Nuclear structure effects revealed by inelastic scattering

"uclear Physics I1í35(1980)365-374 .0 9ottL-Hollend Publishing Co ., Aasterdes Pot to be reproduced by photoprint or sicroliln uithout written permission Erna the publisher.

NUCLEAR STRIICTURE EFFECTS REVEALED BY INELASTIC SCATTERING R .J . Peterebn Physics Division, National Science Foundation and Nuclear Physics Laboratory, IIniversity of Colorado, Boulder, Colorado

Recent azparinaatal results with inelastic pion scattering on complex nuclei are surveyed . Collective transitions are adequately described by the DWBA for all energies and targets . A valuable sensitivity to the isospin content of transitions is found by co~ariag +~ and *- data . Ezcitations with spin transfer are found, but simple quasifree ratios are not measured . Giant resonance states have finally bean seen . 0.

Introduction

My summary will emphasise nuclear structure effects se seen by inelastic The first report ie on scattering to low lying, known states is complez nuclei . the undarstaadiag, or at least the adequate description, of the reaction mechanisms . Inelastic scattering on a complex nucleus uses the spectrum of known witipolarity, known isospin, known collective or eingle~particla nature and known binding energies to isolate specific features of the pionic interaction . At some level of adequate theoretical description, and we seem to have such, the pion . ecattering can be used to provide new nuclear structure information, particularly on the isospin composition of nuclear transitions . My main. points are assertions, backed up by results in subdivieione taken from contributed papers (a few from other sessions) and recent publications . A few unifying analyses of ny own are included . I.

The DiTBA approach ie valid for collective transitions .

A.

The pred icted shapes asree with data .

1 At beam energies near the 3-3 resonance this has been known for same time ) . Predictions with a deformed optical model or with realistic microscopic wave The predicted shapes are largely deters~tned functions both show this success. The details of ~ small angles by the strong absorption of the pion beam . large angle data are not always fit, and second order processes are probably required thareíZ Even at a bean energy as lw ae 35 MaV, the 4 .4 MaV 2+ C is adequately fit, .provided that the daforned 2optical transition in These results potential is that which reproduces the elastic scattering data ) . are shown as figure 1 . B. The sagn~.tudas of pion ecattariug cross sections are in agreement with other results for collactiv® lover. This is of course another teat of our uadaretaading of the pion scattering mechanism. If a collective description is valid for transitions induced by many other probes, we should be most surprised if pioae differed, at least on a T-0 target . More detailed studies of isospin effects will ~á considered Si [ref .3)] below . A careful comparison has bean carried out at SIN for Fasults sumarised in table 1 . For 2 ~Pb, where large Coulosb effects need to be corrected through the DfiBA, recent data are compared to collective predictiooa is figure 2 [raf .~)] . The strength parematere era found to be the sane for both 365

36 6

R .J . PETERSON

pion charge states, and to compare well with the electromagnetic results .

w a w E

40

80

ecm

120

figure 1 : Data for inelastic scattering with a beam energy of 35 MeV arè compared to a DWBA prediction obtained by deforming the optical potential which fits the elastic data . The standard deformation parameter is used . These results were obtainèd by the Carnegie-Mellon group, using a germanium detector at the LEP line at LAMPF . Comparisons with electromagnetic transition rates in the lp shell s ), and in 2 ~Pb [ref .] have also been carried out in a microscopic framework . The collective enhancements needed for picnic and electromagnetic transitions agree . C . Trends of cross sections, rather than isolated magnitudes, also are found to agree with other studies . The locking effects seen for octupole transitions in the Ca isotopes illustrate this ) . Within a single nucleus, picnic data have bean shown to agree with the accepted rotational model in the case of 9Be [ref . e )] . II . Iaelastic pion scattering is very sensitive to the isospin structure of nuclear transitions . A.

The relative role of isovector eacit ation may be determined .

The basic pion-nucleon scattering amplitude provides AS~0,1 ; ATti0,1 transfers to the struck nucleon, and hence to the nuclear system . All four such amplitudes are dominated by thn 3-3 resonance . A ratio of n- to n+ scattering yields for a transition of mired isoepin is linearly sensitive to the magnitude and phase of the miring due to the interference of isoecalar and isovector effects . (Isotensor terms, akin to double charge ezchange, are small and not included .) The ratio for a-one step operation, not forming any resonant state, is of the

NUCLEAR STRUCTIIRE EFFECTS REVEALED BY INELASTIC SCATTERING

367

form : R a

~ da a

_

da(a+)

