This work was supported by National Science Foundation Grant PHY 75-00289 and Indiana Universit

Adams, G.

Becchetti, F.D.

Jacobs, W.

Jånecke, J.

Kaitchuck, M.

Nadasen, A.

Ploughe, W.

Schwandt, P.

Singh, P.P.

English

IUScholarWorks

SCATTERING OF 99-MeV 6 ~ i  IONS 
P. Schwandt, P.P. Singh, A. Nadasen, G.  Adams, M. Kaitchuck, W. Jacobs, F.D. Becchetti*, J. Janecke*, and 
W. Ploughe** 
F i r s t  measurements of t h e  d i f f e r e n t i a l  c ross  
s ec t ions  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  of 
6 ~ i  ions a t  99.1 MeV bombarding energy have been 
made. P a r t i a l  angular  d i s t r i b u t i o n s  have been 
obtained f o r  t a r g e t s  of 12c, 28~i, 4 0 ~ a ,  58~i, 
9 0 ~ r  and 2 0 8 ~ b  i n  two experimental runs.  Addit ional  
runs w i l l  be scheduled ( a f t e r  f u r t h e r  development 
t o  increase  t h e  L i  beam i n t e n s i t y  on t a r g e t )  t o  
extend some of t h e  present  angular  d i s t r i b u t i o n s  
towards l a r g e r  angles  and t o  ob ta in  da t a  f o r  ad- 
d i t i o n a l  t a r g e t s .  
The f i r s t  run a t  t h e  end of November 1976, 
wi th  only 0.1 t o  1 enA of 6~i3+ on t a r g e t ,  y ie lded  
angular  d i s t r i b u t i o n s  f o r  t h e  above t a r g e t s  over 
a range of lab .  angles  from 6O t o  about 30-40° 
(47O f o r  12c ) .  I n  t he  second run a t  t h e  end of 
February 1977, wi th  5-15 enA on t a r g e t ,  t h e  
angular  d i s t r i b u t i o n s  f o r  28~i,  "21 and 2 0 8 ~ b  
were extended t o  eL=500, 41°, and 54O, r e spec t ive ly ,  
where t h e  e l a s t i c  c ros s  s ec t ion  i n  a l l  cases had 
plummeted t o  roughly lOpb/sr. For t he  e l a s t i c  
s ca t t e r ing ,  t h e  combined experimental da t a  a r e  
presented i n  Fig. 1 which d isp lays  t h e  e l a s t i c  
c ross  s ec t ion  a s  ratio-to-Rutherford a s  a funct ion  
of c.m. s c a t t e r i n g  angle.  I n e l a s t i c  s c a t t e r i n g  
da t a  have not  y e t  been ex t r ac t ed  from t h e  spec t ra .  
The measurements were c a r r i e d  out  i n  t h e  64" 
s c a t t e r i n g  chamber. I so top ica l ly  enriched t a r g e t s  
(except f o r  S i )  of th ickness  from 11 t o  33 mg/cm2 
Figure 1. 
were used. The s c a t t e r e d  L i  ions  were de tec ted  i n  3 
AE-E s i l i c o n  sur face-barr ie r  de t ec to r  te lescopes  
(200 pm + 1000 pm) wi th  angular  acceptance of %lo. 
Hardware pulse-height d iscr iminat ion  e f f e c t i v e l y  
el iminated a l l  r eac t ion  products o the r  than 6 ~ i  and 
7 ~ i .  With the  exception of  2 0 8 ~ b ,  t h e  ( 6 ~ i ,  7 ~ i )  
r eac t ion  Q-values a r e  h ighly  negat ive  (Q 5 - 5 MeV) 
f o r  t h e  t a r g e t s  s tudied ,  e l iminat ing  t h e  need f o r  more 
soph i s t i ca t ed  p a r t i c l e - i d e n t i f i c a t i o n  techniques 
(a lso ,  t e s t  runs made e a r l i e r  a t  55 MeV had shown 
t h e  7 ~ i  y i e l d  f o r  9 0 ~ r  a t 300 t o  be  of order 1% of' t he  
6 ~ i  y i e l d ) .  To ta l  energy r e so lu t ion  i n  these  measure- 
ments was t y p i c a l l y  300 t o  500 keV. Fig.  2 shows 
a spectrum f o r  2 8 ~ i  (before d iscr iminat ion  aga ins t  
'LI + % I ,  99 MeV 
4 = 16.5. 
Figure 2. 
t h e  l a r g e  but  well-separated break-up a group), 
i l l u s t r a t i n g  t h e  r e l a t i v e l y  c lean  region  up t o  7 
MeV e x c i t a t i o n  and below the  f i r s t  7 ~ i  group 
(Q = -9.97). For t he  f i r s t  run a t  beam cu r ren t s  
below 1 enA, a fou r th  de t ec to r  te lescope  was 
used a t  a  f i xed  forward angle  t o  s e rve  a s  a 
monitor f o r  r e l a t i v e  normalizat ion of t h e  da t a  
s ince  subnanoamp cu r r en t s  could not  be r e l i a b l y  
i n t eg ra t ed .  In  t he  second run  the  beam current  
was s u f f i c i e n t  f o r  accu ra t e  charge in t eg ra t ion ,  
allowing determination of t h e  absolu te  c ros s  
s ec t ion  t o  + 10%. The r e l a t i v e  accuracy of t he  
da t a  ranges from + 3% t o  + 30% a t  some of t h e  
l a r g e s t  angles.  
The abso lu t e  e l a s t i c  c ros s  s ec t ions  f o r  t h e  
S i ,  Z r  and Pb t a r g e t s  span a range of values 
covering 7 t o  8 decades over t h e  angular  range 
