This work was supported by National Science Foundation Grants PHY 76-84033A01, PHY 78-22774, and Indiana Universit

Baker, F. Todd

Jones, W.P.

Love, W.G.

Scott, Alan

Wiggins, J.D. Jr.

English

IUScholarWorks

CORE POLARIZATION AMPLITUDES FOR SINGLE-NEUTRON-HOLE TRANSITIONS 
EXCITED I N  THE 2 0  7 ~ b  (p,p ') REACTION AT 135 MeV and 61 MeV 
Alan ~ c o t t *  F. Todd ~ a k e r * ,  W.P. Jones,  J .D.  Wiggins, Jr. and 
- -9  
W.G. ~ o v e *  
DWBA semi-microscopic f i t s  have been made by Love 
t o  our data1r2) a t  p r o j e c t i l e  energies  Ep = 61 MeV and 
135 MeV f o r  low-lying single-neutron-hole s t a t e s  i n  
2 0 7 ~ b .  Love used t h e  M3Y force3) f o r  r e a l  valence 
amplitudes, f i xed  c o l l e c t i v e  deformed-spin-orbit (DSO) 
and imaginary amplitudes (with eS0 = eLmG = eEXP from L L 
e n t i r e l y  c o l l e c t i v e  model f i t s  t o  t h e  d a t a ) ,  and t h e  
s t r eng th  of each c o l l e c t i v e  r e a l  core amplitude (de- 
formation of t h e  r e a l  o p t i c a l  model p o t e n t i a l  wi th  
?(core) = fAL) was adjus ted  t o  ob ta in  t he  bes t  f i t  
L 
t o  t he  o v e r a l l  shape and magnitude of each measured 
c ros s  s ec t ion  a t  each p r o j e c t i l e  energy. The core- 
coupling parameter AL has been defined e a r l i e r 4 ) .  The 
S=l amplitudes f o r  t he se  t r a n s i t i o n s  a r e  known t o  be 
quenched5). For a given L-transf e r  t r a n s i t  ion ,  t h e  
shapes of t h e  p a r t i a l  c ros s  s ec t ions  a r e  q u i t e  d i f -  
f e r en t  f o r  t h e  M3Y r e a l  valence,  imaginary, sp in-orbi t  
(DSO) and r e a l  core cont r ibut ions ,  s o  t he  combination 
of amplitudes, with i n t e r f e r ences ,  produces an  o v e r a l l  
shape of each t h e o r e t i c a l  c ros s  s ec t ion  which is sen- 
s i t i v e  t o  t h e  magnitudes of each of t he se  p a r t i a l  c ros s  
sec t ions .  For t h i s  reason,  g rea t  ca re  has been taken 
with t he  peak-stripping of our da ta6)  t o  ensure t h e  
ex t r ac t ion  of accu ra t e  shapes of t h e  measured c ros s  
sections, which then provide more s t r i n g e n t  t e s t s  of 
assumptions of a l l  microscopic ca l cu l a t i ons  including 
those of t h e  present  semi-microscopic model. 
The va lues  of core-coupling parameters AL, which 
Love found gave t h e  bes t  f i t s  of h i s  semi-microscopic 
ca l cu l a t i ons  t o  our IUCF d a t a  a t  135 MeV and our e a r l i e r  
data1), a r e  shown i n  column 5 of t he  t a b l e  below. A 
recent  a r t i c l e 7 1  repor ted  experimental s ca l ing  f a c t o r s  
(we c a l l  s p p ( e , e ' )  ) f o r  t h e  r a t i o  s ec t ions  f o r  cor- 
responding core  and t o t a l  cont r ibut ions  i n  t r a n s i t i o n s  
i n  07pb(e, e ') and 20 8 ~ b ( e ,  e l )  experiments, respect ive ly .  
To co r r ec t  f o r  m u l t i p l i c i t y  f a c t o r s  we write s;(e,e1) = 
{ 2Ji+1) ( 2 )  / ( 2 ~ + 1 )  1 sEn(e, e ' ) where Ji and Jf des- 
c r i b e  t h e  i n i t i a l  and f i n a l  sp ins  of s t a t e s  i n  2 0 7 ~ b .  
