This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

Bacher, A.D.

Brown, J.D.

Emery, G.T.

Jacobs, W.W.

Jones, W.P.

Nann, H.

Stephenson, E.J.

English

IUScholarWorks

PROTON GROUND-STATE CORRELATIONS I N  THE EVEN CALCIUM-ISOTOPES 
H.  Nann, W.W. Jacobs ,  A.D. Bacher,  J .D .  Brown, G.T. Emery, W.P. Jones ,  and E.J. Stephenson 
Ind i ana  U n i v e r s i t y  Cyclo t ron  F a c i l i t y  Bloomington, I nd i ana  47405 
The ex t remely  s t r o n g  s e l e c t i v i t y  of t h e  ( d , a )  components of t h e  t a r g e t  ground s t a t e  wave f u n c t i o n  a r e  
r e a c t i o n  on I f - s h e l l  t a r g e t  n u c l e i  a t  80 MeV bombarding weaker. 
energy f o r  p i ck ing  up proton-neutron p a i r s  i n  t h e  Unambiguous L = 6, J = 7 t r a n s i t i o n s  were 
comple te ly  a l i g n e d  ( 1 f 7 / 2 ) 2 7 , 0  con f igu ra t i on1  was used i d e n t i f i e d  l e a d i n g  t o  t h e  s t a t e s  a t  4.54 and 5.95 MeV 
i n  t h e  eVenCa(d,a)K r e a c t i o n  t o  de termine  t h e  ex tend  t o  i n  4 6 ~ ,  a t  1.91 MeV i n  4 2 ~ ,  a t  2.54 MeV i n  4 0 ~ ,  and a t  
which pro ton  co re  e x c i t a t i o n s  e x i s t  i n  t h e  ground 5.28 MeV i n  3 8 ~ .  Some measured angu l a r  d i s t r i b u t i o n s  
s t a t e s  of t he  even ca lc ium i s o t o p e s .  Although t h e s e  of t h e  d i f f e r e n t i a l  c r o s s  s e c t i o n  a r e  shown i n  t h e  
p ro ton  core  e x c i t a t i o n  components i n  t h e  ground s t a t e  le f t -hand pane l s  of F ig .  3  wi th  t h e  cor responding  
wave f u n c t i o n s  a r e  q u i t e  sma l l ,  t h e  s t r o n g e s t  peak i n  v e c t o r  ana lyz ing  powers i n  t h e  r ight-hand panel .  It is 
t h e  s p i n  up ( d , a )  spec t rum ( t h e  d e t e c t i o n  system being  i n t e r e s t i n g  t o  n o t e  t h a t  i n  4 6 ~  two J n  = 7+ s t a t e s  a r e  
on t h e  r i g h t  s i d e  of t h e  beam) on each Ca-isotope a t  popula ted  but  not  i n  t h e  o t h e r  K-isotopes.  I n  3 8 ~ ,  
@l ab  = 14" belongs t o  a  L = 6,  J = 7 t r a n s i t i o n .  This  t h e r e  is ano the r  7+ s t a t e  known a t  3.46 MeV. However, 
is  dep i c t ed  i n  F igs .  1 and 2. T r a n s i t i o n s  t o  s t a t e s  t h i s  s t a t e  is  very weakly e x c i t e d  i n  t h e  4 0 ~ a ( d , a ) 3 8 ~  
popula ted  by t h e  pickup of o t h e r  c o n f i g u r a t i o n  r e a c t i o n .  Th i s  is brought f o r t h  only  from a  channel  by 
pro ton-neut ron  p a i r s  from t h e  major shell-model channel  a n a l y s i s  of t he  vec to r  ana l zy ing  power of t h e  
peak around 3.4 MeV. 
1 From t h e  exp re s s ion  f o r  t h e  s p e c t r o s c o p i c  m 
Figu re  1. Alpha -pa r t i c l e  spec t rum of t h e  
' " ~ a ( d , a ) ~ ~ ~  r e a c t i o n .  
1 W z
4 1 ~ ) -  
CHANNEL NUMBER 
0 SPIN W 
B : 
3 .  
8 - 
0 
I00  3ca 500 7M) 
CHANNEL NUMBER 
- N 0
- ' IO~olxa) "K 
r loo- 
z 3 0 U
0 
p t g u r e  2. A lpha -pa r t i c l e  spec t rum of t h e  
~ a ( d , a ) ~ O ~  r e a c t i o n .  
Ed  =79 4 MeV 
8,., = 14. 
ampl i tude  f o r  t h e  pickup of a  pro ton-neut ron  p a i r  i n  
N 
100 300 500 700 900 
\ n;*, : 
t h e  s t r e t c h e d  ( l f 7 / 2 ) 2 7  ,0  c o n f i g u r a t i o n ,  t h e  p ro ton  
- 
- 
- 
Figu re  3. Angular  d i s t r i b u t i o n s  of t h e  d i f f e r e n t i a l  
c r o s s  s e c t i o n  ( l e f t - hand  pane l )  and v e c t o r  ana lyz ing  
% 
2 
power ( r ight -hand pane l )  f o r  L = 6 t r a n s i t i o n s  i n  t h e  
4 0 , 4 2 , 4 4 ~ a ( d , a )  r e a c t i o n s .  

