NUCLEAR STRUCTURE WITH HEAVY-ION
TRANSFER REACTIONS
G. Morrison
To cite this version:
G. Morrison.
NUCLEAR STRUCTURE WITH HEAVY-ION TRANSFER REACTIONS. Journal de Physique Colloques, 1972, 33 (C5), pp.C5-111-C5-126.
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JOURNAL DE PHYSIQUE
C o l l o q u e C 5 , supplement au n o 8-9, Tome 33, AoGt-Septembrc
1972, page C 5 - i l l
G.C. MORRISON
Argonne N a t i o n a l L a b o r a t o r y , U.S,A.,and
C.E.N.
S a c l a y , France.
A b s t r a c t . - A t t h e p r e s e n t t i m e t h e s t u d y of n u c l e a r s t r u c t u r e w i t h heavy-ion t r a n s f e r rea c t i o n s i s t h e f o c u s of i n c r e a s e d a t t e n t i o n , b o t h e x p e r i m e n t a l and t h e o r e t i c a l . The g e n e r a l
f e a t u r e s e n c o u n t e r e d i n t h e m a j o r i t y of s u c h r e a c t i o n s a r e surveyed i n terms of t h e w e l l known s e m i - c l a s s i c a l d e s c r i p t i o n . T h i s i s followed by a d e s c r i p t i o n of c u r r e n t DWBA app r o a c h e s and t h e i r u s e t o e x t r a c t q u a n t i t a t i v e s p e c t r o s c o p i c i n f o r m a t i o n from s i n g l e and
multi-nucleon t r a n s f e r r e a c t i o n s . F i n a l l y t h e s t r i k i n g s e l e c t i v i t y i n l e v e l s e x c i t e d and
o t h e r f e a t u r e s revealed i n recent experimental r e s u l t s a t high energies a r e discussed.
-
R6sum6,
A l ' h e u r e a c t u e l l e 1 1 6 t u d e de l a s t r u c t u r e n u c l s a i r e 3 l ' a i d e des r i a c t i o n s de
t r a n s f e r t p a r i o n s l o u r d s e s t un c e n t r e d ' i n t i r z t c r o i s s a n t a u s s i b i e n s u r l e p l a n e x p i r i men,tal que t h s o r i q u e . Les a s p e c t s gdn6raux r e n c o n t r h s dans l a m a j o r i t i d e c e s r i a c t i o n s s o n t
e x p o s i s e n termes d e l a d e s c r i p t i o n s e m i - c l a s s i q u e b i e n connue. S u i t une d e s c r i p t i o n d e s app r o c h e s c o u r a n t e s en DWBA e t d e l e u r u t i l i s a t i o n pour e x t r a i r e l e s i n f o r m a t i o n s s p e c t r o s c o p i q u e s q u a n t i t a t i v e s 1 p a r t i r d e s r g a c t i o n s 1 un ou p l u s i e u r s nucl8ons. Finalement l a s 6 l e c t i v i t i f r a p p a n t e dans l c s n i v e a u x e x c i t i s e t l e s a u t r e s a s p e c t s r i v 6 l i s p a r l e s r s s u l t a t s
expirimentaux 3 haute 6nergie sont d i s c u t e s .
I
. Introduction.
-
During t h e p a s t few y e a r s an
i n d i c a t i o n b o t h of p r e s e n t t r e n d s and t h e d i r e c -
i n c r e a s i n g f r a c t i o n of n u c l e a r r e a c t i o n s t u d i e s h a s
t i o n of f u t u r e developments. But by way of i n t r o -
i n v o l v e d t h e u s e of heavy i o n s a s p r o j e c t i l e s . Such
d u c t i o n i t would seem a p p r o p r i a t e t o b r i e f l y s u r -
i n v e s t i g a t i o n s o f heavy-ion
vey some f e a t u r e s which a r e e n c o u n t e r e d i n t h e ma-
t r a n s f e r r e a c t i o n s have
been s t i m u l a t e d by t h r e e r e c e n t developments : ( a )
j o r i t y of heavy-ion
t h e a v a i l a b i l i t y o f a v a r i e t y of h i g h - q u a l i t y
be based on t h e well-known s e m i - c l a s s i c a l
[I:,
r e a c t i o n s , The d i s c u s s i o n w i l l
descrip-
heavy-ion beams of s u f f i c i e n r e n e r g y and i n t e n s i t y ,
tion
t o g e t h e r w i t h improved p a r t i c l e - i d e n t i f i c a t i o n
a c t i o n s . T h i s d e s c r i p t i o n has t h e a d v a n t a g e s of
and
d a t a - h a n d l i n g systems ; (b) t h e i n t e n s i v e work on
o r i g i n a l l y developed f o r sub-Coulomb
re-
b e i n g t r a n s p a r e n t , of i n d i c a t i n g t h e main f e a t u r e s
r e a c t i o n t h e o r i e s and codes based on s e m i c l a s s i c a l
of t h e r e a c t i o n mechanism, and o f b e i n g a p p l i c a b l e
and d i f f r a c t i o n models a s w e l l a s on t h e DWBA, and
even a t e n e r g i e s above t h e Coulomb b a r r i e r .
( c ) t h e i n t e r e s t i n few-nucleon c o r r e l a t i o n s , espec i a l l y t h e p o s s i b i l i t y o f q u a r t e t t i n g phenomena i n
fp-shell nuclei.
2 . S e m i - c l a s s i c a l D z s c r i p t i o n . - a ) Cenemz
twes.
-
feu-
Because o f t h e i r l a r g e c h a r g e p r o d u c t
Z t.Z 2 and s m a l l v e l o c i t y v , heavy i o n r e a c t i o n s a r e
-
The u s e o f complex n u c l e i a s p r o j e c t i l e s l e a d s t o
c h a r a c t e r i z e d by l a r g e v a l u e s of t h e Sommerfeld
b o t h q u a l i t a t i v e and even q u a n t i t a t i v e d i f f e r e n c e s
p a r a m e t e r ri = z 1 z 2 e 2 / 6 v = b/2K, where b i s t h e
from t h e f a m i l i a r t r a n s f e r r e a c t i o n s produced by
d i s t a n c e o f c l o s e s t approach i n a head-on
l i g h t i o n s , More than i n l i g h t i o n t r a n s f e r t h e
s i o n . A l a r g e n i m p l i e s a small. X and hence a w e l l
colli-
s t r u c t u r e o f t h e p r o j e c t i l e and t h e dynamics of t h e
localized Rutherford t r a j e c t o r y f o r the s c a t t e r i n g
reaction a r e interlinked.Thus the s p e c i f i c features
process.
o f t h e r e a c t i o n p r o c e s s have t o b e w e l l u n d e r s t o o d
n s m a l l . ) For a f i x e d s c a t t e r i n g a n g l e 8, t h e d i s -
t o hope t o r e a c h t h e l e v e l where n u c l e a r s t r u c t u r e
t a n c e of c l o s e s t a p p r o a c h i n such a t r a j e c t o r y
p r o p e r t i e s c a n be d e t e r m i n e d . Much o f t h e i n i t i a l
( F i g . 1 ) i s g i v e n by :
( o f course,
x
may
be smalleven for
s t u d i e s have i n v o l v e d t h e t r a n s f e r of s i n g l e nuc l e o n s whereby t h e n o v e l f e a t u r e s o f heavy-ion
re-
a c t i o n s may b e d e t e r m i n e d by comparison w i t h c o r responding l i g h t-ion reactions.
I n t h i s p a p e r , I c a n n o t of n e c e s s i t y r e v i e w ex-
Rmin
=
n
(1 +
CSC
1
8)
2
( 1 + CSE
=
f
8 ) . (1)
2Ec.m.
This r e l a t i o n a l s o gives the distance of c l o s e s t
approach i n t h e i n i t i a l and f i n a l t r a j e c t o r i e s , R;
t e n s i v e l y t h e f i e l d of heavy-ion r e a c t i o n s , b u t
and Rf f o r a t r a n s f e r r e a c t i o n a t a n a n g l e 8.
r a t h e r s h a l l c o v e r a few t o p i c s i n some d e t a i l a s an
Semi-c-assically t h e r e a c t i o n w i l l o n l y t a k e p l a c e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972509
G.C. MORRISON
which the a n g u l a r d i s t r i b u t i o n s peak is mainly determined by the e l a s t i c s c a t t e r i n g b e f o r e and
a f t e r the t r a n s f e r , even f o r 2 t r a n s f e r o t h e r than
optimum.
The matching requirements on t h e ingoing and
outgoing o r b i t s i n coordinate o r a n g u l a r momentum
space lead t o an optimum Q value [2]
f o r the t r a n s -
f e r r e a c t i o n . The value can be found from the semic l a s s i c a l condition f o r an undisturbed t r a j e c t o r y
a t the n u c l e a r s u r f a c e , i . e .
2 Ref.
and ROi
Fig. 1.
-
2
BE
(2
Ograzing),
Hence :
-2.
