserves gauge invariance and, consequently fulfils the low energy theorem . In an other contribution, Federics et al .g) report about a monochromatic and polarized photon beam at Frascati . For further information see, e .g ., the talk of Matone at the Mainz conferencel 0 ), In the following I shall address myself to some aspects of electromagnetic interactions, which are related with the remaining contributions to this session : elastic electron scattering from light nuclei, electroproduction above pion threshold and magnetic sum rules . 2 . Elastic electron scattering from the deuteron Elastic electron scattering from light nuclei is of fundamental interest, because these targets are projectors of the electromagnetic current operator in spin and isospin . In particular, the deuteron projects out the isoscalar contributions of the charge monopole, FC, the magnetic dspole, FM, and charge quadrupole, FQ, operators . However, only two form factors can be measured independently by scattering from an unpolarized target, da/dn = °Mott [A(Q2 ) + B(Q2 ) tan t e/2]

,

(1)

where B is determined by magnetic and A by electric contributions, A = (GEp + GEn)2 (F~ + FQ) ,

(2)

with GEp and GEn the electric form factors of the proton and neutron, respectively. We note that this separation of electric and magnetic effects is on~,y possibl~ in the non-relativistic domain . In fact, at large momentum transfer ; Q~ s 50 fm - , l7

1S

D . DRECHSEL

the structure function A is essentially determined by magnetic contributionsll), which have been neglected in eq . (2) . In impulse approximation and with non-relativistic wave functions we have FC = f (u 2 + w2 )j o (gr/2)dT and F Q = f 2w(u - w/~j 2 (gr/2)dT

,

(3)

where q = ~q~ is the three-momentum transfer, while the relativistic struçture functions in eq . (1) are functions of four-momentum transfer, Q = q2 - wZ . Relativistic corrections may be taken into account . by replacing F(~2 )+ F(Q2 ) . However, there are additional corrections, which are not unique and dependent on potential energy terms . In more recent developments this ambiguity has been shifted to the infinite number of ways by which the four-dj~gnsional Bethe-Salpeter equation can be mapped into a three-dimensional equatio 1 )n Fig . 1 shows the results of a relativistic impulse approximation (RIA) 11,13 )~ obtained with the prescription of Gross for treating the off-shell problem in the reduction of the Bethe-Salpeter equation . The effects of relativistic kinematics and admixture of relativistic P-states cancel partly, the net effect giving somewhat worse agreement with experiment . The remaining discrepancy may be taken as an indication of the influence of internal degrees of freedom of the nucleon, though most of this effect could be already due to the uncertainty in the neutron form factor . Since the RIA treats negative energy states explicitly, it contains already the pair current contributionll) . However, there exist other "genuine" meson exchange ~~ rents (MEC) which may give a substantial increase at larger momentum transfer ~ . The effects of isobar currents (IC), at least of the e isobar, seem to be relatively small in the deuteronl5), While the structure function A, an incoherent sum of monopole and quadrupole contributions, is a relatively smooth function dropping monotonically with momentum transfer, the individual form factors show sharp diffraction features . Therefore, a separate measurement of monopole and quadrupole contributions would be invaluable for a better understanding of the discussed phenomena . This would require polari ation experiments . As Arnold points outll~, there exists unfortunately no "technology for either polarized deuteron targets which can stand the high beam currents necessary for low cross section measurements, or a deuteron polarimeter with known analyzing power for use at large recoil momentum" . Since many experimentalists like to do the impossible rather than bread- and-butter experiments, it is not completely useless, though, to repeat that experiments with polarized deuterons would be extremely helpful in order to analyze the individual effects of RIA, MEC, IC etc .

