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

Byrd, R.C.

Carey, T.A.

Gaarde, C.

Goodman, C.D.

Larsen, J.S.

Rapaport, J.

Sugarbaker, E.

Taddeucci, T.N.

van Heerden, I.J.

Welch, T.P.

English

IUScholarWorks

SPIN TRANSFER HEASUREMENTS FOR (p,n) REACTIONS AT INTERMEDIATE ENERGY 
T.N. Taddeucci  
Ohio Un ive r s i t y ,  Athens,  Ohio 45701 and Ind i ana  U n i v e r s i t y  Cyc lo t ron  F a c i l i t y ,  Bloomington, I nd i ana  47405 
C.D. Goodman, R.C. Byrd, and I.J. Van Heerden+ 
I n d i a n a  Un ive r s i t y  Cyclo t ron  F a c i l i t y ,  Bloomington, I nd i ana  47405 
T.A. Carey 
Los Alamos Na t i ona l  Labora tory ,  Los Alamos, New Mexico 87545 
D.J. Horen 
Oak Ridge Na t i ona l  Labora tory ,  Oak Ridge, Tennessee 37830 
J . S .  Larsen  and C. Gaarde 
N i e l s  Bohr I n s t i t u t e ,  U n i v e r s i t y  of  Copenhagen, DK-2100, Copenhagen, Denmark 
J. Rapaport  and T.P. Welch 
Ohio Un ive r s i t y ,  Athens,  Ohio 45701 
E. Sugarbaker  
Ohio S t a t e  Un ive r s i t y ,  Columbus, Ohio 43214 
We have p r ev ious ly  repor ted1  t h e  r e s u l t s  of  t h e  t h e  low momentum t r a n s f e r  s t r e n g t h  of t h e  t e n s o r  
f i r s t  s p i n  t r a n s f e r  measurements f o r  (p ,n)  r e a c t i o n s  a t  i n t e r a c t i o n .  Some measured v a l u e s  of  DNN(8)  f o r  
i n t e r m e d i a t e  energy (160 MeV). These i n i t i a l  1 3 ~ ( p , n ) 1 3 ~ ( g . s . )  and 6 ~ i ( p , n ) 6 ~ e ( g . s . )  a t  Ep=160 MeV 
measurements demonst ra ted  t h e  f e a s i b i l i t y  of  u s ing  a r e  shown i n  Fig.  1. Also  shown i n  t h i s  f i g u r e  a r e  t h e  
hydrocarbon s c i n t i l l a t o r  (NE102 i n  t h i s  c a se )  a s  a  r e s u l t s  of  d is tor ted-waves  impulse  approximat ion  
n e u t r o n  p o l a r i z a t i o n  a n a l y z e r  and confirmed t h e  (DWIA) c a l c u l a t i o n s  employing t h e  140-MeV t -mat r ix  
expec t ed  s p i n  t r a n s f e r  s i g n a t u r e  f o r  Gamow-Teller (GT) i n t e r a c t i o n  of Love and ~ r a n e ~ ~  and t h e  l p - s h e l l  wave 
t y p e  t r a n s i t i o n s  (AJn=l+, AL=O). A d d i t i o n a l  f u n c t i o n s  of Cohen and ~ u r a t h . ~  The d a t a  seem t o  f a v o r  
measurements c a r r i e d  ou t  i n  March 1984 a s  a  
c o n t i n u a t i o n  of IUCF exper iment  186 have y i e l d e d  
s e v e r a l  s i g n i f i c a n t  new r e s u l t s .  These a r e :  
1. s p i n  t r a n s f e r  angu l a r  d i s t r i b u t i o n s  f o r  6 ~ i ,  
13c, and 1 5 ~  a t Ep=160 MeV, 
2. h igh  q u a l i t y  s p i n  t r a n s f e r  d a t a  f o r  9 0 ~ r ( p , n )  
a t  160 MeV and 8=0°,  f o r  e x c i t a t i o n s  up t o  Ex=50 
MeV, 
3. expe r imen t a l  c a l i b r a t i o n  of  t h e  a b s o l u t e  
magnitude and energy  dependence of t h e  p o l a r i -  
me t e r  ana lyz ing  power f o r  neut ron  e n e r g i e s  
117 MeV < En < 160 MeV. (New r e s u l t s  from a 
J anua ry ,  1985 run have now extended t h i s  
c a l i b r a t e d  range  t o  77 MeV.) 
Angular  d i s t r i b u t i o n s  of t h e  t r a n s v e r s e  s p i n  