1
1 1
C l a s s i c a l Rutherford t r a j e c t o r y .
Bi
( 1 + csc - 8 . ) =
2 1
2Ec.m.
with appreciable probability i f t h e i r difference
does n o t exceed t h e o r d e r of A.
The f u r t h e r c h a r a c t e r i s t i c f e a t u r e of the heavy
ion r e a c t i o n i s t h e s t r o n g absorption a t small
which f o r €Ii
= 0
f
leads t o an optimum r e a c t i o n Q
value :
i n t e r - n u c l e a r d i s t a n c e s . A s the overlap between the
two n u c l e i i n c r e a s e s the p r o b a b i l i t y f o r t r a n s f e r
i n c r e a s e s . However, i f the minimum d i s t a n c e becomes
s m a l l e r than a c e r t a i n r a d i u s - t h e s t r o n g i n t e r a c t i o n r a d i u s , Ro
-
t h e p r o b a b i l i t y f o r a d i r e c t re-
For e n e r g i e s below the Coulomb b a r r i e r ,
a c t i o n decreases d r a s t i c a l l y and the incoming f l u x
8. = 8 = 180°, and the matching condition i s inde1
f
pendent of P t r a n s f e r ; above t h e b a r r i e r , Q i = O f
is absorbed i n t o a compound nucleus. Thus the s t r o n g
implies Li # Lf (equ. 2) and hence t h e c a l c u l a t e d
a b s o r p t i o n optimizes the t r a n s f e r r e a c t i o n t o t r a -
Qopt d e s c r i b e s a p a r t i c u l a r L
j e c t o r i e s matched a t t h e n u c l e a r s u r f a c e .
The l o c a l i z a t i o n i n coordinate space has an equiva l e n t l o c a l i z a t i o n i n angular momentum space
-
which
has the advantage t h a t t h e angular momentum t r a n s f e r
I
-
I.
= L~
L
DeviOP t
f
a t i o n s from the optimum Q value r e s u l t i n a de-
crease i n t h e t r a n s f e r c r o s s s e c t i o n . However, the
heavy-ion
r e a c t i o n i s c h a r a c t e r i z e d by a s e v e r i t y
of Q dependence not found i n l i g h t - i o n r e a c t i o n s .
is made e x p l i c i t . Associated with a p a r t i c u l a r t r a -
The r e a c t i o n i s e i t h e r a t t e n u a t e d by the Coulomb
j e c t o r y i s a w e l l defined angular momentum L where :
b a r r i e r (Q
) o r is forced t o take p l a c e f a r
OP t
out with l i t t l e overlap (Q
Q
) The semi-clasOP t
s i c a l c o n s i d e r a t i o n s can a l s o be extended t o o b t a i n
Q
.
the optimum Q value f o r o t h e r .P t r a n s f e r s - o r t h e
Because of t h e s h o r t wavelength ?C of t h e heavy-ion,
causing both l a r g e L values and rapid changes i n
barrier penetrability,
only a narrow band of L v a l -
ues marks the n u c l e a r s u r f a c e . For t h e t r a n s f e r rea c t i o n t o proceed s t r o n g l y , the few values of L
a s s o c i a t e d with t h e n u c l e a r s u r f a c e i n the ingoing
optimum k t r a n s f e r f o r a p a r t i c u l a r Q value. However, f o r % ' c
kept,
t h e optimum c r o s s s e c t i o n s
a r e smaller i n magnitude and t h e i r dependence on Q
value i s l e s s sharp.
The expression f o r Qopt
(equ. 4) a l s o d i s t i n -
guishes t h e s p e c i f i c t r a n s f e r process which occurs
and outgoing channels must be matched a p p r o p r i a t e l y
(Fig. 2). For neutron t r a n s f e r o r t h e t r a n s f e r o f
-
which d e f i n e s an optimum a n g u l a r momentum t r a n s f e r
charge between n u c l e i w i t h s i m i l a r charges,
9,
=
l~~ - ~ ~ I t1 can
.
a l s o be understood t h a t , s i n c e
the momentum t r a n s f e r t o t h e t a r g e t is much l e s s
Qopt
2
0 . For n u c l e i w i t h d i f f e r e n t charges, t h e
than t h e momentum of the heavy-ion p r o j e c t i l e ( a t
i s negative o r p o s i t i v e , depending on
s i g n of Q
OP t
whether charge is t r a n s f e r r e d i n a s t r i p p i n g o r a
l e a s t f o r few nucleons t r a n s f e r r e d ) , t h e a n g l e a t
pick-up r e a c t i o n . Since t h e Q values of mcst heavy-
HEAVY-ION TRANSFER REACTIONS
F i g . 2.
-
Q dependence f o r d i f f e r e n t
transfer reactions.
ion reactions a r e negative, stripping reactions a r e
strongly favored. Semi-classically
d i s t r i b u t i o n around Q
t h e w i d t h of t h e
a l s o depends on t h e t y p e of
opt
t r a n s f e r reaction, being l e a s t f o r neutron t r a n s f e r
and low i n c i d e n t e n e r g i e s .
b) Comparison w i t h experiment. - The v a l i d i t y of
the foregoing semi-classical
c o n s i d e r a t i o n s may b e
e x e m p l i f i e d w i t h r e s u l t s taken from a s u r v e y [3] of
lp t r a n s f e r induced by 160 p r o j e c t i l e s i n t h e f p
s h e l l . For e n e r g i e s above t h e Coulomb b a r r i e r
(Q &
Fig. 3 . - 4 8 ~ a ( 1 6 01, 5 ~4) 9 ~ ca n g u l a r d i s t r i b u t i o n
a t Elab = 42, 48 and 56 MeV f o r t r a n s i t i o n s t o
t h e 712- ground s t a t e and t h e l o w e s t 312- e x c i t e d
s t a t e . The L v a l u e s d e n o t e t h e t o t a l a n g u l a r
momentum t r a n s f e r . The s o l i d c u r v e s a r e f i n i t e range DWBA c a l c u l a t i o n s .
1 5 ) , one o b s e r v e s t h e c h a r a c t e r i s t i c b e l l -
shaped a n g u l a r d i s t r i b u t i o n s shown i n f i g u r e 3.
T h e i r s i m p l e shape h a s a n a t u r a l i n t e r p r e t a t i o n
based on t h e c l a s s i c a l r e l a t i o n ( I ) . The t r a n s f e r
c r o s s s e c t i o n i n c r e a s e s w i t h a n g l e because of t h e
i n c r e a s i n g o v e r l a p between t h e two n u c l e i , r e a c h e s
a maximum a t an a n g l e
-
the grazing angle
-
which
d e f i n e s an i n t e r a c t i o n r a d i u s , Ro f o r t h e c o n t a c t
c o l l i s i o n , then f a l l s a t backward a n g l e s a s absorpt i o n p r o c e s s predominate o v e r t h e s i m p l e t r a n s f e r
p r o c e s s . Moreover, t h e g r a z i n g a n g l e i s found t o be
r e l a t i v e l y i n s e n s i t i v e t o t r a n s f e r r e d .t.
Equation ( I )
a l s o p r e d i c t s thar the t r a n s f e r re-
a c t i o n should peak a t more backward a n g l e s f o r
l o v e r bombarding e n e r g i e s , more n c g a t i v e Q v a l u e s ,
and i n c r e a s e d Z of t h e t a r g e t - a s i s indeed found.
For E
Q
VALUE,
MeV
d EB, t h e g r a z i n g a n g l e i s 180°, a s i t u a -
c.m.
t i o n c h a r a c t e r i s t i c of t h e sub-Coulomb
domain. Kela-
t i o n ( I ) a l s o implies f o r the t r a n s f e r reaction the
e q u i v a l e n c e o f e x c i t a t i o n f u n c t i o n s and a n g u l a r d i s t r i b u t i o n s ; i n b o t h c a s e s t h e peak i n t h e c r o s s
section defines R
.
The s i n g l e n u c l e o n t r a n s f e r d a t a a l s o d e m o n s t r a t e
F i g . 4 . - Experimental peak c r o s s s e c t i o n s d i v i d e d
by t h e c o r r e s p o n d i n g ( 3 ~ e , d ) s p e c t r o s c o p i c f a c t o r s
f o r t h e f 7 / 2 ground s t a t e and f c r prominent ~ 3 1 2
s t a t e s . 'The s o l i d c u r v e s a r e DlJM peak c r o s s
s e c t i o n s ( m u l t i p l i e d by a n o v e r a l l n o r m a l i z a t i o n
f a c t o r N = 1.5).
C5-i 14
G .C.
MORRISON
t h e s e v e r e e f f e c t o f Q v a l u e on t h e magnitude of
t h e peak c r o s s - s e c t i o n .