Fi

I : The deuteron structure funcon Q ) . Solid line : non-relativistic, other lines : relativistic impulse approximation with diff ~ ; ent pseudoscalar/vector mixingl~

In a contribu~j n to this conference, A11en and Fiedeldeyb~ investigate whether or not the percentage of D-state (PD ) in the deuteron could be measured in suci~ experiments in spite of the uncertainties of the neutron form factor . The additional information in such experiments is the tensor polarization

ELECTROMAGNETIC INTERACTIONS

Pe = (2F C FQ + FQ/~)/(F~ + FQ)

19

(4)

In conjunction with eq . (2), the tensor polarization allows to determine F and FQ separately . Given a sufficient accuracy of the experimental data, eq . (~) may be used to obtain the wave functions u and w as Fourier-Bessel transform . Fig . 2 shows the Q-dependence of the tensor polarization Pe for various potential models, which are obtained by unitary transformation of the SSC poPQ tential . Even a 45i experiment on Pe in the momentum range below Q = 4 .5 fm - I does not 1 .2distinguish between those potentials, whose D-state probabilities vary between 4 .5 and 7 .5~ . Qß -. _ These results seem to be at varianç~ with those of Heftel et al . ), who find a much stronger dependence of the Q4polarization tensor on various potential models (Read, Paris and Doleschall potentials) In arguing about the ~ i~. l 0 ~;, sensitivity to the D-state v v, . probability one should keep \.y. .. in mind, however, that dify .. . ferent non-relativistic rev . . . . .~ . . . . . . . ductions of the fundamentally - 0.4.w . v ~._ ._ relativistic problem differ in non-static terms . The different approaches are re__lated b~y nitary transforniatlonsl2 .1~), which change Ha4 10 6 ~ 8 miltonians potentials q (tma) used by ref (li . )have quite different energy dependenF_iQ~2 : The electron deuteron tensor polarizaces!), current operators o as function of momentum transfer Q for (size of the energy dependent various potentials obtained by unitary transMEC) and wave functions . formation f the SSC potential (solid line), Hence, the parameter P does from ref . ~ 6) . not have a direct phys~cal meaning, and it is impossible to disentangle PD and the amount of MEC in a model-independent way . Even though the theoreticians are free in choosing one or the other of an infinity of unitary transformations, polarization experiments would be invaluable for future progress in this field . 3 . The charge form factors of 3 He and 3H The behaviour of the charge form factor of 3He at large momentum transfer has been one of the most puzzling problems in nuclear physics for quite a few years now . Th s't ation has recently been reviewed and corroborated by new experimental data~9 . I10~ . From a model-independent evaluation of the experimental cross section measured up to momentum transfer Q2 ~ 20 fm - 2 and after unfolding the nucleon size from the distribution, the point density has a striking central depression for a radius r < .8 fm . This structure resembles a "bubble nucleus", an object which has been looked for in the region of heavy nuclei . The central depression of the point-

20

D . DRECHSEL

density is related to a rathgr high secondary maximum of thq cr~is2~gction around 1 yield form Q2 = 18 fm- 2 . Both Faddeev e nations and variational techni ues factors which are too low by about a factor of three or more in this region . Borysowicz and Riska23 ) have found that meson exchange currents, particularl the pair term, improve the situation . Recent relativistic calculations by Rinat2~) seem to give similar results, in agreement with the mentioned connection between pair current and negative energy states . In a systematic study with various nuclear forces and exchange currents, Haftel and Kloet25) obtain form factors which are too low in the region of the secondary maximum by at least a factor of 2-3 . The influence of two-boson exchange currents is small compared to one-boson effects, at least in the region of the secondary minimums) . We shall hear about this effect later in the session . In a contribution to this conference, Giannini et a1 . 26 ) point out that the analysis of the data in terms of spherical nucleons may be partly responsible for the discrepancy. In fact recent calculations of nucleon polarization in bag models2~+28) indicate that quark degrees of freedom may lead to a substantial oblate deformation of bound nucleons . In a classical model of deformed nucleons with quadrupole moments Q = B and symmetry axis oriented towards the nuclear center of mass, the authors obtain a form factor with

F = Fo fo + B F 2 f 2 Fl

= f

dT pp(r) ~l(qr) :

(5 ) fl =

1

dT pl(r) Jl(gr) "

