Coupled channel effects in the scattering of 6,7Li BY 58Ni

Volume 161B, numbe 1,2,3 PHYSICS LETTERS 24 Oc obe 1985 COUPLED CHANNEL EFFECTS IN THE SCATI'ERING OF 6'7Li BY 5SNi ~ ~,J. GOMEZ-CAMACHO 1, M. LOZANO Depa a nen o de Fisica A omica y Nuclea , Facul ad de Fisica, Uni e sidad de Se illa, Apa ado 1065, 41080 Se illa, Spain and M.A. NAGARAJAN SERC, Da esbu y Labo a o y, Da esbu y, Wa ing on W4A 4AD, England Recei ed 15 Ap il 1985; e ised manusc ip ecei ed 20 June 1985 Using a single-pa icle desc ip ion o 6.7 Li and Woods-Saxon gene a ed wa e unc ions o 58 Ni ma e densi y dis ibu ion, he diagonal and ansi ion densi ies a e calcula ed. Folding hese densi ies wi h he M3Y e ec i e in e ac ion, he coupling and diagonal po en ials a e ob ained. Coupled channel calcula ions o 6'TLi on 58 Ni a bomba ding ene gies in a ange om 12 o 74 MeV a e pe o med. I is shown ha he p edic ions o he coupled channel calcula ions a e consis en wi h hose o op ical model calcula ions using olded po en ials eno malized by a ac o 0.6 in he en i e ange o ene gies. In ecen yea s he sca e ing o ligh hea y ions such as 6'7Li and 9Be ha e ecei ed conside able in e es . This is due o he ailu e o he double olding po en ial [1] ob ained om an e ec i e nucleon-nucleon in e ac ion [2], which ha e o be eno malized by a ac o a ound 0.6 in o de o i he elas ic sca e ing da a o hese nuclei. This anomaly has been a ibu ed o b eak-up e ec s which become impo an due o he low b eak-up h eshold o hese nuclei [3]. This idea has been con i med by calcula ions desc ibing 6Li and 7Li, espec i ely, as (a + a) and (a + ) sys ems. I is ound ha o ep oduce he elas ic sca e ing da a o 6'7Li in e ms o he op ical po en ials o he a ge wi h he agmen s o he p ojec ile, he b eak-up s a es mus be conside ed. The clus e model is also success ul in explaining Wo k pa ially suppo ed by he Spanish Comision Aseso a de In es igacion Cien i ica y Tecnica, con ac numbe 2868-83. 1 Cu en ly a Da esbu y Labo a o y, Da esbu y, Wa ing on W4A 4AD, England. he beha io o pola ized p ojec iles. I is shown [4] ha he coupling e ec s be ween he clus e - desc ibed exci ed s a es ha e a e y impo an e ec on he enso analyzing powe s, e en a e y low ene gy. O pa icula in e es is he wo k o Saku agi e al. [5], who use a de ailed clus e desc ip ion o 6Li, disc e izing he con inuum o b eak-up s a es in se e al bins o each ele an pa ial wa e. The diagonal and ansi ion po en- ials a e ob ained om an e ec i e nucleon- nucleon in e ac ion con olu ed wi h he a ge densi y and he co esponding p ojec ile diagonal and ansi ion densi y. I is shown ha he main con ibu ion on he elas ic sca e ing comes om he esonances which a ec mainly he eal po en ial. Recen ly we ha e de eloped a single-pa icle desc ip ion o 7Li [6], assuming a (0s)4(0p) 3 con igu a ion in a single-pa icle well o he ele an s a es o 7Li. The di e en nega i e pa i y s a es o his nucleus a e ob ained by diagonalizing a esidual hamil onian, and he diagonal and 0370-2693/85/$ 03.30 © Else ie Science Publishe s B.V. (No h-Holland Physics Publishing Di ision) 39 Volume 161B, numbe 1 ~, ,3 PHYSICS LETTERS 2 4 Oc obe 1985 ansi ion densi ies a e ound o be ela ed wi h he single-pa icle wa e unc ions. We ha e shown ha a coupled channel calcula ion including he ele an s a es explains he expe imen al da a o 7Li + 4°'48Ca a 89 MeV. In his wo k we use he same o malism o analyze he elas ic sca e ing o 6Li and 7Li by 58Ni o e a wide ange o ene gies. The in e media e coupling model [7] has explained success ully he s uc u e o he 0p nuclei. I is shown ha he e ec i e nucleon- nucleon in e ac ion o he 0p shell has a la ge Majo ana componen which a ou s he s a es wi h maximum spa ial