t r a n s f e r  c o e f f i c i e n t  DNN can  p rov ide  i n fo rma t ion  about  
F igu re  1. T ransve r se  s p i n  t r a n s f e r  angu l a r  
d i s t r i b u t i o n s  a t  Ep=160 MeV. The s o l i d  l i n e s  a r e  t h e  
r e s u l t  of  DWIA c a l c u l a t i o n s  employing c e n t r a l ,  
s p i n - o r b i t ,  and t e n s o r  components i n  t h e  i n t e r a c t i o n .  
The dashed l i n e s  cor respond t o  c a l c u l a t i o n s  employing a  
c e n t r a l  i n t e r a c t i o n  only .  
t h e  c a l c u l a t i o n s  employing t h e  f u l l  ( c e n t r a l  + sp in-  
o r b i t  + t en so r )  i n t e r a c t i o n  ( s o l i d  l i n e s ) ,  and a r e  i n  
poo re r  agreement w i th  c a l c u l a t i o n s  done w i th  a  c e n t r a l  
i n t e r a c t i o n  only  (dashed l i n e s ) .  
At z e ro  deg ree s  t h e  e f f e c t  of  t h e  t en so r  
i n t e r a c t i o n  is  minimized and s imple  p r e d i c t i o n s  can  be 
made f o r  t h e  va lue  of DNN(OO) t o  be expec ted  f o r  a  
p a r t i c u l a r  m u l t i p o l a r i t y  .4 For  GT t r a n s i t i o n s ,  t h e  
expec t ed  va lue  i s  h N ( O O )  = -1/3, and an  e m p i r i c a l  
ave r age  f o r  pure  GT t r a n s i t i o n s  ( i . e . ,  AJ"=~+,  AL=O 
t r a n s i t i o n s  w i th  no i n t e r f e r i n g  background) a t  Ep=160 
MeV i s  DNN(OO) = -0.33 + 0.05. The u n c e r t a i n t y  i n  t h i s  
ave r age  va lue  r e p r e s e n t s  r e a l  d e v i a t i o n s  from t h e  
nominal  va lue  a s  w e l l  a s  s t a t i s t i c a l  and s y s t e m a t i c  
u n c e r t a i n t y  i n  t h e  measurements. For o t h e r  mul t i -  
p o l a r i t i e s ,  t h e  v a l u e s  expec ted  f o r  AS=1 t r a n s i t i o n s  
a r e  
DNN(OO) = 0  A J  = AL 
< -1/3 A J  = AL t 1 
and f o r  AS = 0  t r a n s i t i o n s  
DNN(OO) = 1. 
Note t h a t  t h e  va lue  of -1/3 f o r  GT t r a n s i t i o n s  i s  t h e  
l e a s t  n e g a t i v e  DNN expected  f o r  an  u n n a t u r a l  p a r i t y  
( A J f A L )  e x c i t a t i o n .  
The most i n t e r e s t i n g  a s p e c t s  of  t h e  9 0 ~ r ( p , n )  d a t a  
a r e  i l l u s t r a t e d  i n  Fig.  2. The s p i n - f l i p  c r o s s  s e c t i o n  
GSNN ( t o p ) ,  non-sp in- f l ip  c r o s s  s e c t i o n  o(1-SNN) 
(middle) ,  and DNN (bottom) a r e  p r e sen t ed  a s  f u n c t i o n s  
of  e x c i t a t i o n  energy i n  1 MeV energy  b in s .  T r a n s i t i o n s  
t h a t  a r e  pure s p i n - f l i p  (DNN = -1) o r  pure  non-spin- 
f l i p  (DNN=l) w i l l  appear  i n  only  one of t h e  two c r o s s  
s e c t i o n  s p e c t r a .  The obvious example he r e  is  t h e  
i s o b a r i c  ana log  s t a t e  ( IAS)  t r a n s i t i o n  t h a t  s t a n d s  ou t  
prominent ly  a t  Ex=5 MeV i n  t h e  non-sp in- f l ip  spectrum 
and i n  t h e  NN spectrum. The continuum r eg ion  i n  t h e  
s p i n  f l i p  spectrum i s  r a t h e r  f l a t  and f e a t u r e l e s s ,  
50 40 30 20 10 0 
excitation energy Ex (MeV) 
Figu re  2. Sp in  f l i p  c r o s s  s e c t i o n  ( t o p ) ,  non-sp in- f l ip  