(6)

where p ~r) is the Schrödinger density of point nucleons and p (r) and p2(r) are the int~insic monopole and quadrupole densities of a bound nucleon . It is easy to show that this effect does not change the rms radius an~ that an oblate quadrupole moment is necessary to improve the fit to the data for He . In fact, an oblate deformation of ß ti- 0 .3 gives qualitative agreement. Of course, the existence of a quadrupole moment of the bound nucleon is related to the admixture of nucleon isobar states with spin = 3/2, the most prominent candidate being the e(1232) isobar with a probability PD of the order of 1%29 .30) . While diagonal t rms give only small corrections29 ), which ~ma,y even go in the opposite direction3 l~, the non-diagonal terms are weighted by 2~ » Pe and give a ~~ relevant coupling concontribution of about 50% of the remaining discrepant stants are relatively well known from photoproduction~~ " ~ and the only other ingredients of the calculation ~re the Nn-r~~rrelation functions (assumed to have the same form as evaluated for He by ref . ) and the resonance admixture probability Pa ti 1% . Fig. 3a shows the result of the impulse approximation with Faddeev wave functions3 5), the contribution of meson exchange currents (from ref. 25) and the nondiagonal Nn current. The theoretical form factor reaches the value ~Fth~ = 4 .1 " 10-3 in the secondary maximum at Q2 = 16 fm -2 , compared to the experimental value ~FexP~ _ (5 .5 ± 0.6) " 10-3 . Even though the mechanism discussed above reduces the gap between theory and experiment considerably, some contributions are still missing . Furthernare, this mechanism is not effective in He, where a similar discrepancy exists . Though the conventional calculations for 4He are not as reliable as for three-nucleon systems, this may be an indication of additional iscscalar contributions . A prominent candidate ~~ld be the Regge recurrence of the nucleon, Nß(1688), as suggested by Kisslinger .Recently, Riska3~) has estimated that this effect gives only 20-30% of the important pair current contribution . This, however, would explain about 30%

ELECTRdlfAGNETIC INTERACTIONS

21

of the remaining discrepancy and it is certainly hot impossible that the Na(1688) and higher resonances could bridge the remaining gap, if they add coherently to describe a collective quadrupole deformation of the bound nucleon . Finally, it should not be forgotten that also the "conventional" ny~~l~~r physics results of the impulse approximation have not completely converged ~ , variational wave functions giving somewhat better descriptions of the three-body form factors than Faddeev calculations . Similar and complementary questions can also be studied with quasifree scattering of electrons from nuclei . We shall hear about these problems later in the session . Finally, I shou~~ like to point out that the isobar contributions considered by Giannini et al . )are of isovector nature . As shown in fig . 3b, the non-diagonal e-contributions give opposite effects for 3H, shifting the diffraction minimum to higher momentum transfer ~nd lowering the secondary maximum by about a factor of two .According to refs ?9, 5), meson-exchange currents are less effective for 3 H . In view of the purely isovector nature of the Ne-transition terms, experimental data of the 3H form factor in the region of the expected secondary maximum would be of great interest .

Fig . 3 : a) The 3 He charge form factor. Solid curve : impulse approximation, dotted c~urv~e : ~A plus diagonal e contribution, dash-dotted curve : IA plus diagonal plus non-~iagonal Ne contributions, dashed curve : IA plus e plus Ne plus MEC . b) Same for H . Note that for 3H the dashed and dash-dotted curves are practically the same . 4 . Eleçtron scatters above lion prroduction threshold Inclusivg electron scattering in the e resonance region has been studied by Franz et a1 .381 at DESY . They have investígated this process in a large ~inematical regíon, for primary energies of 2-3 GeV and four-momentum t~ansfer Q of 5-10 fm - 2 . A similar experiment, inclusive electron scattering from He, will be reported later in this sessionó) . The motivation of that experiment, however, seems to be more connected with analyzing the quasielastic peak and comparing the momentum distribution of"the nucleons with realistic Faddeev calculations .