symme y. When he spin-o bi o ce is small, as happens in he i s hal o he shell, he di e en s a es can be labelled wi h he i educible ep esen a ions o he pe mu- a ion g oup o spa ial symme y [X] o which hey belong, as well as by he o bi al (L), spin (S) and o al (J) angula momen a and he isospin (T). Fo 6Li all he low-lying s a es belong o he con igu a ion (0s)a(0p)2 wi h he maximum spa ial symme y [2]. The g ound s a e is assumed o be labelled by L = 0, S = 1, T = 0 and he mul iple wi h J=3,2,1 co esponds o L=2, S=I, T=0. Fo 7Li he low-lying s a es co espond o he (0s)4(0p) 3 con igu a ions, wi h he maximum spa ial symme y [X]= [3]. The g ound s a e (3/2-) and he i s exci ed s a e (1/2-) co e- spond o L = 1, S = 1/2, T = 1/2 and he 7/21 and 5/2~- s a es co espond o he L = 3, S = 1/2, T = 1/2 double . The densi y ope a o can be w i en as P( ) = E E [o~'b Yx(~)] "R*( )R j( ), , (1) I~lj X whe e O~ ' ~= [a~ .a ,]X.(ljl[Yx[[l,). (2) a + 1, (a ,) is he c ea ion (annihila ion) ope a o o a pa icle in he shell labelled by lj(lg), and R b ( ) (R i,( )) he co esponding adial wa e unc- ion. When only s a es o he (0s)4(0p) n con igu a- ions a e allowed, hen eq. (1) can be ew i en as ~( ) = po( ) + [O2" YE( )] pE( ), (3) Table 1 Reduced ma ix elemen s o 6Li. 1 + 3 + 2 + 1~- 1 + 0 -0.6750 -0.5705 -0.4419 3 + -0.6750 -0.7394 -0.4773 -0.3375 2 + 0.5705 0.4773 -0.3773 0.4465 12 ~ -0.4419 -0.3375 -0.4465 -0.3458 Table 2 Reduced ma ix elemen s o 7Li. 3/2- 1/2- 7/2 5/2- 3/2 - 0.4841 0.4841 - 0.6454 0.2635 1/2- - 0.4841 0 0 - 0.4930 7/2- - 0.6454 0 - 0.7469 0.2587 5/2- - 0.2635 - 0.4930 - 0.2587 - 0.6338 whe e po( )=(1/nc )[aR2os( )+nRZp( )], (4) 0 2 = (6/4~')l/21a~p • aop[ x=2, (5) P2( )=RZop( ). (6) The ma ix elemen s o 02 be ween he ele an s a es o 6Li and 7Li a e shown in ables 1 and 2. In o de o i he quad upole momen and B(E2) o 7Li we had o in oduce an addi ional cha ge o 0.215e o each one o he 0p shell nucleons, and om ha , we jus i ied he inclusion o an addi ional mass o 0.43 o each nucleon in he 0p shell [6]. This is main ained o 6Li also in his wo k. The densi y o 58Ni was ob ained om a single-pa icle desc ip ion [8] which ag ees wi h elec on and p o on sca e ing da a. The e ec i e nucleon-nucleon in e ac ion [2] is o he o m V( ) = 7999 exp ( - 4 )/a - 2134 exp ( - 2.5)/2.5 - 262 8 ( ). (7) The densi y dis ibu ion o 7Li is desc ibed elsewhe e [6]. Fo 6Li, we ha e jus aken o 7Li one neu on om he 0p-shell, keeping he same single-pa icle wa e unc ions. Wi h hese densi ies and e ec i e nucleon- nucleon in e ac ion he eal po en ials o he 40 Volume 161B, numbe 1~.,3 PHYSICS LETTERS 24 Oc obe 1985 1-00 e. I I I I n 12 MeV 10 ° ..... 10 ° - ,--.~-,-~_ 10 °. ~ "~ -o o 'k 18MeV l I : I ' O eVl 0 60 120 180 O(deg) 100 I [ " W---T-- 100 b ~ a~D 73 10 -~ 10 -2 10- _ ~ ~ 50.6~ MeV (b) I ~Li+ S~Ni ~ I I I~P 10' 20 30 40 (9 (deg) I 50 60 Fig. 1. (a) Elas ic c oss sec ions o 6Li wi h 5SNi a 12, 14, 16, 18 and 20 MeV. The dashed ine line is ob ained including only he elas ic channel wi h he olding po en ial wi hou eno maliza ion. The do -dashed ine line co espond o he olding po en ial eno malized by a ac o 0.6. The con inuous line is he ull coupled channel calcula ion. The expe imen al da a a e om e [9]. (b) Same as (a) bu a 50.6 MeV (expe imen s om e . [10]) and 73.7 MeV (expe imen s om e . [11]) bomba ding ene gies. P edic ions o he un eno malized po en ial a e no shown because he o al disag eemen wi h he da a. eac ions 6Li + 5SNi and 7Li + 58Ni a e de- e mined. Following he p ocedu e o Saku agi e al. [5] we ix he imagina y po en ials as 0.6 imes he eal ones. This is equi alen o assuming an imagina y e ec i e nucleon-nucleon in e ac ion which is 0.6 imes ha o