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E4·84·837

J.Bang,' S.N.Enbo", S.A.Faynns,z " .A.Garee" , N.I.Pyatov

MICROSCO P IC DESCRIPT ION

OF THE (p,n) SPECT RA AT E P = 200 Me V

Su bmitt ed t o I nte rnational Ctmfcrenc e on Anti nu c l eons and Nuc l eon-Nucleus I n t e rac tions (Colo r ado, Ma rch 18-2 1 , 1985)

J Th e Ni e l s Bohr I ns t itut e , Copenhagen, De nma r k

1 I. V. Ku r chatov Atomic Ene r gy Inst itute , HoseDw, US SR

1984

The charge exchange r eaction (p, 0) at intermediate proton energies i s a ver y useful tool for the study of the ef f ective interactions and the nuclear structure i n the sp i n- isospin channel / l - 4 / . For such energi e s a description of the cross sec04

tion in terms of the distorted wave impul se ,pproximation with the free N -N t - matrix seems well found ed 15. The observed spectr a are char acterized by the dominance of s pin-flip par­tic le-hole transitions compared to those wi t hout spin-flip which can be exp l ained in the f ramework of the one-meson ex­change model/6/ , From the observed neutron spectra at 0:: 0 0

one gets evidence of Gamov-Tel l er resonances (GTR) in a large number of nucle i t hroughout the periodic table, and by means of normalization to the {3-decay the relation bef:ween the ob­s erved cross sections for L = 0 (8= l )and the GT ma t rix elements has been estab l ished. In t his wayan estimate of the total GT strength for transi t ions wi th excitation energi es up to 30 MeV was obtained . The comparison be tween these data and the model­independent s um r ule showed, tha t this energy r e,ion contains not more than 50-65~ of t he expected GT strength 4/ . i. e ., one sees a quenchi ng of the lOW-lying branch of the s pi n-isospin excitations i n nuclei . Quantitative estimates of this effect in middle and heavy nuclei are rather uncertain due to the un­certainty in estimating t he background in t he region of the continuous spectrum. Such a background may arise both from par­ticle-hole transitions with L >0 and from contributions of many­particle pr ocesses (2p-2h trans it ions, etc.),

The effect of quenching of the low-lying GT transitions with small transferred momentum has been discussed intensively in the literature . Among t he possible explanations, the most popular has been the hypothesis of the coupling between the GTR and the 6 - isobar-nuc l eon hole exci~}ions, which are exoected t o lie at an energy Ex - 300 MeV . An important source of quenching may a l so be t he coupling between CTR and the multipair excitations which l eads to a considerable transfer of GT strength to the high-energy region up to E" _ 45 MeV/S/. In the framework of the theory of finite Fermi -systems (TFFS) the quenching effect is connected with the phenomenological quantity e larj, the local ~uasi-particle charge with respect to the spin-i~ospin field 19 . Its deviation from unity is condi­tioned by the nonconservation of the axial-vecto r current and for low-lying exci t ations it is possible to parametrize th is charge as e laT]". 1_2~r,/~eYE! the q ualiti t~"'f i s believed to

q 8 .; : '. _ . .i :' :n'T1 8 : r_ ~ • . .. . .. I . f "~.' " '. ,­ _",,,, I'''''::

be universal for all spin-f l ip tranSl.tlons at low encr·gy and small momentum transfe r s . The best es timate of e(llar l C"H1 be obta ined from the total obse rved GT stre ngth in t he low-lying part of the excitation spec trum (E x.$ 30 MeV). Th us, .1 theo­retical ca l c ula t ion of the back3round under the CTR, or more precise ly, in the re gi on of Ex S 30 l-1eV , is impor ta nl [or ge t ­ting a quantitative es timate of the quenching effect .