D. DRECHSEï

22

The cross section for electroexcitation of a nucleus with mass number A is given by (7) oA . d Z aA/dE dn = QMott(W2(Q2' w) + 2 W1(Q2 . w) tan 2 e/2) , where w is the excitation nergy and e the scattering angle . The two structure function of the nucleus,W~, are obtained by folding the nucleon structure functions, W~, with the momentum distribution ~(P) of the interacting nucleon . Following ref . 39, the nucleon structure functions are calculated for constant Q2 but eynergy transfer,w~`, evaluated in the rest frame of the struck nucleon . Decomposing Wi into elastic and inelastic contributions, the authors obtain the cross section as sum of quasielastic and inelastic terms, v

A ° C {( A éff l/A ) a quel + ( A eff l / A ) ° inel } '

(8)

Since Pauli blocking should be negligible for Q2 > 5 fm 2, they assume Aal~¬ 1 = A and use the parameter C (absolute normalization) to fit the data to the quasielastic peak . A best fit to the e resonance region shows that within the error bars Qf about 10%, there is no significant deviation for the effective mass number, A~~#7, from the actual mass number, A . As seen in fig .4, both width and shift of the peaks are well described, and there is no suppression of electroexcitation in the p region . This is in contradiction to earlier DE$Y experiments by Heimlich et a1 . 40 1 and Kharkov experiments by Titov and Stepula4l), who found a substantial sup ression in similar experiments . The main difference in the analysis of refs . 3 $~~0 ) seems to be in th folding procedure (folding of the structure functions according to ref . 3 ~) vs . folding of the total nucleon cross sections with the nucleon momentum distribution) and in the description of the nucleon structure functions . While the experiments of Franz et al . can be inter rgted in .terms of the impulse approximation, recent Saclay data of Mougey et a1 .~2 ) cannot be explained in an impulse approximation : the dip between quasifree and resonance production is filled in, the effect becoming more pronounced with increasing scattering angle . With primary energy of 500 MeY and scattering angles of 60 0 and 1300, the Saclay experiment covers roughly the same region of Q and W as the DESY experiment, the only difference being the larger scattering angle . A possible explanation is that "non-trivial" effects of isobar propagation in nuclei (i .e . effects not described by Fermi motion, Pauli blocking and binding energy) show up much stronger in the transver e structure function W1, which is enhanced by larger scattering ang1es43,44 }~, Coherent collective phenomena in isobar and pion propagation in nuclei (like opalescence phenomena45), pionic resonance fluorescence~J etc .) should indeed show up in nuclear transitions with the quantum numbers of the pion (unnatural parity), which peak at backward scattering angles . Experiments of the type (e, e' n), which are a great challenge to both experimentalists and theoreticians, could help to isolate the contributions of individual multipoles by measuring angular distributions . In a second contribution Franz et a1 . 4 ~) investigate the shadowing effect in inclusive electron scattering in .the vector meson dominance region . The delicate parts óf the data analysis are the radiative corrections from coherent elastic, quasielastic (Pauli blocking effects are quite essentially and inelastic scattering from the nucleon . The vector dominance model (VDM) predicts that the photon has a hadronic component of vector mesons with mass mV and quantum numbers of the photon4a) . Since these mesons are strongly absorbed, the mean free path of the photon in the nucleus is strongly reduced, leading to a surface absorption, the "shadowing ffect" . Vector mesons contribute to forward photon scattering and absorption ti(mY~ + Qz)-2 .

ELECTROMA(RiETIC INTERACTIONS

23

_Fig 4 :_The differential cross section per nucleon as function of invariant mess Tl-för--eLi and 1ZC at different electron energies and angles . The dashed cu~ve~ give the quasi elastic and inelastic contributions separately . Note W =(m+W) q .

Therefore, the shadowing ~ffect is damped out rapidly for virtual (space-like) photons with increasing Q > 0 . Close to the photon line, the absorption cross section for virtual photons, aA, is obtained by dividing the differential cross section by the flux of virtual photons . An effective number of nucleons is obtained by

where a and an are the absorption cross sections on free protons and neutrons, respectQvely . For the neutron cross section the authors use the empirical relation an = (1 - x')op , ~. s

with x' = Q 2 /(~ + m2 ) .

Note that it is not justified to use the deuteron cross section directly, because shadowing is already present in the deuteron .