20 40 60 80 100

P

o +~ P1 1 Pl

IP -

20 40 60 80 100

figure 2 : Data from EPICS obtained by an Argonne-Colorado~roningen-LAMPF-New Mexico State-Northwesters-Oregon State group at,162 MeV are compared to DWIA predictions . Both pion charge states provide the same strength parameter . If the pion field forms .a resonance which then decays, in what I will call a two-step operation, the ratio is : Po+~1

I2

Po - ~1 The coefficients are determined by application of the aligner- Eckart theorem to the pion, and the Po and P1 are the picnic amplitudes for AT~O (isoscalar) and AT~1 (isovector) transitions . A similar development of the two-step equation was discussed by Schiffer in 1975 ~ref . 9)] . A distinction between these two reaction models may be drawn, at least in principle, by comparison to the electromagnetic isoscalar and ieovector amplitudes, Mo and M~, determined by comparisons of gamma ray transition rates in mirror pairsl ~) . Although these matriz elements are obtained for rather different operators there are several cases naw where picnic and electromagnetic measurements of the relative isovector strength may be made . I will quote results without reduced matrix elements in thn target isoepin .

R.J . P$TERSON

36 8 Table 1 :

Deformation lengths for the 1.78 MeV 2+ transítion in ZB Si ia,e')

~P .P~)

(n,n')

id,d')

ía,a')

(a,a')

1 .22

1 .28

1 .47

1 .41

1 .50

1.50

For the electromagnetic transitions in two P0~ P1

Rem

mirror nuclei, with Mp, M1 akin to + M1

Batas for Tr ~ -T o -

M

Bate for TZ ~ To

Mo - Mi

2

It should be pointed out that these matrix elements of isoepia operators are the true observablea, and that only for absolutely pure transitions of single-particle nature does it make sense to speak of a neutron or proton excitation ; then R~9 at the 3-3 resonance. Ia a complex nucleus, the strong neutron-proton interaction will give a great collective preference to the isoscalar amplitude, and the relative+ieovector stren$~h should be smaller for the }~w-lying states . For the lowest 2 excitation of 0, two ezparimeate are F.PICS ) and one at SIN12) now agree that X1 .75 . The ratio R~ of n to a+ inelastic cross sectíone ie predicted from electromagnet c matrix elements for two models, and compared to data for two targets . predicted Level R one step two step Target

Table 2 :

~Li 1 ~0 19 0

2g0

6,~~ 3pSi 3a s

42Ca

4 .63 0.87 1 .98 5 .09 1 .81 2 .24 . 2 .13 1 .52

1 .48 t -1 .75 0 .92 t 0 .66 f _-1 .05 t

.07 .08 .09 .02

4 .84 3 .51 0 .64 1 .67 1 .77 1 .53

t .16 ± .4 t t t t

.17 .29 .46 .26

2 .96 2 .40 0 .73 1 .44 1 .50 1 .35

t .06 t .2 t t ± t

.13 .17 .25 .16

This ie compared in ~~ble 2 to e he ratiol g~redicted for the two models using the electromagnetic data ) . The ~Mg data )are also compared . On the basis of this small sample, we can see that the relative phase of ieovector to ieoecalar amplitudes is the a for both interactioae, and that the two-step model, a other way to, for 1~0 the electromagnetic, one-step picnic and two-step picnic determinations gf the ratio of ieovector to isoscalar strength are O.á3 : 0 .20 : 0 .28, and for 2°Mg we obtain -0 .16 : -0 . 15: -0 . 20. Only picas data are available for ~Li [ref .i 3 )], as shows in figure 3 . Thaw trends are intriguing, but I have ignored all distortion effects, which could be roved through the DWBA, and we must re~membar that the picnic and electromagnetic operators are not the same . We may, however, hope to find here a means to distinguish the pion~nucleus reaction mechanism through further work . A very rich set of these comparisons of picnic and electromagnetic matrix The lifetimes, branchinf4 elements ie awaiting exploitation in A - 23,25,27 . ratios and mixing ratios for many transitions are known in the mirror paire ) and these data may be used to obtain M=/Mp for a vida variety of transitions. The relevant pion data are recommended. Measured differences in the groom-state quadrupole moments of mirror pairs may also be used to predict the a -a differences i~r elastic scattering . A particularly large difference ie predicted for 0 . No such quantitative couparieone have yet been carried out .

NQCLEAR STRIICTQRE EFFECTS REVEALED BY ïNELASTIC SCATTERING

369

The role of ieovector and isoecalar scattering may also be obtained by a c~The syatematics of the diffareacee are parison of (p,p') and (n,n') scattering . The in accord with core-polarization modela for the series of tin isotopes .ls) (p,a) reaction aide these analyses, and picnic charge euhanga data are eapectad to be of equal value .

7Li 4~63 MeV 3/2=+7/2 10 164MeV ~, ~,-y. 61ab r'S _

.

.

~+ ..