f o r  gene ra t i ng  a  more r e a l i s t i c  form f a c t o r ,  i t  is One p o s s i b l i t y  i s  t h a t  t h e  If712 p ro ton  pickup s t r e n g t h  
probably  not  only s u f f i c i e n t  t o  change t h e  r a d i u s  but i n  t h e  4 8 ~ a ( d , 3 ~ e ) 4 7 ~  r e a c t i o n  is  much more fragmented 
a l s o  t o  vary i t s  depth.  Th i s  means t h a t  t h e  
t r a n s f e r r e d  nucleon is no l onge r  bound by t h e  observed 
s e p a r a t i o n  energy.  From a  comparison of t h e  pro ton  
s e p a r a t i o n  e n e r g i e s  of A ~ a  and A + l ~ c  one deduces t h a t  
t h e  shell-model If712 o r b i t a l  i n  t h e  ca lc ium-iso topes  
l i e s  about 6  t o  7  MeV above t h e  ld3/2-2s112 o r b i t a l s .  
Use of an e f f e c t i v e  b inding  energy f o r  a  If712 p ro ton ,  
which i s  sma l l e r  by t h i s  amount t han  t h e  a c t u a l  
s e p a r a t i o n  energy ,  y i e l d s  If712 p ro ton  occupat ion  
numbers of 0.9 2 0.2, 0.9 2 0.2, 1.2 + 0.3, and 
0.7 + 0.2 f o r  t h e  Ca-isotopes 40, 42, 44, and 48, 
r e s p e c t i v e l y  . 
These l a s t  occupat ion  numbers a r e  be l i eved  t o  be 
t h e  most r e a l i s t i c  ones t h a t  p r e s e n t l y  can be de r i ved  
from t h e  ( d , a )  d a t a  a t  80 MeV bombarding energy.  I n  
Fig.  4  t hey  a r e  compared t o  r e s u l t s  from s ingle-nucleon  
s t r i p p i n g  and pickup r e a c t i o n s .  The agreement i s  
q u i t e  good wi th  excep t i on  of t h e  r e s u l t s  from t h e  
4 8 ~ a ( d ,  'H~)"K r e a c t i o n 7  which y i e l d  a  very sma l l  i f  712 
p ro ton  occupancy i n  t h e  ground s t a t e  wave f u n c t i o n  of 
4 8 ~ a .  At p r e s e n t ,  it  is unc l ea r  how t o  e x p l a i n  i t .  
ol- 
PICKUP 
A STRIPPING 
o (d, a) 
Figu re  4. Number of l f 7 1 2  p ro tons  i n  t h e  ground 
s t a t e s  of t h e  even ca lc ium i so topes .  
t han  t h e  (1f 7 / 2 )  2 7  ,0 pro ton-neut ron  pickup s t r e n g t h  i n  
t h e  ( d , a )  r e a c t i o n  and has t h e r e f o r e  escaped  d e t e c t i o n .  
Th i s  is co r r abo ra t ed  by t h e  f a c t  t h a t  i n  t h e  
4 8 ~ a ( d , 3 ~ e )  s t udy  both t h e  2 ~ 1 1 2  and t h e  Id312 p ickup 
s t r e n g t h  were observed t o  be fragmented.  It may be 
r e l e v a n t  t h a t  i n  a  weak coup l i ng  p i c t u r e  712- s t a t e s  i n  
4 7 ~  can be c o n s t r u c t e d  by coupl ing  a  2s112 o r  ld312 