I n  a c o l l e c t i v e  model descr ip t ion ,  8f07 cOre(e,e') = 
{ s t ( e , e ' ) ~ ~ / ~  {8 i08 (3 ,3 ' ) } ,  where we use t h e  d e f i n i t i o n  
of c o l l e c t i v e  deformation parameters BL which y i e l d s  a 
sum of weighted va lues  of p i f 2  f o r  a weak-coupling 
- - - - -  - 
Eex Hole E~ Extracted d i r e c t l y  With assumed { s i  ( e , e l ) )  1/2 (MeV) con£ ig-  (MeV) f r o m ( p , p l )  caln.  a n d ~ : O * ( ~ , ~ ' )  f o r E p = 6 1 M e V  
ura t n  . with r e a l  M3Y 
( i n  2 0 7 ~ b )  AL(P,P') A~ 
1.63 iii12 7 61.2 0 . 0 0 4 ~  
134.8 0.004d s i  ( e  , e ' ) not ava i l ab l e  
a~~~ amplitude has  small  e f f e c t  a t  61  MeV(L=2), s imi l a r  A2 f o r  B ~ S O  = 0.00 
b ~ i t h  smaller  BS0 and same AL t he  f i t  is a s  good t o  da t a  
CWith 620 = 0.00, l a r  e r  Aq y i e l d s  a s  good a f i t  t o  da t a  
d ~ i t  t o  shape with By8 used is b e t t e r  than wi th  smaller  67' 
mul t ip l e t  equal  t o  t h e  fiL2 f o r  t h e  corresponding 
core  t r a n s i t i o n  amplitude. 
The AL-values of column 6 a r e  obtained with t h e  
expression AL = { 8 i 0  'Ore (p, p' ) } /{ ( 2 ~ + 1 )  (~-L)M= 
(hi -t h f ) ) ,  where a s  a guess we assumed t h a t  t h e  (p ,p l )  
core  amplitude i n  each of our 2 0 7 ~ b  t r a n s i t i o n s  is a l s o  
r e l a t e d  t o  t h e  c o l l e c t i v e  amplitude i n  t h e  correspond- 
ing  2 0 8 ~ b ( p , p ' )  t r a n s i t i o n  a t  t he  same Ep by t h e  same 
correc ted  sca l ing  f a c t o r  {s ; (e ,e ' )} l l2  a s  i n  t h e  ( e , e ' )  
experiment f o r  t h e  same 2 0 7 ~ b  t r a n s i t i o n .  With t h i s  
assumption our va lues  of { 8 i 0 7  core(p,p ')} = 
{ s;(e,ev) 11/2[ 82°8(p,p ')  I ,  with t h e  va lues  of ~ i O ~ ( p , p ' )  
ex t r ac t ed  from c o l l e c t i v e  model f i t s  t o  our e a r l i e r  
2 0 8 ~ b ( p , p ' )  data8) a t  E = 6 1  MeV. The ML a r e  t h e  P 
matr ix  elements f o r  t h e  single-hole t r a n s i t i o n s  i n  
2 0 7 ~ b .  
We note  t h a t  both neutrons and protons con t r ibu t e  
t o  t h e  amplitudes described by 8207 cOre(p,p') and L 
20 8 
BL ( p , p l ) ,  but  only protons con t r ibu t e  t o  t h e  ampli- 
tudes described by 8E07 cOre(e,e') and 8 i 0 8 ( e , e ' ) .  We 
a l s o  note  t h a t  deformed-spin-orbit (DSO) con t r ibu t ions  
make neg l ig ib l e  con t r ibu t ions  t o  t h e  shapes and magni- 
tudes of c o l l e c t i v e  model c ros s  s ec t ions  a t  Ep = 6 1  
MeV f o r  t he  2 0 8 ~ b ( p , p ' )  r e a c t i o n  (even f o r  an  angular  
momentum t r a n s f e r  a s  l a r g e  a s  L=7), but  t h e  c o l l e c t i v e  
DSO amplitude has a very s i g n i f i c a n t  e f f e c t  on t h e  
shape and magnitude of each c o l l e c t i v e  c r o s s  s e c t i o n  
a t  Ep = 135 MeV i n  t h e  2 0 8 ~ b ( p , p ' )  r eac t ion9 ) ,  f o r  
a l l  L-transfers  from L=2 t o  L=7. 
At Ep = 135 MeV t h e  va lues  of AL f o r  (p ,p l )  i n  
column 6(deduced assuming t h e  s;(e,e1) r a t i o s  may be 
used f o r  (p ,p l ) )  a r e  s t r i k i n g l y  c lo se ,  f o r  both L=2 