0~1 30 60 90

a

el ab

E

30 60 90

figure 3 : SIN data for suiting the 7/2- stets of ~Li are compared to give a ratio of x- to x+ cross sections of 1 .48 t 0.07 [ref . 13 )] . Although only a fear picnic results have yet been completed, several advantages over electromagnetic studies may be noted . The experimental aquípment is the same with both x- a~ ~, and systematic errors era lees . The picnic ratios may ba measured for a much wider range of nuclear transitions in a síagle spectrum . Careful and systematic studies of x- and ~ inelastic scattering will be able to clarify the role of iaovector~and isoecalar nuclear matrix elemeata, which in turn are valuable for determining the effects of core polarization . B.

Some striking pure single nucleon traaeitiona have been lean .

Recent comparisons of x- to x+ scattering on 13 C show very striking differences for several states . The SIN data of Schwarz et al 16) will be presented here, so I will emphasize the EPICS results of Dehnhard et al .l~) Figure 4 shows a xepectrum and the differencs between x- and n+ spectra. Great excursions fsom zero are noted, up to the mazimum expected for scattering from a free neutron for the 9.5 MeV state . The wall known collective states have an isoepia asymmetries near zero, representing a pure isoepia transfer ; DT ~ 0 is expected . Other states szhibít strong isoepia mixing, with positva and negative asymmetries . One problem faced now is the lack of spectroscopic information on the high-lying levels of 13C . Studies with conventional probes are needed to clarify these pica results.

37 0

R.J . PETERSON

Excitation 10

Energy 20

figure 4 : Positive and negative pion scattering at 162 MeV on EPICS vas studied by a ?itnnesota-hA?~F group . Several transitions of strongly mixed isoepin are These results have also been noted at SIN . 16 ) seea .l~) Similar striking results of isoepin mining are seen for a system of states is C, ae seen in Figure 5 [ref . For l8 )], and for known 4- states in 160 [ref .l`~] . both 12 C and 13C, these pion results are being compared to the magnetic scatterinv of electrons . 2 ~) C. Isospin matrix elements may be obtained for ecatterin8 from known, simple s~atems. The best ezample is found for the two 1+ states of 12C, where a small difference in the scattering to these weak states is used to measure their ieospin mining . A preliminary value of the off-diagonal ieospin mining matrix element has been determined to be 125 t 35 keV.~) A variety of earlier measurements provide results from 110 to 180 keV . With improved background rejection, resolution and counting time , the pion scattering method promises to be of great value, not only for this teat case of 12C, but for many other levels, even those not accessible to other methods . This sensitivity is due to the fact that the difference of a- and ~ cross sections measures the isoepin mixing linearly, through the interference of isovector and isocalar amplitudes as shove above .

NIICLEAß STRÜCTQRE SFFECTS REVEAIED BY INELASTIC SCATTEßING

371

figure 5 : The difference of n- and +~ spectra at 162 McV~on EPICS was measured by a group from Texas and LA!lPF . Strong isoepin mizing of two states at 19 .25 and 19 .65 MeV ie indicated . Thane data are taken near 70 ° . III . A.

Pion scattering can ezçite spin degrees of freedom and shows a specific signature to notice these . Data for the T~0 and 1~1 1+ states of 12C are available .

Positive pion scattering to the 12 .7 and 15 .1 HeV 1+ states of 12C finds weak cross eectíone with angular distributions at several beam energies with a shape given by ~J1(kß sin6)I~[ref .ZZ)] . The energy dependence of the peak cross section is shown in Figure 6 . At the 3-3 resonance; a siaple quesifree model predicts the the ~1L0 cross section should be four times thpt for G1~1 . This ratio is found to be 1.4 at 180 MeV, but rises to nearly three at 116 MeV. B. Tha stretched configuration 6- states in Z88í have also bean populated by lion scattering . Metinctive sha~3s, not like the 5- state, are seen, as shown in Figure 7 for positive pious . ) The curves are DWIA predictions with microscopic wave functions. The ratio of the GT-0 to ~7~1 yields ie 1 .5 for n+ scattering at' 162 MeV, in agreement ~+ith the 1+ result from 12C. A slight difference between n- and +~ cross sections is found, 23 ) which can be used to meseura the isoepin P urity of these states, with a structure so unlike the 1+ spin-flip states of ZC. C. Spin-flip transitions may be noted by thn beam-energy dependence of the cross sections . The energy dependence of the peak yield of pion scattering cross sections shows a rise with greater beam energy for many known transitions but a drop for several known spin excitat~~ns . Abstract ID4 shows one ezample,~~) but others are becoming known as well . ) Those energy depeadences are azpected on kinematic grounds, with the forward compression of the angular distribution tending to raise yields, but the ein6 in the pion-aucleoa spin flip amplitude decreasing strengths at these samQ forward eagles for spin-transfer ezcitations.