p ro ton  ho l e  t o  t h e  c o l l e c t i v e  3- s t a t e  i n  4 8 ~ a ,  whi le  
i n  4 6 ~  one cannot make a  7+ s t a t e  by coupl ing  a  
pro ton-neut ron  p a i r  i n  t h e  2 ~ 1 1 2  and Id312 o r b i t a l s  t o  
any low-lying c o l l e c t i v e  s t a t e  i n  4 8 ~ a .  On t h e  o t h e r  
hand, i f  a  s o l u t i o n  f o r  t h i s  d i s c r epancy  is sought  i n  
terms of an i n t e r f e r e n c e  between one- and two-step 
p roce s se s ,  i t  would have t o  be c o n s t r u c t i v e  i n  t h e  
( d , a )  c a s e  and d e s t r u c t i v e  f o r  ( d , 3 ~ e ) .  Moreover, t h i s  
i n t e r f e r e n c e  could  not  a l t e r  t h e  shape of t h e  one-step 
( d , a )  VAP angu l a r  d i s t r i b u t i o n s ,  expe r imen t a l l y  
observed  t o  be s t a b l e  f o r  t h e  t r a n s i t i o n s  t o  both 4.54 
and 5.95 MeV s t a t e s  i n  4 6 ~  and a l l  o t h e r  7+ t r a n s i t i o n s  
s t u d i e d  a c r o s s  t h e  1 f 7 j 2  s h e l l  (up t o  6 4 ~ i ) .  
Un fo r tuna t e ly ,  a b s o l u t e  mu l t i - s t ep  c a l c u l a t i o n s  of t h i s  
kind a r e  p r e s e n t l y  not f e a s i b l e .  
These pro ton  occupat ion  numbers f o r  t h e  l f 7 / 2  
o r b i t a l  ag r ee  q u i t e  w e l l  w i th  t h e  r e s u l t s  of 
shell-model c a l c u l a t i o n s  by zucker8  who o b t a i n s  0.57, 
0.72, 0.83 and 0.64 f o r  t h e  ca lc ium-iso topes  40,42,44 
and 48, r e s p e c t i v e l y .  The agreement f o r  4 8 ~ a  is  
a s t o n i s h i n g  . 
1) H. Nann, e t  a l . ,  Nucl. Phys. A406, 81  (1983),  and 
Phys. Rev. C 30, 1509 (1984).  
2 )  R.M. DelVecchio and W.W. Daehnick, Phys. Rev. C 5, 
2095 (1972). 
3)  I. S i ck  e t  a l . ,  Phys. Rev. L e t t .  38, 1259 (1977) ;  
I. S i ck ,  Commun. Nucl. P a r t .  Phys. 9, 55 (1980).  
4 )  S.K. P la tchkov e t  a l . ,  Phys. Rev. C 25, 2318 
(1982).  
5 )  A.E.L. Dieper ink  and I. S i ck ,  Phys. L e t t .  1093, 1 8 )  A.P. Zucker,  Proc.  Top. Conf. on t h e  S t r u c t u r e  of 
(1982).  I f717  Nucle i ,  Legnaro (Padova) 1971, ed. R.A. R i c c i  
( E d i t r i c e  Composi tor i ,  Bologna, 1971),  p. 94. 
6 )  P. Dol l  e t  a l . ,  Nucl. Phys. A263, 210 (1976).  
7 )  S.M. Banks e t  a l . ,  Z. Phys. A316, 241 (1984),  and 
Nucl. Phys. A437, 381 (1985). 
STUDY OF THE 1 2 ~ ( 7 ~ i , t ) 1 6 0  a-TRANSFER REACTION AT HIGH ENERGIES 
Fred  B e c c h e t t i ,  P.M. L i s t e r ,  and J .  Janecke  
U n i v e r s i t y  of Michigan, Ann Arbor, Michigan 48109 
A. Nadasen 