9~

~ .o

o.s

o .o

.oi

.os

.a3

.W

(10)

s~

F ig . 5 : Shadowing effect R=Aef~/A oar ~e as function of the sca ing variable x' defined in eq . (10) :

Fig . 5 shows the ratio R = Aeff/A for gBe . We note that shadowing dies out for large values of x' . Similar results have $ n obtained in experiments at DaresburyA ~ These experiments seem to prove-the existence of shadowing for virtual photons in general agreement with theoretical predictions, while some earlier experiments did ~8t show convincing evidence for this effect ) .

m aPost aMagnetic obtains larger dominant content influence 3experimentally contribution et contribution valid sum corrections by while M[L~ t1 the results the mn~-sum t2) p(f) contributions the ~0>I2 to the combined tosubmitted is In 2(DDHFB magnetic 20 familiar of reported derived 1proton measured less terms the distribution range Jrule the potential this this of shape for Rms isexchange to course, the p2(r) strength ~<0~ 80% expectation the compared and than calculations radius conference, is context conference, the 2L+1 radii of proton analysis isoscalar moments Kurath by of valence to elastic potential substantial r2L-4 ground 10%, For are neutron 10-80% ~M[L~, gives Zamick4~54) the 2LNucl currents for t~A parameters dipole always it of and to Traini521 dt/f sum highest 2tfof and state neutrons only will neutron, the DDHFB electron transition value [H, (e(u DßEQíSEL Montgomery They We Platchkov distribution neutron Phys these energy rule by wn p(r)r2L-4 M[LI~~ note transitions, deviations and f7/2 Using adensity Dbe -un will find the ~3 allowed calculations of 5-10% has of core Gogny) and data ) scattering f7/2, proton radii that terms the )2L(L-1)(2L-1)(1+BL) excitation the For also et varying aoperator, d0> interest etand shown protons Hamiltonian dt spin-orbit correction polarization multipole momentum-dependent The a1 inThe a1in higher from in are predict While be previous deriving expression that numerical 49Ti degrees effective ~esult identical (D more to 1V in from contributions energies have multipolarities, present the Gogny, study the They 27, Table potential, to 40Ca Hones or studied effects the former is offrom influence with eq neutron calculations less (11) whether within for estimate compared up afrom saturation 1sum The (11) magnetic Skyrme shows two terms vanishes well magnetic which to do rule the ofStanford enhancewhich radius the of The similar not terms magnethe estabto that force howthey the in the error (11) presum of give is insigthe and sum to

D.

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where ment

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(12)

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ELECTRO~lAQ1STIC INTERACTIONS

25

allows a model-independent derivation of the charge density to within 1% . Fig . 6 shows the cross sectionmeas~red over more than 12 orders of magnitude, down to cross sections of 5 10 -38 cm~ . The resulting charge density is given in fig . 7, and compared to calculations of Negele (dash-dotted curve) and Gogny (D1, dashed curve) . The full curve shows a recent calculation of Gogr~y, which includes RPA correlations . This mechanism is obviously very effective in describing the depopulation of the 2s-shell states . It seems to describe much of the suppression of the central density that has been traditionally described by strong density-dependent forces .

~°G -. svwro"o . 41eui

á~

áo >f i

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Fi 6 : Cross section for elastic electron seing from 4oCa as function of momentum transfer (according to ref . 54) .

Fi 7 : Experimental charge density o ~ a as function of the radius r for various calculations (see text) .

References : 1) Proc . Int . Conf . on Nuclear physics with electromagnetic interactions, Mainz, 1979, eds . H . Arenhövel and D . Drechsel, Lecture Notes in Physics, vol . 108 (Springer-Verlag, 1979) 2) Abstracts of contributed papers, Int . Conf . on Nuclear~physícs with electromagnetic interactions, Mainz, 1979 ~Inst .f .Kernphysik and MPI f . Chemie, 1979) 3) Abstracts of contributed papers, 8t Int . Conf . on High energy physics and nuclear structure, Vancouver, 1979 4) L . Zamick, in ref . 3 5) T . Sato, H . Ohtsubo, H . Hyuga, in ref . 3 6 D . Day et al ., in ref . 3 7) P . Barreau et a1 ., in ref . 3 B) L . Resnick, M . K . Sundaresan, P .J .S . Watson, in ref . 3

26

9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22 .) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32 33 ; 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) 51) 52) 53) 54) 55) 56)

D . DREQiSBL

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