This i s displayed i n a p l o t
o f t h e "reduced" peak c r o s s s e c t i o n s - t h e e x p e r i m e n t a l v a l u e s d i v i d e d by t h e p r o t o n s p e c t r o s c o p i c
s t r e n g t h (25 + 1 ) ~ ' s from ( 3He,d) e x p e r i m e n t s - a s
a f u n c t i o n o f t h e Q v a l u e ( F i g . 4 ) . The optimum Q
v a l u e demonstrated i n t h i s way i s a p p r o x i m a t e l y
?, - 2.9 MeV and
OP t
m e c r o s s s e c t i o n f o r low II t r a n s f e r i s
t h a t given by equ. 4 , namely Q
II
I.
OP t
a l s o s e e n t o b e more r a p i d l y a f f e c t e d a s Q d e v i a t e s
-
from t h e optimum v a l u e
a consequence of t h e
t i g h t e r a n g u l a r m o m e n t u ~ m a t c h i n gr e s t r i c t i o n s .
Such a Q window r e p r e s e n t s b o t h an a d v a n t a g e and
d i s a d v a n t a g e f o r t h e heavy-ion
reaction. I t has the
obvious advantage of any window e f f e c t f o r t h e f a v o r e d r e g i o n of e x c i t a t i o n , b u t t h e d i s a d v a n t a g e
that Q
"t
may be such a s t o s e v e r e l y l i m i t t h e range
of e x c ~ t a t i o ne n e r g i e s . However, t h e wide v a r i e t y of
heavy-ion p r o j e c t i l e s now a v a i l a b l e f a c i l i t a t e s t h e
s e l e c t i o n of p a r t i c u l a r e x c i t a t i o n e n e r g i e s . F i g u r e
5 shows t h e Ip pick-up r e a c t i o n on 4 0 ~ ai n i t i a t e d by
two d i f f e r e n t p r o j e c t i l e s . F o r t h e ( 1 8 0 , 1 9 F ) and
( I 5 ~ , l 6 0 ) r e a c t i o n s t h e optimum Q v a l u e s a r e + 2 . 3
and + 3.0 MeV, r e s p e c t i v e l y . Thus Q
f a l l s well
OP t
beyond t h e ground s t a t e i n t h e former r e a c t i o n and
a t about E
=
0 . 8 MeV i n t h e l a t t e r . The e f f e c t s on
t h e Q window a r e o b v i o u s .
The s y s t e m a t i c f e a t u r e s a s have been p r e s e n t e d
h e r e have been found f o r a v a r i e t y of heavy-ion r e a c t i o n s on medium t o heavy n u c l e i f o r e n e r g i e s a t
and above t h e Coulomb b a r r i e r (n >> I ) .
Thus t h e i r
c o n s i s t e n t e x p l a n a t i o n w i t h a s e m i - c l a s s i c a l des c r i p t i o n serves t o confirm t h e i r i n t e r p r e t a t i o n a s
a direct reaction
-
even f o r t h o s e r e a c t i o n s i n -
v o l v i n g t h e t r a n s f e r of s e v e r a l n u c l e o n s , where a
d i r e c t comparison w i t h l i g h t i o n r e a c t i o n s i s n o t
p o s s i b l e . However, e v i d e n c e now e x i s t s [3]
simple semi-classical
that the
p i c t u r e based on R u t h e r f o r d
t r a j e c t o r i e s appears inadequate t o i n t e r p r e t "interaction radii" etc.
-
particularly for reactions in-
F i g . 5. - Energy s p e c t r a of 3 9 p~o p u l a t e d in two
d i f f e r e n t p r o t o n pick-up r e a c t i o n s on 4 0 ~ a .
3 . DWBA A n a l y s i s . - A l l c u r r e n t a p p r o a c h e s t o t h e
e x t r a c t i o n o f s p e c t r o s c o p i c i n f o r m a t i o n from heavy
i o n t r a n s f e r r e a c t i o n s a r e based on o r d e r i v e from
DWBA a n a l y s i s . Although such a framework i s w e l l
a c c e p t e d f o r l i g h t i o n s , i t s a p p l i c a t i o n t o heavy
i o n s r a i s e s c o n s i d e r a b l e problems i n p r a c t i c e (and
in principle).
These p r i m a r i l y a r i s e from t h e
need t o t r e a t t h e f i n i t e e x t e n s i o n of t h e heavy
ion
which makes d i f f i c u l t b o t h t h e c o r r e c t t r e a t -
ment of t h e k i n e m a t i c s and t h e complete d e s c r i p t i o n
of t h e form f a c t o r .
F u r t h e r d i s c u s s i o n r e q u i r e s a b r i e f s k e t c h of t h e
v o l v i n g more than one n u c l e o n t r a n s f e r . Thus t h e
DWBA formalism. Let u s c o n s i d e r a t r a n s f e r r e a c t i o n
f o r e g o i n g d e s c r i p t i o n i s mainly u s e f u l a s a f i r s t
A(a,b)B, where a = b
A detailed
i n t e r p r e t a t i oonf the angu-
+ x and B
=
lar d i s t r i b u t i o n and t h e e x t r a c t i o n o f q u a n t i t a t i v e
r e a c t i o n ( F i g . 6),
s p e c t r o s c o p i c i n f o r m a t i o n r e q u i r e a complete and
ten i n the post approximation :
a c c u r a t e t r e a t m e n t of t h e n u c l e a r d i s t o r t i o n s . Such
an approach i s c o n t a i n e d i n t h e DWBA a n a l y s i s .
a + x. R e f e r r i n g
t o t h e f a m i l i a r " t r i a n g l e " diagram f o r a t r a n s f e r
t h e DWBA a m p l i t u d e can be w r i t -
H E 4 W-ION TRRNSFER REACT IONS
C 5 - i 19
t h a t the t r a n s f e r r e d p a r t i c l e i s on the s u r f a c e of
a, t h i s approach [2]
permits a r e d e f i n i n g of t h e
r e l a t i v e c o o r d i n a t e s i n the i n i t i a l and f i n a l chann e l , namely :
This expression e x p l i c i t l y r e v e a l s the i n t e r l i n k e d
dependence on the coordinates of the system. Since
f o r heavy ions the s i m p l i f y i n g zero-range approximat i o n ( r x b = 0) i s c l e a r l y i n j u s t i f i e d , t h e evaluat i o n of the DWBA t r a n s i t i o n amplitude is formidable.
-f
The c o r r e c t treatment of t h e kinematics r e q u i r e s
where r i s t h e d i s t a n c e between t h e two cores.
e i t h e r the c a l c u l a t i o n of the f u l l six-dimensional
While a n a l y s i s i n v o l v i n g the use of these "scaling"
i n t e g r a l o r i t s reduction t o two three-dimensional
f a c t o r s has been mainly a t e n e r g i e s about t h e
i n t e g r a l s by reasonable approximations wich permit
Coulomb b a r r i e r , t h e approach would appear t o o f f e r
a s e p a r a t i o n of v a r i a b l e s .
wider a p p l i c a b i l i t y . I t a l s o l e a d s t o an e x p r e s s i o n
which i n c l u d e s r e c o i l c o r r e c t i o n s ( t h e
OP t
term zfZf/ziZi i n equ. 4 being m u l t i p l i e d by ulv).
for Q
F i n a l l y t h e r e now e x i s t various DWBA codes [7]
which perform the f u l l six-dimensional i n t e g r a l
(equ. 5). Their wide spread a p p l i c a b i l i t y i s l i m i t e d by the s i z e of the computer r e q u i r e d and by
the time involved i n t h e c a l c u l a t i o n
-
t h e i r use
becomes u n f e a s i b l e f o r e l a s t i c channels involving
Fig. 6 .
a l a r g e number of p a r t i a l waves (>50-80). Neverthe-
- Relative
coordinate system f o r
transfer reaction.
l e s s , t h e i r e x i s t e n c e i s comforting, p a r t i c u l a r l y
i n view of the need t o t h e t e s t the r e l i a b i l i t y of
A common approximation i s the n e g l e c t of so-called
r e c o i l terms, which assumes t h a t the mass of the
t r a n s f e r r e d p a r t i c l e i s small compared t o t h e cores
A and b , and hence t h a t a and b have t h e same cent r o i d . This approach has been used by Tobocman [4]
and e a r l i e r by B u t t l e and Goldfarb [5]
t o achieve a
s e p a r a t i o n of v a r i a b l e s . However, t h e s e treatments
s t i l l take f i n i t e range i n t o account i n t h e formf a c t o r i n t e g r a t i o n . They should be most a p p l i c a b l e
f o r single-nucleon
t r a n s f e r where the r e c o i l terms
(% I/ma) w i l l be s m a l l e s t .
programmes u t i l i z i n g v a r i o u s kinematic approximat i o n s . In p a r t i c u l a r the approximate methods d i s cussed above obey the usual f a r i t y r e s t r i c t i o n s on
1+L2+L
the it t r a n s f e r , namely ( - I )
should be even,
where i t I and it2 r e f e r t o the angular momentum i n
t h e p r o j e c t i l e and f i n a l nucleus, r e s p e c t i v e l y . The
f u l l f i n i t e range c a l c u l a t i o n r e l a x e s t h i s r e s t r i c tion
- possible
L t r a n s f e r being determined by t h e
more general s e l e c t i o n r u l e ,
I jl -
j214i<jl + j2.