c r o s s  s e c t i o n  (middle) ,  and DNN(O ") (bottom) f o r  
g o ~ r ( p , n )  a t  8=0° and Ep=160 MeV. 
wh i l e  two wide "bumps" appear  i n  t h e  non-sp in- f l ip  
spectrum a t  Ex=20 MeV ("a")  and Ex=35 MeV ("c") .  The 
appearance  of t h e s e  f e a t u r e s  i n  t h e  non-sp in- f l ip  
spectrum but  no t  i n  t h e  s p i n - f l i p  spectrum s u g g e s t s  t h e  
e x c i t a t i o n  of AS=O s t r e n g t h .  The v a l u e s  of  DNN f o r  
t h e s e  r eg ions  conf i rm a  s u b s t a n t i a l  amount of  n a t u r a l  
p a r i t y  s t r e n g t h .  The bump a t  Ex=20 MeV i s  a t  t h e  same 
e x c i t a t i o n  energy a s  a  resonance  p r ev ious ly  i d e n t i f  i ed5  
a s  AL=l. The measured va lue  of L)NN t hu s  sugges t s  t h a t  
a  l a r g e  f r a c t i o n  of t h e  s t r e n g t h  is AJn=l '  (and 
p o s s i b l y  2+ a s  we l l ) .  It is i n t e r e s t i n g  t o  no t e  t h a t  
t h e  p o s s i b l e  AS=O bump a t  E,=35 lYeV ("c") is  a t  t h e  
e x c i t a t i o n  energy p r e d i c t e d  f o r  t he  0' i s o v e c t o r  
monopole (IVM) resonance6 and has approximate ly  t h e  
width  (-12 MeV) expected  f o r  t h e  IVM. Other  n a t u r a l  
p a r i t y  e x c i t a t i o n s ,  such  a s  3' o r  2+, could  a l s o  
c o n t r i b u t e  i n  t h i s  r eg ion ,  however. New DNN 
measurements a t  120 MeV, where AS=O e x c i t a t i o n s  should  
be  enhanced by a  f a c t o r  of  11.75 r e l a t i v e  t o  160 MeV, 
may h e l p  c l a r i f y  i n t e r p r e t a t i o n  of t h e  s t r e n g t h  i n  t h i s  
r e g ion .  F i n a l l y ,  no t e  t h a t  t h e  r eg ion  marked a s  "b" i n  
t h e  s p i n - f l i p  spectrum corresponds  t o  a  r e l a t i v e l y  
l a r g e  n e g a t i v e  va lue  of DNN. P o s s i b l e  c a n d i d a t e s  f o r  
e x p l a i n i n g  t h e  d a t a  i n  t h i s  r eg ion  a r e  1+ (AL=2) o r  
0- e x c i t a t i o n s .  
The p o l a r i m e t e r  used t o  make t h e  above 
measurements has  been p r ev ious ly  d e ~ c r i b e d . ~  It 
c o n s i s t s  of  two p a r a l l e l  p l anes  of  s c i n t i l l a t o r  
o r i e n t e d  pe rpend i cu l a r  t o  t h e  i n c i d e n t  neu t ron  f l u x .  A 
c r u c i a l  requi rement  f o r  t h e  a n a l y s i s  of  t h e  h igh  
e x c i t a t i o n  9 0 ~ r ( p , n )  d a t a  was t h e  c a l i b r a t i o n  of t h e  
p o l a r i m e t e r  ana lyz ing  power a s  a  f u n c t i o n  of energy.  
The c a l i b r a t i o n  was achieved  by obse rv ing  neu t rons  
produced by t h e  0++0+ 14c (p  ,n)  1 4 ~ ( 2 . 3 1 - ~ e ~ )  IAS 
r e a c t i o n  a t  Ep=120 MeV and 160 MeV. The p o l a r i z a t i o n  
of  such  neu t rons  a t  z e ro  deg ree s  i s  equa l  t o  t h e  
p o l a r i z a t i o n  of  t h e  i n c i d e n t  p ro ton  beam. The r e s u l t s  
o f  t h e  120 MeV and 160 MeV c a l i b r a t i o n s  a r e  shown i n  
Fig .  3. The e f f e c t i v e  p o l a r i m e t e r  ana lyz ing  power 
Aeff i s  s m a l l e r  by a  f a c t o r  of  0.83 + 0.08 from t h e  