exp ession [7]. We compa e he expe imen al da a wi h (a) he p edic ions o he double olded po en ial wi hou eno maliza ion, (b) he p edic ions o he double olded po en ial eno malized by a ac o 0.6 and (c) he p edic ions o he coupled channel calcula- ions wi hou any eno maliza ion. These compa i- sons a e shown in igs. la and lb o he elas ic sca e ing o 6Li by 58Ni a a ange o ene gies om 12 MeV o 74 MeV. I was obse ed ha o 6Li ene gies g ea e han 20 MeV, he ene gy di e ence be ween he s a es o ming he iple (L = 2, S = 1) can be igno ed. Thus, ea ing hese as degene a e he esul s o a coupled channel calcula ion wi h wo channels o ou channels yields he same esul . (In he wo-channel calcula ion, he L = 2 le el is ixed a he cen oid o he iple ). Fo ene gies below 20 MeV, i was obse ed ha he dominan coupled channel e ec a ose om he 3 ÷ membe o he iple . Howe e , he o he wo s a es (2 ÷ and 1 +) could no be o ally igno ed when la ge angle sca e ing was conside ed. The analyses o he elas ic sca e ing o 7Li by 5SNi a e shown in ig. 2 o p ojec ile ene gies om 14.2 o 20.3 MeV. I was ound ha he e ec o he 5/2- s a e o 7Li on he elas ic sca e ing was negligible a all he ene gies and a ene gies below 20 MeV, he coupling e ec o he 7/2- 41 Volume 161B, numbe 1,2,3 PHYSICS LETTERS 24 Oc obe 1985 10 o 10 0 I 0 ° % "D 10 o IO-T io- o I I I I I ~ 18.3 M eV - 2 0.3 MeV k'. ~- ~ *,. %., 7Li +58N i 2 I I I I I 60 120 180 0 (deg) Fig. 2. Elas ic c oss sec ions o 7Li wi h 58Ni a 14.2, 16.3, 18.3 (expe imen s om e . [9]) and 20.3 (expe imen s om e . [12]) MeV. The lines ha e he same meaning as in ig. la. s a e on he elas ic sca e ing was also small. Thus, in he ene gy ange om 12 o 20 MeV, he only s ong coupling a ises om he 1/2- s a e a 470 keV. I can be seen in bo h cases o elas ic sca e ing o 6Li and 7Li ha he esul s o he coupled channel calcula ions a e almos iden ical o hose o he double olded po en ial eno mal- ized by a complex cons an ac o (0.6 + 0.6i). F om he igu es i is seen ha whe eas ag eemen be ween he coupled channel calcula- ions and he expe imen al da a is e y good, a he lowe ene gies (E < 20 MeV) we see dis- c epancy be ween heo y and expe imen a la ge angles. These may be due o ou choice o he same geome y o he eal and imagina y po en- ial. These esul s con i m wha was sugges ed in a p e ious pape [6], his is, ha he eno maliza- ion o he eal po en ial can be explained wi h a single-pa icle exci a ion mechanism, which does no ake in o accoun he con inuum na u e o he b eak-up s a es, bu which allows o a complex e ec i e in e ac ion. I seems necessa y o ha e mo e p ecise expe imen al da a a low ene gy in o de o decide i he e is a change in he cha ac e is ics o he 6Li and 7Li op ical po en ials. Such a change in he cha ac e is ics ha e been obse ed by Lilley e al. [13] in he elas ic sca e ing o 160 on 2°8pb a ene gies close o he Coulomb ba ie . Re e ences [1] G.R. Sa chle and W.G. Lo e, Phys. Le . 76B (1978) 23; G.R. 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A440 (1985) 543. [7] D.R. Inglis, Re . Mod. Phys. 25 (1953) 390; S. Cohen and D. Ku a h, Nucl. Phys. 73 (1965) 1. [8] F. Malagu i, A. Uguzzoni, E. Ve ondini and P.E. Hodgson, Nucl. Phys. A297 (1978) 287. [9] K.O. P ei e , E. Spe h and K. Be hge, Nucl. Phys. A206 (1978) 545. [10] LT. Chua, F.D. Becche i, J. Janecke and F.L. Milde , Nucl. Phys. A273 (1976) 243. [11] R. Hu man, A. Galonsky, R. Ma kham and C. Willianson, Phys. Re . C22 (1980) 1522. [12] G. Tunga e, R. BS ge , P. Egelho , K.-H. M~Sbius, Z. Mo oz, E. S e ens, W. D e es, I. Koening and D. Fick, Phys. Le . 98B (1981) 347. [13] J.S. Lilley, B.R. Ful on, M.A. Naga ajan, I.J. Thompson and D.W. Ba nes, Phys. Le . 151B (1985) 181. 42