Such r e c o i l e f f e c t s a r e expected t o be of i n c r e a s i n g importance a t h i g h e r e n e r g i e s and f o r h e a v i e r
targets
.
More r e c e n t approximations attempt t o allow corr e c t l y f o r t h e t r a n s f e r of mass by appealing t o phys i c a l i n s i g h t t o determine from where the maximum
c o n t r i b u t i o n t o the i n t e g r a l a r i s e s and t o determine
the r e l a t i o n between the c o o r d i n a t e s a t t h a t p o i n t .
The usual assumption i s t h a t the p a r t i c l e is on t h e
i n t e r c o n n e c t i n g l i n e of the two n u c l e i . (The "fixed
range" approximation of Piihlhofer 161 i s an e a r l y
example of such a method although i t reduces t o a
zero-range c a l c u l a t i o n ) . When i t i s f u r t h e r assumed
A d i f f e r e n t approach t o the heavy-ion
reaction i s
the s e m i - c l a s s i c a l treatment of Broglia and
Winther r8]. Although i n s p i r e d by an a n a l y s i s of
the s e m i - c l a s s i c a l l i m i t of DWBA i91, i t i s formul a t e d i n t h e framework of the coupled-channel
theory of Coulomb e x c i t a t i o n
- extended
i o include
nucleon t r a n s f e r r e a c t i o n s . I t s advantages should
become i n c r e a s i n g l y more important when thq number
of p a r t i a l waves becomes very l a r g e and when 2nd
order e f f e c t s involving i n e l a s t i c e x c i t a t i o n s have
MORRISON
C.C.
t o be considered.
Even i f the kinematic e f f e c t s a r e t r e a t e d properl y , t h e r e s t i l l a r i s e s the problem of c a l c u l a t i n g
form f a c t o r s f o r more than one nucleon t r a n s f e r
-
a
problem whose complexity i n c r e a s e s r a p i d l y f o r t h e
t r a n s f e r of s e v e r a l nucleons. I n p a r t i c u l a r f o r
heavy ions, t h e convenient assunrption of a r e l a t i v e
Is c o n f i g u r a t i o n f o r the i n t e r n a l motion of t h e
t r a n s f e r r e d c l u s t e r , i s n o t v a l i d [gal. Thus the
t r a n s i t i o n amplitude has t o be considered a s a coh e r e n t sum over a l l p o s s i b l e internrediate s t a t e s of
the t r a n s f e r r e d nucleons, and ltence a l l p o s s i b l e
quantum numbers of t h e c l u s t e r r e l a t i v e ntotion.
This f a c t may lead t o considerable d i f f i c u l t i e s f o r
t h e conventional treatment.
4. Conrparison w i t h Experimnt.
tmsfe'ep.
- The
- a)
Oyla-nuoleon
success of t h e DWBA d e s c r i p t i o n of
one-nucleon t r a n s f e r t o g i v e q u a n t i t a t i v e spectros c o p i c information i s now w e l l e s t a b l i s h e d f o r ene r g i e s a t and above t h e Coulomb b a r r i e r [3,10].
5-
p i c a l l y , i t has been demonstrated i n a comparison
of t h e ( l 6 0 , I 5 ~ ) r e a c t i o n on n u c l e i i n t h e f p s h e l l
133 w i t h the p r e d i c t i o n s of t h e RDXC program of
Tobocman [4]. Examples of t h e goodness of the f i t s
both f o r angular d i s t r i b u t i o n s and f o r t h e v a r i a t i o n o f peak c r o s s s e c t i o n with Q value a r e shown
Fig. 7.
on
- Energy st apregcet rt as ofa t ~t h(e1 6( 01 )6- ~48, i MeV,
S ~r e)a c t i o n
62364Ni
i n F i g s . 3 and 4. The t h e o r e t i c a l curves were c a l c u l a t e d with s t r o n g l y absorbing p o t e n t i a l s [I l]
which o b v i a t e the need f o r a cut-off r a d i u s . The
p a r a m t e r s f o r t h e ingoing 160 c h a n ~ % egli v e a good
d e s c r i p t i o n of t h e e l a s t i c s c a t t e r i n g d a t a ;
the parameters f o r t h e outgoing 15N channel a r e t h e
same except t h a t the d i f f u s e n e s s was s l i g h t l y increased t o y i e l d a b e s t f i t t o t h e 48 MeV d a t a of
f i g u r e 3 , A t p r e s e n t no "N
exist
e l a s t i c scattering data
i n t h i s mass region.
I n t h i s work a somewhat unexpected J dependence
of the ( 1 6 0 , 1 5 ~ )c r o s s s e c t i o n was found. The e f f e c t i s demonstrated i n the s p e c t r a of t h e
6 2 7 6 4 ~ i ( 1 61 ~5 ,~6) 3 7 6 5 r~e~a c t i o n s (Fig. 7). For
example t h e 0.67 KeV 112- s t a t e i n 6 2 ~
i si conside r a b l y weaker than the 312- ground s t a t e , whereas
t h e measured s p e c t r o s c o p i c s t r e n g t h s a r e comparable
2
CC S = 0.66 and 0.70 f o r t h e 312- and 112- s t a t e s ,
r e s p e c t i v e l y ) . The observed reduction i s w e l l des c r i b e d by DWBA c a l c u l a t i o n s (Fig. 8).
It can be
-
Fig, 8.
Calculated DWBG d i s t r i b u t i o n s f o r
L = 0, 2, 4 t r a n s i t i o n s l e a d i n t o various f i n a l
s t a t e s i n t h e 62Ni(i60, 15N)68Cu r e a c t i o n a t
~ ( ~ =~480 MeV.
)
HEkW-ION TRANSFER REACTIONS
e x p e c t e d t o be a g e n e r a l f e a t u r e o f heavy-ion
C5-117
The j u s t i f i c a t i o n f o r u s i n g p o t e n t i a l s from e l a s -
- 112 o r b i t a l t o
I =R1
112 o r b i t a l , f o r which t h e s e m i - c l a s s i -
t i c scattering to describe t h e transfer reaction i s
c a l l y f a v o r e d L! t r a n s f e r (= L I + 2, ) i s n o t a l 2
lowed. The J dependent f a v o r i n g of j 2 = i 2 + 112
f e r r e a c t i o n s owing t o t h e i n c r e a s e d p o s s i b i l i t y of
t r a n s f e r from a j
j2
= E2
-
l e s s c l e a r f o r heavy-ion
than f o r l i g h t - i o n t r a n s -
core-core e x c i t a t i o n s . Even t h e u s e of " s t a n d a r d "
o p t i c a l p o t e n t i a l s f o r heavy-ion
s c a t t e r i n g has
m y be e x p l o i t e d by comparing t h e r e l a t i v e i n t e n s i 160 15
N) r e a c t i o n of t h o s e s t a t e s
t i e s i n the (
3
which have t h e same 2 t r a n s f e r i n t h e ( He,d) r e -
been r e c e n t l y q u e s t i o n e d [13],
a c t i o n . Moreover, d i f f e r e n t i n t e n s i t y r a t i o s should
a c c o u n t of t h e s i z e of t h e p r o j e c t i l e . However, i t
be e x p e c t e d i n a comparison of j 2 = R 2
can be n o t e d a t t h i s p o i n t t h a t a v e r y s e n s i t i v e
,
f
112 s t a t e s
and i t has been sug-
gested t h a t c o r r e c t procedure should take proper
p o p u l a t e d by two heavy i o n r e a c t i o n s such a s
t e s t of o p t i c a l p a r a m e t e r s now e x i s t s a s a r e s u l t
(I60,l5N) a n d ( 1 2 ~ , 1 1 ~ f) o, r which t h e t r a n s f e r r e d
o f t h e r e c e n t d i s c o v e r y of t h e d e s t r u c t i v e i n t e r -
n u c l e o n comes from a p I l 2 and p31Z o r b i t a l , r e s p e c -
f e r e n c e between Coulomb and n u c l e a r e x c i t a t i o n i n
tively.
heavy-ion
Perhaps a p a r t i a l f a i l u r e of t h e DWBA a n a l y s i s of
r e)a c t i o n was an i n a b i l i t y i n some
the ( 1 6 ~ , 1 5 ~
c a s e s t o r e p r o d u c e t h e d a t a a t t h e most f o r d a r d ang l e s , e s p e c i a l l y a t v e r y n e g a t i v e Q v a l u e s ( F i g . 9,
i n e l a s t i c s c a t t e r i n g [14].