v a l u e s  a b t a i n e d  by ave rag ing  t h e  f r e e  n-p ana lyz ing  
power over  t h e  accep t ance  of t h e  po l a r ime t e r .  Th i s  
r e d u c t i o n  is  mainly t h e  r e s u l t  of  contaminent  
c o n t r i b u t i o n s  from 12c (n ,n ' x )  r e a c t i o n s .  
An impor t an t  parameter  r e l a t e d  t o  po l a r ime t e r  
performance is t h e  e f f e c t i v e  a r e a  a & ,  t h a t  is,  t h e  
p r oduc t  of t h e  doub l e - s ca t t e r i ng  e f f i c i e n c y  and t h e  
a r e a  of t h e  f r o n t  f a c e  of t h e  ana lyze r .  Th i s  q u a n t i t y ,  
when m u l t i p l i e d  by t h e  i n t e g r a t e d  neu t ron  f l u x  In 
(neut rons /cm2) ,  g i v e s  t h e  number of u s e f u l  double- 
neutron energy En (MeV) 
Figu re  3. The measured e f f e c t i v e  ana lyz ing  power Aeff 
o f  t h e  p o l a r i m e t e r  . The c r o s s e s  r e p r e s e n t  c a l c u l a t i o n s  
of t h e  n-p ana lyz ing  power averaged  over  t h e  accep t ance  
o f  t h e  po l a r ime t e r .  The a s t e r i s k s  a r e  t h e s e  same 
c a l c u l a t i o n s  normalized t o  t h e  da t a .  
s c a t t e r e d - n e u t r o n  even t s .  For t h e  p r e s e n t  p o l a r i m e t e r ,  
w i th  a n  i n t e r p l a n e  s e p a r a t i o n  of 0.85 m, t h e  e f f e c t i v e  
a r e a  is aE=(4590 cm2)(5.0t0.5)x10'4=2.3+0.2 cm2 f o r  
120 MeV neu t rons .  Th i s  is achieved  w i t h  a  t o t a l  
s c i n t i l l a t o r  volume of on ly  137,700 cm3. 
Another impor t an t  q u a n t i t y  i s  t h e  f igure-of -mer i t  
FOM, de f i ned  a s  
FOM = a E b f f 2 .  
The s t a t i s t i c a l  u n c e r t a i n t y  i n  a  measurement of  t h e  
neu t ron  p o l a r i z a t i o n  is  g iven  by 
For t h e  p r e s e n t  p o l a r i m e t e r ,  FOM=0.21t0.02 cm2 f o r  120 
MeV neu t rons .  
'present add re s s :  U n i v e r s i t y  of  t h e  Western Cape, 
P r i v a t e  Bag X17, B e l l v i l l e ,  7530, South Af r i c a .  
1) T.N. Taddeucci  e t  a l . ,  Phys. Rev. L e t t .  52, 1960 
(1984);  IUCP S c i e n t i f i c  and Techn i ca l  Report  1983, 
p. 37. 
2) W.G. Love and M.A. Franey,  Phys. Rev. C 24, 1073 
(1981).  
3 )  S. Cohen and D. Kurath,  Nucl. Phys. 73, 1 (1965). 
4) W.D. Co rne l i u s ,  J .M.  Moss, and T. Yamaya, Phys. 6)  N. Auerbach, J.D. Bowman, M.A. Franey,  and W.G. 
Rev. C 23, 1364 (1981); J.N. Moss, Phys. Rev. C 26, Love, Phys. Rev. C 28, 280, (1983); Phys. Kev. C 
727 (1982). - 30, 736 (1984). 
5 )  D.E. Bainum e t  a l . ,  Phys. Rev. L e t t .  44, 1751 7) T. Izumoto, Nucl. Phys. A395, 189 (1983); N. 
(1980);  W.A. S t e r r enbu rg ,  Sam M. Aus t i n ,  R.P. Auerbach and A m i r  IUein ,  Phys. Rev. C 30, 1032 
DeVito, and Aaron Galonsky, Phys. Rev. L e t t .  45, (1984); F. O s t e r f e l d ,  D. Cha, and J. Speth ,  Phys. 
1839 (1980); D.J .  Horen e t  a l . ,  Phys. L e t t .  99B, Rev. C ( t o  be pub l i shed ) .  
383 (1981); C. Gaarde e t  a l . ,  Nucl. Phys. A ~ K  258 
(1981). 
MEASUREMENTS OF GAMOW-TELLER STRENGTH DISTRIBUTIONS I N  MASSES 13  AND 15 
C.D. Goodman, R.C. Byrd, and I. van ~ e e r d e n +  