372

R.J . PETERSON

100 50

f 100

150

200 250 300

T~ (MeV) figura 6 : The peak differential cross sections for exciting the 12 .7 [1+;0] state of 11C are plotted for several positive pion beam energies . These results were obtained on F.PICS by a Colorado-LAMPF-Texas collaboration .

28S1(~r±~r+)

162 MeV

100 10 100 10

10

figure 7 : Data to high spin states in 28 51 were measured by an ArgonneNorthwestern-0regon State-Colorado-New Mexico State-LAMPF group, and compared to arbitrarily normalized DWIA predictions . The ratio of the T-0 to T~1 cross sections for the 6 states is 1 .5 (+0 .4,-0 .2) [ref .23)] .

NIICLEAR STRÛCTORE EFFECTS REVEALED BY INELASTIC SCATTERING IV .

A.

373

Giant resonances are excited by pions The first çlear ezampla ie in 40 Ca .

A cross section exhausting the sum rule was found for a state corresponding to the 4T~0 giant quadrupole lave1 . 26) This result at a resonant beam energy from SIN lose bean verified at BPICS, albeit with poorer statistical significance so far. s) B. Aa interesting energy dapmdeace for this H2 state in 4~Ca is suggested st lower eaergies . An 18 13eV bump ie seen at 67 MeV, but bacomes:weaker at 60 and 75 MeV[ref .Z~n. This result, measured at the LEP line of Ll~èflsF, has recently been reaffirmed with yet weaker yields at 50 and 80 MnV [ref . 2 )] . C.

No comparison of +~- sud +~ data for giant ra sosances are yet available .

Although long rues are needed, the difference betweea tr- and ~ yields to gust resonsaces would be of great value to determine the ieoepin structures of these importast states . After all, the photonuclear people have been making a living out of this for years . In summary, the DWBA succeeds for pion inelastic scattering for just the same states for which it succeeds in the ecattariag of conventional projectiles . Some new classes of transitions are sees in pion scattering, and the hole-delta model may be suited to explain these results . Intriquing and potentially valuable ieoepin information ie already kaown from n- - ~ differences. If you want to study isoecalar excitations, you now scatter alphg particles . For sensitivity And to study the to magnetic excitations,-you scatter electrons through 180° . ieoepin structure of inelastic transitions, you should be measuring pion scattering, cross ssctions . This survey would not have bees possible witkou" the willing cooperation of many researchare, and I wish to thank them all for their help . I am grateful to Lynx Martin for typing this manuscript . Refereaces 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19)

G.W . Edwards ß 8. Roet, Phye . Letters 37B (1979) 247. 8 . Dytnaa at al ., Private communication ß J .F . Amann et al ., B . Preedom et al ., to appear in Nuclear Phyeice . 'C . Olmen et al ., to be published. T .S .H . Lea and D. wrath, to be published. A. Anita, iC . Ys~e ß H. Ohteubot abstract 1D5. C .L . Morris at al ., Houston Meeting, and W.J . Braithwaite et Aa . Phys . Soc., 24, (1979) 668. D.F . Geaeanann et al ., Phye . Rev C18 (1979) 2223 . J .P . Schiffer et al ., Sull . Am . Phye . Soc. 20 (1975) . 663 . A.M . Bernstein, Y.R . Brown ß V .A . Madam, Phye . Rev . Letters 8 . Ivaresn at al ., Phye . Rev . Letters 40 (1978) 17 aad to be J. Bolgat et al, abstract IC17 . J . Holger at al ., Houston Meeting. P .M . Endt ß C. van der Leun, Nucl . Phys . A310 (1978) 1 . R.W . Fishy et al ., Phya . Letterre 84BII (1979) 169. 8. Schwerts at al ., abstract D10 . D. Dattnhard et al ., abstract 1D1, and to be published . W. Cottiagams at al ., abstract 1D3, and to be published . D.B . Hopkamp at al ., abstract 1D6 .

abstract 1C21

al ., Bull .

43 (1979) 425 . published.

374 20) 21) 22) 23) 24) 25) 26) 27) 28)

R.J . PETERSON L.W . Fagg et al ., private communication . C.L . Morris et al ., abstract 1D8 aad to be published . R.J . Peterson et al . to be published. 8 . Zeidman et al ., abstract 1D2 and C . Olmer et al ., to be published. W. Allbright et al ., abstract 1D4 . H.A . Thiessen, private communication. J . Arvieux et al ., Phys . Rev. Letters _42 (1979) 753 . S . Dytman, private communication 6 D. Chiang et al ., abstract 1E21 . D. Storm, private communication.