The experimen-
t a l e f f e c t i s shown i n F i g . 10 f o r e x c i t a t i o n of
byi 160 ; t h e c u r v e s a r e p r e t h e 2+ s t a t e i n 5 8 ~
d i c t i o n s of t h e a n g u l a r d i s t r i b u t i o n s by semi-class i c a l and q u a n t a 1 c a l c u l a t i o n s D 5 j .
s o l i d l i n e s ) . T h i s c a u s e s some concern i n view of
the semi-classical picture that a t these angles
o n l y Coulomb d i s t o r t i o n s s h o u l d be e f f e c t i v e .
However, a b e t t e r f i t t o t h e d a t a can be o b t a i n e d
( F i g . 9, d a s h e d l i n e s ) w i t h a s l i g h t l y m o d i f i e d s e t
of p a r a m e t e r s l123, b u t one which d o e s n o t now r e p r o d u c e t h e e l a s t i c s c a t t e r i n g . (The same s i t u a t i o n
1Fmi
3.L 1.56 0.60
imaginary 6.0 1.27 0.5L
1fiO+5BNi
E~~~= LLMeV
w i l l b e a g a i n found i n t h e a n a l y s i s o f s e v e r a l nucleon t r a n s f e r ) .
pl
P
160 15
F i g . 9. - Angular d i s t r i b u t i o n s of t h e (
, N)
r e a c t i o n on even-A Ca i s o t o p e s a t 48 MeV l e a d i n g
t o t h e f i n a l s t a t e s shown. DWBA d i s t r i b u t i o n s
a r e discussed i n the t e x t .
quantum mechanical
( qne~astic/ ~ e ~ a s t i c ) e x p t .
F i g . 10. - Experimental and t h e o r e t i c a l a n g u l a r
d i s t r i b u t i o n s f o r e l a s t i c and i n e l a s t i c s c a t t e r i n g
0 )
of 160 on 5 8 ~a it ~ ( ~ =~ 44MeV.
G . C . MORRISON
(25-1 18
F i n a l l y , i t may be remarked t h a t t h e r e s u l t s of
the ( 1 6 ~ , 1 5 ~
experiments
)
i n t h e f-p s h e l l give no
evidence t h a t the r e a c t i o n has any p e c u l i a r a s p e c t
unique t o heavy-ion
reactions, contrary t o e a r l i e r
b e l i e f . The s p e c t r o s c o p i c s t r e n g t h s e x t r a c t e d from
75
-
-
-
"?
"?
r.
-
1
t h e ( 1 6 0 , 1 5 ~ ) r e a c t i o n a r e found t o be c l o s e l y the
3
same a s those e x t r a c t e d from ( He,d) - so t h a t twos t e p processes appear unimportant. The s i t u a t i o n
3
U
should be very d i f f e r e n t f o r h e a v i e r , deformed t a r g e t n u c l e i , and even the p o s s i b i l i t y of a s t r o n g
25 -
c o n t r i b u t i o n of two-step processes i n t h e mass-90
region cannot be excluded [16].
b) MuZti-nuoZeo?~ t r a n s f e ~ .
- As
500
discussed e a r l i e r
t h e DWBA a n a l y s i s of multi-nucleon t r a n s f e r is com-
Fig. 1 1 .
550
-
600
650
700
750
Bill
CHANNEL NUMBER
Energy s p e c t r a of the 4 8 ~ a ( 1 6 0 , 1 4 ~ ) 5 0 ~ i
r e a c t i o n a t ~ ( ' ~ 0= )59.5 MeV.
p l i c a t e d by two f e a t u r e s : the need t o take account
of r e c o i l e f f e c t s and the need to consider i n t e r n a l
c l u s t e r c o n f i g u r a t i o n s . Ln connection with t h e l a t t e r problem, a new approach by Bonche and Giraud
[17] appears of i n t e r e s t . Their a n a l y s i s i s based
-Bonche
---E.FR.
I
on a generator-coordinate
d e s c r i p t i o n of t h e s c a t -
E= L8'M eV
t e r i n g waves. It uses d i r e c t l y s h e l l model wave
f u n c t i o n s , without e x t r a c t i n g t h e c e n t r e of mass
motion, t o d e s c r i b e the t r a n s f e r r e d nucleons i n the
i n i t i a l and f i n a l n u c l e i ,
and thereby takes ac-
count e x p l i c i t l y of a l l o r d e r s of i n t e r n a l configur a t i o n s of the t r a n s f e r r e d c l u s t e r , With such a m i c r o s c o p i c d e s c r i p t i o n of the t r a n s f e r form f a c t o r ,
s p e c t r o s c o p i c wave f u n c t i o n s can be d i r e c t l y analysed. In t h e o p t i c a l waves t h e c e n t e r of mass of
t h e t r a n s f e r r e d p a r t i c l e s i s assumed to be a t the
c e n t e r of mass of t h e two c o r e s . Thus t h e treatment
of r e c o i l e f f e c t s may s t i l l be inadequate f o r c o r e s
of unequal masses.
F i g . 12. - Experimental and t h e o r e t i c a l angular
d i s t r i b u t i o n s of t h e 4 8 ~ a ( 1 b 0 ,4 ~5) 0 ~r eia c t i o n
)
l e a d i n g t o t h e f i n a l s t a t e s shown. ~ ( ~ =~ 480 MeV.
The ' * 8 ~ a ( 1 6 1
~ ,4 ~ ) 5 0 r~e ai c t i o n i s a good t e s t of
t h i s new approach f o r the c a s e of two-proton
trans-
they peak much forward of the "grazing" angle pre-
f e r . Fig. 1 1 shows a spectrum obtained a t 59.5 MeV.
d i c t e d by t h e customary s t r o n g i n t e r a c t i o n r a d i u s .
a rie known t o have
The f i r s t f o u r s t a t e s i n 5 0 ~
This e f f e c t i s not accounted f o r i n DWBR c a l c u l a -
s p i n s 0+, 2 + , 4+ and 6+ r e s p e c t i v e l y based on a
t i o n s i n c l u d i n g r e c o i l with parameters which f i t
r e l a t i v e l y pure (n f 7,Z)2
c o n f i g u r a t i o n . Thus t h e
p r e d i c t e d shape and magnitude of the d i f f e r e n t i a l
c r o s s s e c t i o n s can be compared with experiment f o r
different L transfer, d i f f e r e n t excitation energies
and d i f f e r e n t bombarding e n e r g i e s .
[ ~ e v r i e s ] ) r e q u i r e a l a r g e r value of d i f f u s e n e s s a
(= 0.7)
i n e n t r a n c e and e x i t channels [or equiv-
a l e n t l y a l a r g e r value of r a d i u s parameter ro
Angular d i s t r i b u t i o n s obtained a t 48 MeV f o r t h e
f i r s t f o u r s t a t e s i n " ~ ia r e shown i n Fig.
t h e (160, I5N) r e a c t i o n . The f i t s obtained i n both
c a l c u l a t i o n s (Bonche and exact f i n i t e range, E.F.R.
12.
(- 1.3513
. Such changes
e s s e n t i a l l y force the
r e a c t i o n t o take p l a c e f a r out and hence reproduce
They a r e s i m i l a r i n shape t o those observed i n Ip
the observed forward peaking. However, with t h i s
t r a n s f e r except, a s has been noted p r e v i o u s l y [3],
choice of parameters, the observed q u a l i t y of f i t
HEA W-ION TRANSFER REACI'IONS
was maintained a t 42, 56 and 59.5 MeV bombarding
energy.
T a ~ l eI g i v e s t h e e x p e r i m e n t a l peak c r o s s s e c t i o n
a l p h a t r a n s f e r r e a c t i o n should be p a r t i c u l a r l y sans i t i v e t o 2p3/2 a d m i x t u r e s .
a t 48 MeV and t h e t h e o r e t i c a l p r e d i c t i o n s assuming
t h a t t h e two p r o t o n s i n ' O T ~ occupy e i t h e r I f
2p3,2
712
s u b s h e l l s . The f i n a l column g i v e s t h e re-
q u i r e d n o r m a l i z a t i o n f o r a pure (I f
t i o n . I t i s s e e n t h a t a small (
t h e 0'
2
Or
) 2 configura-
7/$
~ admixture
~ ~ ~ )i n
and 2' wave f u n c t i o n s could l e a d t o an over-
C5-119
The DWBA a n a l y s i s of t h e f o u r nucleon t r a n s f e r by
means of t h e Bonche code i s a l s o p r o c e e d i n g a t
S a c l a y , indeed h i s t o r i c a l l y i t was f i r s t used i n a
r e a c t i o n mechanism s t u d y of t h e (160, "c)
[18]
. In a p p a r e n t c o n t r a s t
reaction
t o t h e ( I 6 0 , l 4 c ) re-
a l l improvement i n n o r m a l i z a t i o n . A s i m i l a r en-
a c t i o n , i t i s found t h a t t h e peak p o s i t i o n i n t h e
a n g u l a r d i s t r i b u t i o n a p p e a r s t o be r e a s o n a b l y w e l l
hancement of t h e 0+ and 2+ c r o s s s e c t i o n s i s found
d e s c r i b e d by o p t i c a l p a r a m e t e r s d e r i v e d from t h e
c o n s i s t e n t l y a t each of t h e o t h e r e n e r g i e s s t u d i e d .
elastic scattering
-
a t l e a s t for the
5 4 ~ e ( 1 4 0 , 1 2 ~ ) 5 8r ~e ai c t i o n . Moreover t h e a n a l y s i s
Table I
EjperimentaZ and calcuZated peak cross sections
for the ( 1 8 ~ a f i Gi 4
~ ,~ . J 5
~ e0
a c~t iio na t 40 MeV.