t r a n s i t i o n s  and f o r  t h e  L=4 t r a n s i t i o n ,  t o  t he  va lues  
A ~ ( p , p ' )  d i r e c t l y  ex t r ac t ed  from Love's DWBA semi- 
microscopic ca l cu l a t i ons  with M3Y r e a l  valence ampli- 
tudes. At Ep = 6 1  MeV, however, only t h e  A2-value 
ex t r ac t ed  d i r e c t l y  f o r  t h e  L=2 t r a n s i t i o n  t o  t h e  ~ 3 / 2  
hole-s ta te  a t  0.898 MeV agrees  with t h e  A2-value of 
column 6 (using t h e  f a c t o r  s ; ( e , e t ) ) ,  whereas t h e  
d i r e c t  va lue  A2(p,p') (column 5) f o r  t h e  f512 ho le  
s t a t e  a t  0.570 MeV is much smal ler  than the  A2-value 
of column 6(us ing  t h e  f a c t o r  s t ( e , e ' ) ) .  A t  Ep = 61 MeV, 
f o r  t h e  L=4 t r a n s i t i o n  t o  t h e  f712 ho le - s t a t e  a t  2.34 
MeV t h e  va lues  of A4 ex t r ac t ed  d i r e c t l y  from t h e  semi- 
microscopic (p ,p l )  ca l cu l a t i ons  (column 5) a r e  much 
smaller  than the  A4-value assuming t h e  f a c t o r  s; (e  , e ' ) , 
bu t  t h e  agreement i s  somewhat b e t t e r  when t h e  deformed- 
spin-orbit  parameter is  taken a s  zero. We a l s o  no te  
t h a t  t h e  DSO con t r ibu t ions  have a n e g l i g i b l e  e f f e c t  on 
the  shape of Love's semi-microscopic ca l cu l a t i ons ,  and 
l i t t l e  e f f e c t  on t h e  magnitudes of o v e r a l l  c ross  
s ec t ions ,  f o r  both L=2 t r a n s i t i o n s  and t h e  lower pro- 
j e c t i l e  energy, Ep = 61  MeV. These disagreements, a t  
Ep = 61  MeV but  not  f o r  Ep = 135 MeV, may poss ib ly  be 
i nd i ca t ing  g r e a t e r  s e n s i t i v i t y  t o  t h e  c o r r e c t  descrip-  
t i o n  of t h e  nucleon-nucleon force  when i t  is overlapped 
i n  t h e  form f a c t o r  wi th  t h e  wave func t ions  of t h e  f5/2 
and f 7 / 2  neutron-hole s t a t e s  a t  0.570 MeV and 2.34 
MeV, and l e s s  s e n s i t i v i t y  f o r  t h e  ~ 3 / 2  ho le  s t a t e  a t  
0.898 MeV. 
It is most unfor tunate  t h a t  t h e r e  is no f a c t o r  
s '  ( e , e l )  a v a i l a b l e  f o r  t h e  L=7 t r a n s i t i o n ,  f o r  which L 
the  DSO amplitude i n  Love's DWBA microscopic ca lcula-  
t i o n  e x e r t s  i t 's  maximum inf luence  on t h e  shape of t h e  
o v e r a l l  t h e o r e t i c a l  c r o s s  s e c t i o n  a t  both Ep = 61  MeV 
and 135 MeV; s o  t h a t  t h e  assumptions of  t h i s  model 
would be t e s t e d  most severely.  
Fu l ly  microscopic DWBA(~P ,p l ) ca l cu l a t i ons ,  with 
t h e  M3Y fo rce  and supposedly complete wave func t ions lO) ,  
have been made by ~ o v e ~ )  f o r our data19 2, a t  Ep = 6 1  
MeV and 135 MeV f o r  t h e  unresolved doublet  a t  2.64 MeV. 
A t  Ep = 61 MeV, t h i s  ca l cu l a t i on  is an exce l l en t  f i t  t o  
t he  shape and magnitude of t he  da t a  without  any ad- 
justment, but  a t  E = 135 MeV it was necessary t o  P 
a r h i t r a r i l y  increase  t he  M3Y r e a l  valence amplitude by 2) Alan Sco t t ,  F. Todd Baker, W.P. Jones, J . D .  
Wiggins, Jr. and W.G. Love, w i l l  s h o r t l y  be 