U n i v e r s i t y  of Michigan, Dearborn, Michigan 48128 
J. Winf i e l d  
NSCL, Michigan S t a t e  Un ive r s i t y ,  Eas t  Lans ing ,  Michigan 48824 
D.L. F r i e s e l  and K.R. Komisarcik 
Ind i ana  U n i v e r s i t y  Cyclo t ron  F a c i l i t y ,  Bloomington, Indiana  47405 
A s tudy  of 1 2 ~ ( 7 ~ i , t ) 1 6 0  a t  E ( ~ L ~ )  = 101 MeV was h ighe r  e n e r g i e s  a t  IUCF us ing  t h e  new k = 600 
completed a t  IUCF us ing  two S i  AE d e t e c t o r s  backed by spec t rome te r .  
t h i c k  i n t r i n s i c  Ge E d e t e c t o r s .  Also,  a - p a r t i c l e s  were The h igh  energy 1 2 ~ ( 7 ~ i , t ) 1 6 0  d a t a  should  provide  
observed i n  co inc idence  a t  back ang l e s  t o  i d e n t i f y  new in fo rma t ion  on high-spin a - c l u s t e r  l e v e l s  i n  160,  
decay from high  s p i n  s t a t e s  i n  160. Th i s  u t i l i z e d  a Ex > 10 MeV. It w i l l  a l s o  permit  comparisons w i th  our  
600 mm2 S i  E d e t e c t o r  w i th  t ime-of - f l igh t  used f o r  e a r l i e r 1  d a t a  and a n a l y s i s  of 1 2 ~ ( 6 ~ i , d ) 1 6 0  done a t  
i d e n t i f i c a t i o n .  IUCF wi th  E ( ~ L I )  = 90 MeV. These d a t a  can be used t o  
I n  a d d i t i o n  t o  t h e  well-known l e v e l s  a t  Ex < 20 
E, (MeV) 
MeV, we may have observed new l e v e l s  a t  Ex > 20 MeV t o  
30 MeV and p o s s i b l y  some at Ex > 30 MeV ( s e e  Figure 1 ) .  
The a n a l y s i s  of t h e  co inc idence  a-par t  i c l e  decay d a t a  
from s p e c i f i c  l e v e l s  has j u s t  begun. 
A r e l a t e d  h igh - r e so lu t i on  s t udy  of 1 2 ~ ( 7 ~ i , t )  f o r  
t h e  r eg ion  i n  160,  Ex < 10 MeV was s t a r t e d  a t  NSCL 
(MSU) u s ing  E ( ~ L ~ )  = 80 MeV wi th  t h e  k = 320 
spec t rometer .  An i n i t i a l  run  r e so lved  both t h e  
7.12/6.92 MeV 1-/2+ doub l e t  and t h e  9.6 MeV 1 - l eve l  i n  
160  which a r e  of i n t e r e s t  i n  a s t r o p h y s i c s  (he l ium 
A 
E = 101 MeV - 
- 
- 
- - 
CHANNEL 
burning) .  A second run  is scheduled  f o r  Sp r ing  1986. F igu re  1. A t r i t o n  energy spec t rum and cor responding  
l e v e l s  i n  160 observed  i n  1 2 ~ ( 7 ~ i ,  t )  a t  E ( ~ L ~ )  = 101 
This  work w i l l  be cont inued  and may be extended t o  MeV. 


Proton Ground-state Correlations in the Even Calcium-isotopes

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Proton Ground-state Correlations in the Even Calcium-isotopes

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