Ex
(MeV)
0
1.55
2.68
3.20
o
J~
s
of
2'
4'
6+
due t o r e a c t i o n mechanism - t h e Q
be e s t i m a t e d .
2
exp
uth(f7/2)
s
200
290
190
85
'th(~3i2)~
'exp
'
( ~ b l s r ) oth(f7,2)
2.8
5.7
4.3
2.1
16.8
32.3
72
51
43
39
-
-
T h i s i n i t i a l s t u d y was based, n o t unreasonably,
2
on t e s t i n g p u r e stretch-scheme f o u r - p a r t i c l e wave
f u n c t i o n s . I-lowever, t h e extreme s e n s i t i v i t y t o t h e
p r e s e n c e of (
t h e l a r g e n o r m a l i z a t i o n f a c t o r s r e q u i r e d -one i s
reminded o f s i m i l a r problems i n t h e a n a l y s i s of
( t , p ) r e a c t i o n s . Furthermore, t h e s i t u a t i o n i s exa c e r b a t e d by t h e extreme o p t i c a l p a r a m e t e r s r e q u i r e d t o f i t t h e a n g u l a r d i s t r i b u t i o n s , Neverthel e s s , i t s h o u l d be renarked t h a t t h e Bonche analys i s s t i l l does n o t g i v e a good d e s c r i p t i o n of t h e
e n e r g y dependence o f t h e c r o s s s e c t i o n
calculations
-
in
- perhaps
2
~
c~o n ~
f i g u~r a t)i o n presumably a l s o
implies a s e n s i t i v i t y t o configurations containing
(
I t is beyond t h e scope o f t h i s review t o d i s c u s s
c o n t r a s t t o t h e E.F.R.
I2c s p e c t r a
dependence - t o
permits the i n t e n s i t y v a r i a t i o n i n the
2
~ components.
~
~
~ I n) t h~i s c o n n e c t i o n , a r e c e n t
comparison
[lq
o f ( a , u t ) and a l p h a t r a n s f e r reac-
t i o n s t o 5 8 ~s iu g g e s t t h e importance o f t r a n s f e r
t o 3- s t a t e s . The s t r o n g e x c i t a t i o n o f s t a t e s based
on such o b v i o u s l y mixed components i m p l i e s t h e need
t o c o n s i d e r t h e c o n t r i b u t i o n of mixed components i n
o t h e r c a s e s ( e . g . even p a r i t y s t a t e s ) . However,
then t h e l a r g e number of p o s s i b l e c o n f i g u r a t i o n s
based on f o u r p a r t i c l e e x c i t a t i o n s , p r e v e n t s a d i r e c t i n t e r p r e t a t i o n from t h e d a t a
- even f o r s t a t e s
i n d i c a t i n g some inadequacy of t h e r e c o i l approxima-
of known s p i n . One is l e f t i n t h e p o s i t i o n o f
tion.
The s e n s i t i v i t y of t h e c a l c u l a t e d c r o s s s e c t i o n s
p r o p o s i t i o n only f o r low-lying s t a t e s .
t e s t i n g t h e o r e t i c a l wave f u n c t i o n s
-
a realistic
t o s m a l l a d m i x t u r e s o f 2p312 i n If7l2 c o n f i g u r a t i o n s h a s been remarked (Table 1 ) .
S i n c e t h e heavy-
i o n r e a c t i o n i s s t r o n g l y l o c a l i z e d a t t h e nucleon
5. T r a n s f e r Keaations a t High E n e r g i e s .
I
would l i k e now t o conclude t h i s review by d i s c u s -
s u r f a c e , t h e d i f f e r e n t magnitude of t h e p u r e con-
s i o n o f some r e c e n t t r a n s f e r e x p e r i m e n t s performed
f i g u r a t i o n s stems from d i f f e r e n c e s i n t h e form f a c -
a t h i g h e r e n c r g i e s (5-10 MeV p e r n u c l e o n ) . These
t o r of the t r a n s f e r r e d n u c l e o n s t h e r e , I n t u r n t h i s
a r e mainly c y c l o t r o n e x p e r i e n t s i n which a v a r i e t y
depends on t h e s i n g l e nucleon bound-state wave
of p r o j e c t i l e s have been used t o bombard mainly
f u n c t i o n s , t h e 2p3,2 p e a k i n g f u r t h e r o u t t h a n t h e
l i g h t and heavy t a r g e t s . T h e i r d i s c u s s i o n h a s t h e
I f l f 2 . ( I t can depend i n a d d i t i o n on t h e matching
advantage o f e n d i n g w i t h r c s u l t s which, i n t h e i r
of t h e t r a n s f e r r e d nucleon c o n f i g u r a r i o n s i n t h e
remarkable s e l e c t i v i t y , r e v e a l new a s p e c t s o f t h e
p r o j e c t i l e and f i n a l n u c l e u s ) . The e f f e c t s h o u l d
heavy i o n t r a n s f e r r e a c t i o n and t h u s a r e a d i r e c t
i n c r e a s e a s t h e p r o d u c t o f t h e number o f n u c l e o n s
encouragement t o t h e more widespread achievement o f
t r a n s f e r r e d , a s i s indeed a p p r o x i m a t e l y observed
h i g h e r e n e r g y heavy i o n s .
i n t h e c a l c u l a t i o n s of a l p h a t r a n s f e r . Thus t h e
C5-120
G.C.
The b a s i c f e a t u r e of t h e heavy-ion
t r a n s f e r reac-
MORRISON
These q u a l i t a t i v e c o n s i d e r a t i o n s have been ex-
t i o n a t h i g h e n e r g i e s a p p e a r s t o be t h e f a v o r i n g of
tended by Brink 1223 t o d e r i v e q u a n t i t a t i v e kine-
l a r g e a n g u l a r momentum t r a n s f e r [20].
m a t i c a l c o n d i t i o n s on t h e t r a n s f e r r e a c t i o n a t en-
t i v i t y i s shown i n F i g s .
three-nucleon
nuclei.
This selec-
13 and 14 f o r one and
t r a n s f e r s [21]
on r e l a t i v e l y l i g h t
I t i s most c l e a r l y demonstrated i n t h e l a t -
e r g i e s w e l l above t h e Coulomb b a r r i e r . These r e l a t e t h e Q v a l u e of t h e r e a c t i o n t o t h e a n g u l a r
momentum o f t h e t r a n s f e r r e d n u c l e o n s i n the i n i -
t e r example i n which the s t a t e s of maximum p o s s i b l e
t i a l and f i n a l n u c l e u s . S i n c e l a r g e c r o s s s e c t i o n s
a l i g n m e n t a r e most s t r o n g l y p o p u l a t e d . T h i s r e s u l t
a r e only possible i f these kinematical conditions
a p p e a r s t o be a n a t u r a l consequence of t h e l a r g e
a r e s a t i s f i e d , one can t h e r e b y o b t a i n d i r e c t i n -
l i n e a r momentum o f the t r a n s f e r r e d nucleon o r c l u s -
formation on t h e s t r u c t u r e o f the s t a t e s s e l e c -
t e r of n u c l e a r
t i v e l y populated.
which h a s t o be c o n v e r t e d i n t o an-
g u l a r momentum. Thus, i f t h e r e a c t i o n t a k e s p l a c e
a t t h e n u c l e a r s u r f a c e , e a c h nucleon c a n be thought
t o t r a n s f e r a n g u l a r momentum L
%
k R , where ko i s
t h e wave number of t h e r e l a t i v e nucleon v e l o c i t y
and R is the r a d i u s of t h e t a r g e t . Moreover, t h e
s e l e c t i v i t y w i l l be g r e a t e s t and t h e c r o s s s e c t i o n
l a r g e s t f o r r e a c t i o n s whose Q v a l u e s f a v o r t h e
l a r g e momentum t r a n s f e r . T h i s c o n t r a s t s w i t h t h e
s i t u a t i o n a t e n e r g i e s n e a r t h e Coulomb b a r r i e r
where k
2
0.