The f irst estima t e of the backgr ound i n 48Ca was give n in re f. 1 10l in which the co ntribution to the (p, n ) s pect r a was ca l­cula t ed f or spi n-f lip particle-hole (p-h ) transi ti ons wi th '\L ~ a without t aking the e ffe ctive in t eractions in to account. The ca l culated backgr ound unde r t he GTR from p-h tra ns it ions with L from 1 to 3 appeared to be about th r ee times sma ller than the one whi ch the experime nta lists separate as the flat part of t he neutron spec trum. As a r e su l t, t he estima te of the total GT st r ength wa s enlarged by _ 25%. Ana l ogous ca l cul ations were made for 90 Ze 1 11 / . I t should be noted tha t i t i s i. mpor tant to take into account t he ef f ec tive int eractions (among these the one-pion exchange) which l ead to the forma t ion of resona nces i n the exc i tation s pectra and the noticeable trans fer of the s trength of transitions wi t h L'> 0 t o t he excitation ene rgy re gi on above the GTR. This effec t is par ti cularly rema rkab le

11fo r charge-exchange excita t ions W}th spi n pa r i ties .T = 0- , )- , 2 + and 3+ a s shown in r e f. 112. Taki ng in to accoun t the ef­fec ti ve interactions natura lly l eads t o dim i nish i ng the back­gr ound under the GTR, since the mai n collective resonances wit h L > 0 energetically l ie above the GTR .

In this work we present microscopic ca l culations of the neut­r on spec t r a for th e r eac tions 90 Zr(P . 0) 90 Nb and 208 Pb lp. n) 2080i a t E p = 200 MeV. We may f ormu la t e the model used here as f ol­lows:

i ) The cr oss sect ion fo r small angles and smal l exci tat i on energ ies is given by the one- step quas i - e las tic sca tt ering process and may be descri bed i n the distor t ed wave impulse appr oxima tion (DWIA).

i i) The effec tive in t e r ac tion between the pro j ectile and /5/target nucleons is the one of ref .

t but t he spin-orbit and

t enso r compo nen ts were omitted, because i t was found by cal­culat i ons with pure ph-conf i gurations tha t they do not change noticeably t he tota l cros s sect i ons at small angles in the vi ­cinity of t h e GTR .

iii) The contribut i ons of spin- f l ip transi tions with multi­polarities O :5L S 7 as well a s t he contribution f r om the lAS were considered.

The s trength f unctions of charge-exchange t r ansitions were ca l culated i n the TFFS wi th the continuum t aken completely into account . As ef fec tive quasi partic l e in terac tions there were used th e ze ro range - interaction with the Landau- Migdal(IT

2

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1 calcula t ed fo~ e In d = 1.0

Fo}> de t ails of t he calculations see r e f. Q/ 12.14l The energy i 8 '" = -Q ( P. n ).

constant ~ ' = 1. 1 ( G 'o = 330 MeV fm 3) and the r enonnalized one­pion exc hange tensor i nteraction. In the description of the exc i ta tions with natura l parity a l so t he density-dependent iso­vec t or interact i ons were inc l uded. A detailed descrip t i on of the method was given in r ef. / 12 / .For each set of J and L := J, J .!.l the loca l r e sonances were extracted (see fig. 1 for 90Zr ) and their transition densities were obtained and used i n cal cula­tions of the reaction c r oss sec t ions.

In t he strength funct ions fo r the spin-f l ip excitations i n 90Zr more than 40 bound s tates and r esonances were located, with angu l ar momenta J from 0 to 8 (L = 0-7 ) in the energy interval 0 < -Q <f.. 40 MeV, and differential cross sections were calcu l ated for them. A detai l ed discussion of t hese calcula­

. . . . f 113 141 I h ' . 1 b . d tlons lS glven 1n re s. . . n t 1S energy l nterva eS1 es the GT transi t ions also transi t ions with L from I to 3 contri­bute to the c ros s sect ion at sma l l e, t he contributions from other transitions decrease fast with increasing L. Ana l ogous calculations for 208 Pb were per formed in pape rs 112-1 41

