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
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(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. Sa chle , Phys. Le . 83B (1979) 284;
J.S. Eck, T.R. Ophel, P.D. Cla k and D.C. Weisse , Nucl.
Phys. A334 (1980) 519;
M.F. S eeden, J. Coope smi h, S.L Ca w igh , M.D.
Cohle , N.M. Cla ke and R.J. G i li hs, J. Phys. G6 (1980)
501;
C.W. Glo e , R.I. Cu le and K.W. Kempe , Nucl. Phys.
A341 (1980) 137.
[2] G.R. Sa chle and W.G, Lo e, Phys. Rep. 55 (1979) 183.
[3] I.J. Thompson and M.A. Naga ajan, Phys. Le . 106B
(1981) 163;
M.A. Naga ajan, I.J. Thompson and R.C. Johnson, Nucl.
Phys. A385 (1982) 525;
Y. Saku agi, M. Yahi o and M. Kamimu a, in: Con ib.
pape s P oc. 1983 RCNP In e n. Sy up. on Ligh ion
eac ion mechanism (Osaka, May 1983) p. 84; and P og.
Theo . Phys. 68 (1982) 332;
M. Yahi o, M. Nakano, Y. Ise i and M. Kamimu a, P og.
Theo . Phys. 67 (1982) 1467.
[4] H. Nishioka, J.A. Tos e in, R.C. Johnson and K.I. Kubo,
Nucl. Phys. A415 (1984) 230.
[5] Y. Saku agi, M. Yahi o and M. Kamimu a, P og. Theo .
Phys. 70 (1983) 1047.
[6] J. Gomez-Camacho, M. Lozano and M.A. Naga ajan,
Nucl. Phys. 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