The Oxford group [23]
has
a l s o used t h e b a s i c
one-nucleon s e l e c t i v i t y a s a b u i l d i n g b l o c k t o
s t u d y t h e same f i n a l n u c l e u s formed by r e a c t i o n s
which t r a n s f e r a d i f f e r e n t number of nucleons. For
example t h e two-neutron
t r a n s f e r r e a c t i o n on 1 2 c
may be compared w i t h t h e one-neutron
a c t i o n on
I3c
state in
14c,
t r a n s f e r re-
( F i g . 15) .One f i n d s t h a t o n l y t h e 3based on t h e diI2 @ p I ,?
configcra-
t i o n , i s p o p u l a t e d i n t h e 2n ( o r 2p) t r a n s f e r
whereas t h e r e a c t i o n on 13c p o p u l a t e s b o t h t h e 3and 2 - s t a t e s (Table 1 1 ) . The i n h i b i t i o n o f unnatu r a l p a r i t y s t a t e s i n 2n ( o r 2p) t r a n s f e r a p p e a r s
a's a n a t u r a l consequence i f t h e two
c l e o n s a r e t r a n s f e r r e d i n a 0'
uration
-
i d e n t i c a l nu-
r e l a t i v e I s config-
t h e c o r r e s p o n d i n g 3- and 2- s t a t e s a r e
both p o p u l a t e d i n np c r a n s f e r l e a d i n g t o I4F4.
How-
e v e r . i t i s a l s o found t h a t t h e 2n and 22 t r a n s f e r
Fig.
(
13. - S i n g l e - p r o t o n t r a n s f e r r e a c t i o n induced
by 1 1 4 MeV I2c i o n s on I ~ c , 160 and , 4 0 ~ a .
12Fi8. 14. - Three-nucleon t r a n s f e r r e a c t i o n
C Be) induced by 1 1 4 MeV 1% i o n s ( a ) on
and (b) on I ~ c , 160 and 4 0 ~ a ,
-
F i g . 15.
P o p u l a t i o n of s t a t e s of I4c by one and
two-neutron t r a n s f e r r e a c t i o n s on 13c and I2c,
r e s p e c t i v e l y . Einc 2 10 MeV/nucleon,
HEAW-ION TRANSFER REACTIONS
Table 11
States select.tvely eazited i n sin Ze-and
two-nsutrm stripping reactions on 2% and 2 3 ~ .
J"
Configuration
~ e atcion
Ex
3~
( a ) 1 2 ~ ( 1 1 ~ , 1 0 ~ ) 10.0
3.85
112-
VP1/2
512'
vd
512
is much reduced compared with the np t r a n s f e r
- and
even with t h r e e nucleon ( t o r 3 ~ e )t r a n s f e r . This
r e s u l t , which i s n o t an e f f e c t of Q value, i s n o t
understood a t p r e s e n t .
The e f f e c t of t h e "spectator" nucleon has been
c a r r i e d t o higher 0rde.r f o r 160 by comparing the
s t a t e s e x c i t e d i n three-nucleon t r a n s f e r r e a c t i o n s
on
12c with
those populated i n two-nucleon t r a n s f e r
r e a c t i o n s on
I3c,
Such s t u d i e s make use of the wide
v a r i e t y of a v a i l a b l e p r o j e c t i l e s so t h a t problems
of d i s t i n g u i s h i n g between e x c i t e d s t a t e s of the
outgoing p a r t i c l e and t h e new s t a t e s of i n t e r e s t i n
t h e f i n a l nucleus can be overcome. This combination
of t h e t r a d i t i o n a l methods used t o examine weak
-excitat~on
energy
channel number-
coupling w i t h the high s e l e c t i v i t y of the heavy-ion
r e a c t i o n appears t o have g r e a t p o t e n t i a l .
A f u r t h e r source of s e l e c t i v i t y i n r e a c t i o n s on
Fig. 16.
-
S e l e c t i v e p o p u l a t i o n of s t a t e s of I5N
by d i f f e r e n t t r a n s f e r r e a c t i o n s .
l i g h t n u c l e i has been e a r l i e r observed by von
Oertzen [24],
nameiy, t h a t t h e t r a n s f e r of s e v e r a l
2 0 8 ~ b ( 1 2"B)
~,
r e a c t i o n s a t 78 MeV [252 a r e shown
nucleons i s s t r o n g l y favored when t h e i r i n t e r n a l
i n Figure 17. (They have been obtained w i t h t h e
s t r u c t u r e i s n o t changed i n the i n i t i a l and f i n a l
Berkeley magnetic spectrometer system using a fo-
nucleus.
c a l plane d e t e c t o r and represent t h e c u r r e n t o p t i -
This i s demonstrated i n Figure 16 which shows
mum i n p a r t i c l e i d e n t i f i c a t i o n and energy r e s o l u -
t h a t t h e 1 2 ~ ( 1 960)
~ , 1 5 ~r e a c t i o n populates most
t i o n f o r heavy ions.) C l e a r l y seen i s the wide
s t r o n g l y t h e 1/2+ s t a t e a t 5.3 MeV i n 15N which was
range of j,R values of t h e s i n g l e p a r t i c l e s t a t e s .
More than i n the r e a c t i o n s on l i g h t n u c l e i , the
the same c o n f i g u r a t i o n a s the p r o j e c t i l e , namely
(Pl12)-4(sd)3.
The d i f f e r e n t s e l e c t i v i t i e s of t h e
( 1 60, 'N) and ( 160,
r e a c t i o n s a r e a l s o apparent.
s p e c i f i c dependence of angular momentum t r a n s f e r on
the p a r t i c u l a r p r o j e c t i l e and r e a c t i o n i s revealed.
The main f e a t u r e s again seem t o have t h e i r i n t e r p r e -
A p r e f e r e n t i a l e x c i t a t i o n of s p e c i f i c s t a t e s i s
observed i n t h e one-nucleon t r a n s f e r r e a c t i o n s on
Pb [23],
[25]
a t high e n e r g i e s
-a
f a v o r i n g of high
s p i n s t a t e s f o r n e g a t i v e Q values is a l s o found 1261
i n two-nucleon t r a n s f e r r e a c t i o n s on some f p - s h e l l
n u c l e i . S p e c t r a o f t h e 2 0 8 ~ b (I2c, I3c) and
t a t i o n i n t h e kinematic s e l e c t i o n r u l e s [22]relating
Q v a l u e and angular momentum t r a n s f e r , One may a l s o
a n t i c i p a t e i n multi-nucleon t r a n s f e r r e a c t i o n s an
i n c r e a s i n g l y important r o l e of r e a c t i o n s such a s
("c,
lone) and ( 1 3 c , ' ~ e ) i t high e n e r g i e s i n o r d e r
t o use t h e i r more negative Q v a l u e s t o enhance high
C.C.
MORRISON
("c."c)
b"
60'
:%a-
- - -.
.-
-
-.
'O'P~
lab
- - -.
I
1
1oaPb(s2C,"8) '098i
60' lob
2' 1.
1
i
'R
CHANNEL
Fig.
17.
- Single-nucleon
t r a n s f e r r e a c t i o n s induced by 7 8 MeV
angular rnomentum s t a t e s .
12c i o n s
on '08pb.
compound nucleus w i l l be r e s t r i c t e d t o small i m -
The Berkeley d a t a a l s o shows c l e a r evidence f o r
p a c t parameters and the c r o s s s e c t i o n f o r d i r e c t
the J dependent e f f e c t s discussed e a r l i e r . A com-
r e a c t i o n enhanced. While t h e experimental conse-
parison of the r e a c t i o n s (160, 1 5 ~ ) and ( 1 2 c , 1 1 ~ )on
quences a r e n o t completely c h a r t e d , i t would ap-
2 0 8 ~ b (Fig. 18) shows the reduction i n i n t e n s i t y of
160 15
N) r e a c t i o n .
the j2 = i2 1 / 2 s t a t e s i n the (
pear most l i k e l y t h a t the phenomenon manifests i t -
-
,
s e l f i n an increased p r o b a b i l i t y of very i n e l a s t i c
However, the r e d u c t i o n i s l e s s than p r e d i c t e d by
s c a t t e r i n g c o l l i s i o n s showing up a t very forward
DWBA c a l c u l a t i o n s [4] which n e g l e c t r e c o i l . Since
angles. W e v e r r e c e n t experiments 1281 a l s o sug-
a t high e n e r g i e s , r e c o i l e f f e c t s a r e not n e g l i g i b l e ,
g e s t an e f f e c t on t h e t r a n s f e r t o low l y i n g s t a t e s
t h i s discrepancy may be evidence f o r t h e p a r i t y -
-
v i o l a t i n g & t r a n s f e r (= t1 + E2
-
1) c o n t r i b u t i n g
t o the r e a c t i o n ;p a r t i c u l a r l y a s t h i s would permit
a l a r g e r angular momentum t r a n s f e r than t h a t a l lowed by p a r i t y . I f confirmed by e x a c t f i n i t e range
c a l c u l a t i o n s , i t would c o n s t i t u t e d i r e c t evidence
f o r the importance of such r e c o i l e f f e c t s i n heavyion t r a n s f e r .
A t s t i l l h i g h e r e n e r g i e s a new f e a t u r e of the
heavy-ion
r e a c t i o n i s revealed. This is the possi-
although the observations do n o t exclude an in-
t e r p r e t a t i o n i n terms of r e c o i l e f f e c t s 1203.