3

Finally , t he cros s sec tions for each r esonance we re fol ded wi t h Br ei t - Wigner shape func tions t o obta in the con t i nuous ener ­gy spec t r a and compar e them with t he experimental ones . Th e par ­tia l widths t yp ical for t he r esonance s t r ucture of t he obser ved spectra were used in t his procedure. For al l spin- flip trans i ­t ions t he quantity e ~ appear s as an exter nal factor i n t he cross sect i on . The magnitude of eq is dete rmi ned from t he assump t i on t hat in the vicinity of the GTR and be l ow i t a l l the observed cross sec tion is given by the one-s t ep react i on mechan i sm, i .e ., an upper l imi t is actua lly found for t he va lue.eq

The e ne r gy spectra calculated with e [a, ·1 = 0 . 8 for all s pi n­mu l tipole t rans itions a r e shown in figs~ 2 and 3 . Such va l ue of '>l[ (1 d mean s t hat the (ph) br a nch of t he low-l y ing spin-fl i p exci ­t ations exhausts only 64% of the possible shell- mode l tr ans i ­t ion stren gth, (quenching effec t ) .

As was expected , the GT transitions domina te the s pec tra a t sma l l angles in the r egion of -Q < 25 MeV, and the cross sections fo r the lAS are small. In 90Zr a t () = 0 ° o f t he to ­t a l cal cula ted c r oss section O"t :: 89 mb/s r be l ow - Q = 20 MeV the contri bution of GT transit i ons amount s t o aCT = 8 1 mb /s r , the r est be i ng shared be tween t he l AS , u1AS = 5 mb/ s r , and tran­s i tions wi t h L> 0 (backgr ound), ';:, 3 mb / sr . Th e ..:o r r e spond­a bi ng va lues i n 208pb at 0 c: 0 ° below - Q = 25 MeV a r e : at ::;; = 173 mb / s r, "GT = 143 mb/ s r, 0 = 18 mb/ s r and a = 12 rob / sr . Thus, in both nuclei a t () = oJA~he backgr ound un~er t he GTR occurred t o be rat her small , t hat agrees wi th t he results ob­t a i ned i n r efs . / 10.1 11 .

The ene r gy int e gr ated (O.s - Q.$ 40 MeV , = 0 . 8 ) t heore ti ­eq ca l GT cros s sections a t () = 0 ° a r e found to be 11 4 and 192 mb /s r in 90 Zr and 208Pb , r espectively, of which appr oxima.­t e l y a qua.rt e r is di s p l ayed above the GTR .

Fo r s pi n-d i pol e t r ans it ions i n 90Zr the ener gy int egr at ed c r os s sec tions calcul a ted with e [a T1 0 .8, amoun t t o 11. 8 , 30 and 48. 4 mb/ s r f or 0 = 0°, 2~ 5° and 4 . 5 °, r espec t ively, whi l e the corre s pondi ng values in 208P b are 26 , 85.6 and 130 mb/sr . The main s trength of these transi tions in both nuc ­l ei is located in the r egion 20 $ -Q $ 30 MeV.

A noticeab l e contribution to t he c r oss sect ion at small an gl es f r om s pin- f lip r e sonances ~ith L = 2 and 3 we obtained only a bove t he GTR. The estima ted wi t h = 0. 8 e nergy integr a ­eq t ed c r oss sec t ions fo r t hem ar e about 10 and 22 mb/ sr in gOZr and 208pb , r es pective l y. But the s e e s t imates might be changed upon i nclusion of t ensor inte r ac tions i n t he reaction calcula ­t i ons . At pr esent our model expl a ins onl y about hal f of the obser ved c r oss sec t ion above the GTR.