I n d i a n a  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 
T.A. Carey 
Los Alamos Na t i ona l  Labora tory ,  Los Alamos, New Mexico 87545 
D . J .  Horen 
Oak Ridge Na t i ona l  Labora tory ,  Oak Ridge,  Tennessee 37830 
J.S.  Larsen ,  and C. Gaarde 
N i e l s  Bohr I n s t i t u t e ,  U n i v e r s i t y  of  Copenhagen, DK-2100, Copenhagen, Denmark 
J. Kapaport ,  and T.P. Welch 
Ohio Un ive r s i t y ,  Athens,  Ohio 45701 
E. Sugarbaker 
Ohio S t a t e  Un ive r s i t y ,  Columbus, Ohio 43214 
T. N. Taddeucci  
Ohio U n i v e r s i t y  and Ind i ana  U n i v e r s i t y  Cyclo t ron  F a c i l i t y  
Allowed Fermi and Gamow-Teller b e t a  decay I n  mass 13 t h e  r a t i o  of  measuredl  and c a l c u l a t e d 2  
t r a n s i t i o n  r a t e s  p rov ide  a s p e c i a l  c l a s s  of nuc l ea r  GT s t r e n g t h s  f o r  t h e  1/2' + 1/2' m i r r o r  t r a n s i t i o n  is  
model i n fo rma t ion  because of t h e  s imple  r e l a t i o n s h i p  0.66. Th i s  r a t i o  is  c o n s i s t e n t  wi th  t h e  " t y p i c a l "  GT 
between t h e  model d e s c r i p t i o n  of t h e  nucleus  and t h e  quenching f a c t o r .  However, t h e  c a l c u l a t e d  B(GT) va lue  
t r a n s i t i o n  process .  The Fermi (F)  o p e r a t o r  changes f o r  t h e  s t r o n g e s t  t r a n s i t i o n s 2  t h a t  from t h e  ground 
on ly  t h e  i s o s p i n  p r o j e c t i o n  of a nucleon.  The s t a t e  of I 3 c  t o  t h e  3/2', 3.51-MeV l e v e l  i n  1 3 ~ ,  i s  
Gamow-Teller (GT) o p e r a t o r  changes t h e  p r o j e c t i o n s  of B(GT)=2.38, wh i l e  t h e  va lue  deduced from our  (p  ,n )  
bo th  i s o s p i n  and sp in .  The t r a n s i t i o n  r a t e  between measurements3 i s  B(GT)=0.85+0.03, a d i s c r epancy  of 
m i r r o r  s t a t e s  is t h e  i ncohe ren t  sum of t h e  r a t e s  f o r  n e a r l y  a f a c t o r  of  t h r ee .  The c a l c u l a t e d  B(GT) summed 
t h e  Fermi and Gamow-Teller components. A l l  of t h e  over  a l l  l e v e l s  i s  3.95. 
Fermi s t r e n g t h  appea r s  i n  t h e  mi r ro r  s t a t e  t r a n s i t i o n ,  For mass 15, i f  we hold on ly  t o  t h e  r e s t r i c t i o n  
bu t  due t o  t h e  s p i n - o r b i t  i n t e r a c t i o n ,  t h e  GT s t r e n g t h  t h a t  t h e  model space  be l i m i t e d  t o  t h e  p - she l l ,  u n l i k e  
i s  d i s t r i b u t e d  between t h e  s p i n - o r b i t  p a i r  s t a t e s ,  and t h e  s i t u a t i o n  i n  mass 13, t h e  t o t a l  GT s t r e n g t h  and t he  
o n l y  a f r a c t i o n  of t h e  t o t a l  GT s t r e n g t h  is con t a ined  d i s t r i b u t i o n  of  s t r e n g t h  between t he  p 1/2 and p 3/2 
i n  t h e  m i r r o r  s t a t e  t r a n s i t i o n .  h o l e  s t a t e s  a r e  independent  of  t he  sp in -o rb i t  s p l i t t i n g  


Spin Transfer Measurements for (p,n) Reactions at Intermediate Energy

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Spin Transfer Measurements for (p,n) Reactions at Intermediate Energy

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