This c l e a r l y is an a r e a of much f u t u r e i n t e r e s t
-
and one whose understanding may provide t h e necess a r y l i n k between heavy-ion t r a n s f e r used t o o b t a i n
t r a d i t i o n a l microscopic n u c l e a r s t r u c t u r e informat i o n , a s discussed i n t h i s review, and the heavyi o n r e a c t i o n used t o explore macroscopic p r o p e r t i e s
of t h e nucleus. One r e a l i z e s a l s o t h a t our c u r r e n t
p r o j e c t i l e s a r e mainly a t t h e l i g h t end of the
b i l i t y t h a t t h e heavy i o n beam may c a r r y i n a n g u l a r
heavy-ion
momenta above t h e c r i t i c a l a n g u l a r momentum of the
beginning of t h e heavy-ion
compound nucleus [ 2 7 ] . Thus t h e formation of the
e x c i t i n g , many-f aceted field of r e s e a r c h .
r e g i s t e r , C l e a r l y we a r e o n l y s e e i n g t h e
transfer reaction a s an
HEA W-ION TRANSFER REACTIONS
P~~~(C
6 "" ),Bi
EC12 = 78 MeV
e,
=
60 Deg
CHANNEL
F i g . 18.
-
Single-proton
Acknowledgements. -
NUMBER
s t r i p p i n g r e a c t i o n s induced by 104 MeV 160 and 7 8 MeV
I am p l e a s e d t o acknowledge
'*c
i o n s on *08pb.
t o spend a y e a r s a b b a t i c a l i n F r a n c e
- and
i n par-
h e l p f u l d i s c u s s i o n s w i t h D r s . P. Bonche, R. DeVries
t i c u l a r t o acknowledge t h e h o s p i t a l i t y extended
and R , ' S c h a e f f e r . I a l s o wish t o t a k e t h i s opportu-
throughout by Mme H. F a r a g g i and D r . E. C o t t o n .
n i t y t o thank C.E.N.
S a c l a y f o r making i t p o s s i b l e
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HEAVY-ION TRANSFER REACTIONS
DISCUSSION
M. DANOS (Washington)
i f t h i s s i t u a t i o n might not be improved by stay-
Concerning t h e r a t h e r l a r g e r a d i u s i n t r a n s f e r
i n g c l o s e r t o t h e Coulomb b a r r i e r , s o t h a t t h i s
r e a c t i o n s i t seems reasonable t h a t i t i s given
dependence on paramekers could be redueed o r
by the sum of the t h r e e r a d i i , two n u c l e a r r a d i i
eliminated.
and t h e diameter of the t r a n s f e r r e d p a r t i c l e ;
a t l a r g e r d i s t a n c e of c l o s e s t approach the
t r a n s f e r r e d p a r t i c l e (e.g,
a - p a r t i c l e ) has t o
tunnel through a b a r r i e r , a t c l o s e r d i s t a n c e s
t h e t r a n s f e r r e a c t i o n w i l l be quenched by comp e t i t i o n from compound processes.
You a r e q u i t e r i g h t . B u t t l e and Goldfarb have
s t r e s s e d f o r a long time t h e advantages of
working a t the Coulomb b a r r i e r . A s you w e l l
know, however, experimentally i t i s not s e f a v c r a b l e t o work a t very f a r back a n g l e s . But
Since t r a n s f e r r e a c t i o n s take p l a c e a t t h e nu-
t h i s i s an a r e a
- and
there a r e r e s u l t s present-
-
where one has been i m -
c l e a r s u r f a c e they a r e expected t o be extremely
ed a t t h i s Conference
s e n s i t i v e t o c o n f i g u r a t i o n mixing ; they may be
4
enhanced by f a c t o r s 10, o r even 10 This h a s
pressed by how s t r o n g c r o s s s e c t i o n s can be near
been a l r e a d y seen i n t h e theory of the a-decay
j u s t what i s happening a t these e n e r g i e s where
by Mang, Glendenning and o t h e r s .
c u r r e n t l y we have problems of a n a l y s i s
.
G. MORRISON (Saclay)
With r e s p e c t t o your suggested e x p l a n a t i o n of
the larger radius i n transfer reactions, the
problem i s t h a t the r e s u l t s a r e n o t c o n s i s t e n t .
The 2p t r a n s f e r appears t o take p l a c e f u r t h e r
i80°. Nevertheless, i t is important t o l e a r n
- and
at
s t i l l h i g h e r e n e r g i e s t h e r e i s the e x c i t i n g
p r o s p e c t t o take advantage of t h e high E t r a n s f e r s e l e c t i v i t y a t c o n d i t i o n s of l a r g e momentum
mismatch.
B. FERNANDEZ (Saclay)
o u t than the alpha t r a n s f e r ; i t appears t h a t
You have shown t h e importance of the extended
the 2p t r a n s f e r d a t a cannot be f i t t e d with e l a s -
n a t u r e of the heavy ions,which manifests i t s e l f
t i c s c a t t e r i n g p o t e n t i a l s , whereas the a l p h a
i n t h e so-called r e c o i l e f f e c t s . I t h i n k i t a l s o
t r a n s f e r can. However your suggestion is very
holds f o r t h e o p t i c a l p o t e n t i a l . A s was shown on
i n t e r e s t i n g i n t h a t i t implies an i n t e r m e d i a t e
Monday i n paper 11.4, t h e s i z e e f f e c t r e s u l t s i n
necking s i t u a t i o n i n m u l t i n u c t e o t ~t r a n s f e r .
p a r t i c u l a r i n l a r g e d i f f u s e n e s s e s . Now, a s you
This i s a l s o something t h a t has been suggested
have pointed o u t , i t w i l l be probably n o t
by Bondorf a s a way t o account f o r t h e non-ob-
p o s s i b l e to determine t h e o p t i c a l p o t e n t i a l
servance of 12c* i n the (160,12c) r e a c t i o n on
shapes from e l a s t i c s c a t t e r i n g , s o we w i l l prob-
heavy n u c l e i . I f some s o r t of e q u i l i b r i u m was
a b l y have t o c a l c u l a t e these p o t e n t i a l s i n t h e
s e t up i n t h e neck, t h e s t a t i s t i c a l d i s t r i b u -
future
t i o n of energy would make i t u n l i k e l y t h a t t h e
l i g h t e r outgoing p a r t i c l e i s e x c i t e d .
J.G.
G , MORRISON (Saclay)
CRAMER ( S e a t t l e )
.
G. MORRISON (Saclay)
I agree
- and
i n f a c t the w r i t t e n version of my
t a l k i n c l u d e s r e f e r e n c e t o your very i n t e r e s t i n g
One of the e a r l y hopes f o r heavy i o n t r a n s f e r
work examining t h e b a s i s of the heavy-ion o p t i -
r e a c t i o n s was t h a t Coulomb d i s t o r t e d waves could
cal potential.
be used t o d e s c r i b e the r e a c t i o n p r o c e s s , e l i m i n a t i n g the n e c e s s i t y of an a c c u r a t e knowledge of
optical-model parameters. Now we f i n d , i n some
of t h e d a t a and a n a l y s i s t h a t you have describe d , t h a t we a r e s t i l l not only dependent on a
knowledge of o p t i c a l parameters, but a l s o t h a t
these parameters a r e r a t h e r d i f f e r e n t from those
which d e s c r i b e the e l a s t i c s c a t t e r i n g . I wonder
FLEROV (Dubna)
F i f t e e n y e a r s ago t h e problem of complex n u c l e i
i n t e r a c t i o n s was discussed i n USSR. The q u e s t i o n
a r o s e about b u i l d i n g a b i g and expensive a c c e l e r a t o r . Academician L. Arzimovich compared i n
t h i s d i s c u s s i o n t h e heavy ion r e a c t i o n s w i t h
c o l l i s i o n s of two c a r s .
Many, people were a f r a i d
G ,C
. MORRISON
t h a t the information observed i n heavy i o n reac-
t i o n mechanism. On the o t h e r hand the s y n t h e s i s
t i o n s w i l l be unimportant. Nevertheless t h e
of new i s o t o p e s by t r a n s f e r r e a c t i o n s appeared
Coulomb e x c i t a t i o n experiments which s t a r t e d i n
t o be r a t h e r f r u i t f u l . Leaving Dubna f o r Aix I
Leningrad and t h e s y n t h e s i s of the f i r s t e l e -
discussed t h i s problem w i t h Doctor V. Volkov
ment-102
t h e l e a d e r of both t h e s e d i r e c t i o n s . We d i d n o t
(Joliotium) showed t h e b i g f u t u r e of
heavy i o n physics.
come t o t h e f i n a l conclusion. P r o f e s s o r
I n a l l t h i s p e r i o d we have had many doubts about
Morrison's r e p o r t w i l l help us very much out-
importance of t h e information which can be ex-
l i n e our p o s i t i o n i n t h i s f i e l d .
t r a c t e d i n t h e i n v e s t i g a t i o n of t r a n s f e r reac-
-