In acco rdance with calculations /1 2/ f or gOZr i n t he neigh­

12

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Fig. 2. Comparison between caZcuUzted and experimentaZ neutron spectra at srrrlH angZes for the reac tion 90 Zr (P . n) 90Nb at Ep = 200 MeV. The contribut ions from GT transiti ons 11+) , lAS (0+) and the background of spin-muZtipoZe transitions with L > 0 are separated. rae totaZ cross section is shown with fu ZZ Zine.

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bourhoo d of GTR t he ma gni t ud e of the GT ma t rix e lement wi th Fig. 3. The same as 1:n fig . 2 for the reaction 208Pb(p,n)208Bi t he e ! quenching f ac t or i nc luded i s M ~T= 1 4 . 7 ,i . e . ,i t ex- at Ep = 200 MeV.

" 5

13 . Bang J. et a l. Prep ri llt NBI 84- 31 , Co pe nhagen, 1984 . haus ts 49% o f the sum r u l e 3 (N - Z) . Below t he GTR onl y 7.5% of 14 . Gare ev F. A. et a 1. Yad. Fiz ., 1984 , 39 , p.1401 .

thi s sum rul e is found. 15 . Buck B. , Pe r ez S .M . Phys . Rev. Le t t., 1983 , 50 , p . 1975 . The ma gnitude of M~ T for 208 Pb calculated with inc lus ion 16 . Wilkin C. et al. Nuc l.Phys ., 197 3, B62 , p . 61; De l orm J.

of t he quenching effect i s= 47 . 2 i n the v i c inity of t he GTR, e t al. Nuc l. Phys . , 1982, A389 , p. 50 9. i.e . , ab out 36% of the sum rule 3 (N- Z). Below GTR about 8% of the to t a l GT strength is found.

The one- seep mechanism with quenching factor e 2 = 0. 64 , t hu5 , allows for a good descriotion of the observed neut~on spectra in the interval _Q < 20-25 MeV. An important part of t he missed GT s trength mi gh t be distributed above the GTR up to Fermi ener­gy 'F where the density of complex states (2p - 2h - t ype ) i s very high 181

The va l ue ~{or] = 0 . 8 obtai ned above siggests the necessity of renormalization of all i sovector axia l - vecto r vertices for low-energy processes accompanied by a small q -transfer. In {3 ­decay the quench i ng effect ma'y l ead to renormal i za t ion of the axi a l coup ling constant of weak interactions in nuclei gA~(g~nm~ = eq . gA::: 1. 0 ( in units of gv ) . This is supported by model­independent analysis of {:3- decay data (or mir ror nuclei / 15/. Analogously, the rrN coupling constant is renormal i zed in nuc­l ei by a factor of e! = 0.64 in qual itative agreement with the conc l usions of ref . 1 16 /

In conc l usion the authors wan t t o thank C.Gaa rde fo r pro­vid i ng us with experimenta l spect ra and for fr uitful discussion.

REFERENCES

I . Bainum D.E. et al. Phys.Lett . , 1980,44, p.175 1; Horen D. J . et al. Phys.Let t. , 1980, 95B, p.27 .

2 . Gaarde C. et al . Nucl.Phys., 198 1, A369, p.258. 3 . Goodman C.D. Nucl.Phys., 1982 , A374, p.24Ic. 4 . Gaarde C. Nuc l. Phys . , 1983, A396 , p .127c. 5 . Love H.G ., Fr aney M.A. Phys.Rev. , 1981, C24, p .1 073 . 6 . Br own G.E. et al. Phys.Rev.Lett., 1981,46, p.1057 . 7 . Ericson M. et al. Phys.Lett., 1973, 45B, p. 19; Bohr A. ,

Mo tte l son B.R. Phys.Lett., 1981, 100B, p.IO. 8. Bertsch G.F., Hamamoto 1. Phys . Rev., 1982, C26, p. 1323;