measured, corresponding t o  an  average r a t e  of 
f a l l -o f f  by a f a c t o r  of 10 over 8O t o  60. For 
t h e  l i g h t e r  mass t a r g e t s  (A ,: 30) t h e  6 ~ i  e l a s t i c  
s c a t t e r i n g  e x h i b i t s  forward-angle d i f f r a c t i v e  
o s c i l l a t i o n s  which d i e o u t  somewhat wi th  i nc reas ing  
angle.  For t h e  heavier  t a r g e t s  (A 60),  on t h e  
o the r  hand, t h e  forward-angle da t a  beyond t h e  
Coulomb-nuclear i n t e r f e r ence  "knee1' s t a r t  ou t  a s  a  
r e l a t i v e l y  smooth exponential  f a l l - o f f ,  wi th  in-  
c reas ingly  pronounced o s c i l l a t o r y  s t r u c t u r e  ap- 
pearing a t  l a r g e r  angles.  These f e a t u r e s  a r e  
t y p i c a l  of t he  s c a t t e r i n g  of s t rong ly  absorbed 
ions  which is charac ter ized  by 2 parameters and 
corresponding f ea tu re s :  The Sommerfeld para- 
meter 0 which cha rac t e r i ze s  t he  Coulomb i n t e r -  
ac t i on ,  and t h e  c r i t i c a l  angular  momentum X f o r  
which I S  I = 0.5 and which cha rac t e r i ze s  s t rong  a 
absorption.  For X >> 1, t h e  nuclear  s c a t t e r i n g  
is d i f f r a c t i v e .  This condi t ion  is f u l f i l l e d  f o r  
a l l  of t h e  present  d a t a  where X=28 and 50 f o r  
S i  and Pb, r e spec t ive ly .  However, t h e  na tu re  of 
t he  d i f f r a c t i v e  s c a t t e r i n g  ( i . e . ,  whether Fraun- 
hofer  o r  Fresnel )  depends on whether t h e  Coulomb 
i n t e r a c t i o n  s a t i s f i e s  t he  condi t ion  p << 1 
(Fraunhof er-dif  f r a c t i o n  s c a t t e r i n g )  o r  p >> 1 
(Fresnel -d i f f rac t ion  s c a t t e r i n g )  where p 2q 
[ 1 - ( 2 ~ / ~ ~ - 1 ) - ~ ] .  For t he  present  6 ~ i  experiment, 
p = 3 f o r  S i  and p = 1 3  f o r  Pb. The s c a t t e r i n g  
from Pb and Z r  a t  t h i s  energy is the re fo re  
q u a l i t a t i v e l y  of t h e  Fresnel  type wi th  a t y p i c a l  
s t r u c t u r e l e s s  exponential  f a l l -o f f  of a/aR wi th  
s c a t t e r i n g  angle  ( i . e . ,  con t r ibu t ions  from only 
one s i d e  of t he  l a r g e  absorpt ive  nuclear  d i s c  a r e  
seen) .  For t h e  l i g h t e s t  t a r g e t s  one observes 
Fraunhofer o s c i l l a t i o n s  a t  t h e  forward angles  
(where one sees  i n t e r f e r i n g  con t r ibu t ions  from 
oppos i te  s i d e s  of  t h e  i n t e r a c t i o n  region) ;  
with increas ing  Coulomb i n t e r a c t i o n  these  o s c i l l a -  
t i ons  move t o  l a r g e r  angles  because of t he  "diverging1' 
lens"  e f f e c t  of t he  r epu l s ive  Coulomb f i e l d .  The 
disappearance of t he  Fraunhofer o s c i l l a t i o n s  a t  l a r g e r  
angles  f o r  t he  l i g h t e s t  t a r g e t s  s i g n a l s  t he  change 
from per iphera l  d i f f r a c t i v e  s c a t t e r i n g  t o  smooth 
r e f r a c t i v e  s c a t t e r i n g  from the  nuclear  i n t e r i o r .  
Previously ava i l ab l e  L i  s c a t t e r i n g  da t a  is 
l imi t ed  t o  energies  below 60 MeV and one recent  
6 ~ i  + 2 8 ~ i  measurement a t  135 MeV. The primary 
motivation f o r  t he  present  s tudy is  t o  p a r t l y  f i l l  
t he  da t a  gap and t o  provide a r e l i a b l e  op t i ca l -  
model parametrizat ion of 6 ~ i  e l a st i c  s c a t t e r i n g  a t  
100 MeV, s u i t a b l e  f o r  use i n  analyses  of r eac t ions  
such a s  ( 6 ~ i , d )  and (6~i,  6 ~ e )  whose s tudy a t  IUCF 
has been proposed and approved. Optical-model f i t s  
t o  the  new data  a r e  i n  progress.  Subject  t o  
6 a v a i l a b i l i t y  of a 100 MeV L i  beam of h igher  in-  
t e n s i t y  (: 50 enA), t he  measurements on the  l i g h t e r  
t a r g e t s  i n  p a r t i c u l a r  (e . g . 2 8 ~ i )  w i l l  be extended 
i n t o  the  smooth f a l l -o f f  o r  "nuclear  rainbow" 
region, which i s  necessary f o r  an unambiguous 
determination of  t he  unique o p t i c a l  p o t e n t i a l  
s t rength .  
*University of Michigan, Ann Arbor, Michigan 48104 
**The Ohio S t a t e  Universi ty,  Columbus, Ohio 43210 


Scattering of 99-MeV 6-Li Ions

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Scattering of 99-MeV 6-Li Ions

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