Arima A. e t al. Phys.Lett., 1983, InB, p. 126. 9. Mi gdal A.B. Theory of Finite Fermi - Systems and Prope r ties

of Atomic Nuc l ei. Wiley, New York, 1967 . 10 . Os t e rfeld F. Phys.Rev. , 1982, C26 , p.762. . II. Oster feld F., Schu l te A. Phys.Lett. , 1984, 138B, p . 23. 12. Fayan s S. A., Pyatov t-I.1. Pr oc. 4th I nt. Conf. Nuclei Far

f r om Stabi l i ty . Helsingor, 1981 . CERN 8 1- 09, Geneva , Received by Publ ishing Depar tment 198 1, p . 287; Pyatov N. l . , Fayans S.A. Sov.J.Part.Nucl . , on December 24 , 1984. 1983, 14 , p . 401 . 7

6

COMMUNICATIONS, J INR RAPI D CO MMUNI CATIONS, PREPRI NTS,AN D PROCEE DINGS OF THE CON FERENCES PUBL ISHED BY THE JO INT IN STI TUTE FOR NUC LE AR RESEARC H HAVE THE STATUS OF OFFIC IAL PUB LICAT IONS .

JI NR Commun icat ion and Preprint references s hould co~taln:

- names and initials of authors, - abb revia t ed name of the Institute (JI NR) and publicat ion

i ndex , - location of publi sher (Dubna), - year of publ i cation - page number (if necessary).

For example :

1. Pervushin V.N . et al. JINR,P2-84 - 649, Dubna, 1984.

Re f erences to concrete articles , incl uded into the Pro­ceedings, shou ld contain

- names and i nit ials of authors , - t itl e of Proceed i ngs , introduced by word "lnJ H

- abbreviated name of the Inst itute (JINR) and publicat ion i ndex,

- location of publ isher (Dubna), - year of pub1 ication, - page number.

for examp l e:

Kolpakov I .F. In. XI Intern. Symposium on Nuclear Electronics, JINR,D13-84-53, Dubna, 1984, p.26.

Savin I.A., Smirnov C.I . In: JINR Rapid Communications, N2-84,Dubna,1984,p.3.

•

EaHr E. HAp . E4- 84-837 ~KpOCKonH~eCKoe onHcaHHC cneXTpOB(p,n) peaK~H npH Ep = 200 M.B

ITpeACTaBneKY MHKpOCKonH~eCKHe pac~eT~ HeATpoHH~ cneKT­POB IUlR peaK1\HA 90 Zr (P. n )90 Nb H 208 Pb (p. n) 208 Bi npH Ep = : 200 M3B. PaCqeT~ nOKa3aJlH, QTO oAHocTyneHqaT~ MexaHHSM

peaK~HH xopomo anHCblsaeT HeATpoHHble cneKTpbl AnR MaJIbIX Y["JIQB pacceRHHH B HHTepnane 0 < -Q .$20- 25 M3B H npH 60nee BblCOKHX

3HeprHRX B030YJK,lJ;eHHR DAHocTyneH1.IaTbie npou,eCCbJ OO'bRCHRIOT npH6nHSHT€JIbHO nonoBHHy HaOroJnaeMOro CeqeHHR.

PaGoTa DblnOJ]HeHa B fla6opaTopHH T€OpeTH"IeCKoi1 ~H3HKH mum.

DpenpKHT O&beAHHeHHOro KHCTHTYT8 RnepHYX HccneAoBaHHA. nYOH8 1984

Bang J. et al. Microscopic Description a t Eo = 200 MeV

of the (P. n) Spectra E4-84-8J7

Microscopic calculations of the neutron spectra for the reactions 90Zr(P. n)90 Nb and 208 Pb(p. n) 208 U1 at Ep = = 200 MeV are presented. It was obtained, that the one-step mechanism allows for a good description of the neutron spect­ra for small angles in the interval 0 < - Q ~ 20-25 HeV, and for a higher excitation energy one-step processes explain only about half of the observed cross sections.

The investigation has been performed at the Laboratory of Theoretical Physics, JINR.

Preprint of the Joint Institute for Nuclear Research. Dubna 1984