a f a c t o r  of 1.4 t o  match the  da ta ,  even though t h e  submitted t o  Nuclear Physics. 
f i t  t o  t he  shape is q u i t e  reasonable. 3) G. Bertsch, J. Borosowicz, H. McManus and W.G. 
Love, w i l l  s h o r t l y  be submitted t o  Nuclear Physics. 
I n  con t r a s t ,  a f u l l y  microscopic DWIA ca l cu l a t i on  A284 (1977) 399. 
a t  Ep = 135 MeV by ~ o v e ' l ) ,  us ing  a nucleon-nucleon 4) M.L. Whiten, A. Sco t t  and G.R. Sa tchler ,  Nucl. 
Phys. A181 (1972) 417. 
p o t e n t i a l  G3Y ca l ib ra t ed  by t h e  f r e e  N-N t-matrix which 
5) F. Petrovich,  Nucl. Phys. A203 (1973) 65, and re- 
f i t s  t he  phase s h i f t s  a t  140 MeV and t h e  supposedly ferences  c i t e d  there in .  
complete wave func t ions lO) ,  f i t s  t he  magnitude of our 6) With t h e  program SESAME (T. P. Cleary, unpublished) 
and the  SEL-840A-C computer a t  ORNL, by permission 
da t a  f o r  t h i s  2 0 7 ~ b  doublet  a t  2.64 MeV without  ad jus t -  of D.C. Hensley. 
ment, bu t  it gives  a poor description of t h e  shape of 7) C.N. Papanicolas, J. Heisenberg, J. Lichtens tadt ,  
A.N. Coutemenche and J.S. McCarthy, Phys. Rev. Le t t .  
t h i s  da t a  i n  t he  angular  region near 20 degrees. - 41 (1978) 537. 
Spin-orbit amplitudes were included i n  t hese  DWIA ca l -  8) Alan Sco t t  Y Mathur and F. Petrovich,  Nucl* 
Phys. A285 (1977) 222. 
cu la t ions .  
9)  Alan Scot t  and F. Todd Baker, unpublished. 
These d i f f e r ences  f o r  t he  doublet  a t  2.64 MeV, 
10) P. Ring and J. Speth, Phys. Let t .  (1973) 477; 
between t h e  f u l l y  microscopic DWBA ca l cu l a t i on  a t  135 Nucl. Phys. A235, (1974) 315. 
MeV and the  microscopic DWIA ca l cu l a t i on  a t  135 MeV, 11) W.G. Love, Alan Sco t t ,  F. Todd Baker, W.P. Jones 
and J . D .  Wiggins, Jr. , Phys. Let t .  73B (1978) 
a r e  found t o  be pr imar i ly  due t o  d i f f e r ences  i n  t he  277. 
i sovector  p a r t  ((Vpp - Vpn) 12) of t h e  M3Y G-matrix 12) H.V. von Geramb, p r i v a t e  communication t o  Alan 
Scot t .  
used i n  t h i s  DWBA ca l cu l a t i on  and the  i sovector  p a r t  
of t he  t-matrix used i n  t h e  DWIA ca l cu l a t i on .  
Overal l ,  these  analyses  appear t o  be cons i s t en t  
with t he  view12) t h a t  over t h e  range from Ep = 61  MeV 
t o  135 MeV the  (p,p ')  e f f e c t i v e  i n t e r a c t i o n  i s  changing 
from one t h a t  is more l i k e  a lower energy G-matrix 
i n t e r a c t i o n  t o  one t h a t  is more l i k e  a f r e e  nucleon- 
nucleon t-matrix, bu t  t he  G-matrix behaviour is s t i l l  
q u i t e  s i g n i f i c a n t  a t  Ep = 135 MeV. A f u r t h e r  compli- 
ca t i on ,  which has  no t  been included s p e c i f i c a l l y ,  is  the  
p o s s i b i l i t y  of mul t i s tep  processes which may wel l  be 
energy dependent. 
A manuscript repor t ing  these  r e s u l t s  i s  almost 
complete, and w i l l  s h o r t l y  be submitted t o  Nuclear 
Physics . 
* The Universi ty of Georgia, Athens. 
1 )  Alan Sco t t ,  M. Owais and W.G. Love, Nucl. Phys. 
A289 (1977) 123. 


Core Polarization Amplitudes for Single-Neutron-Hole Transitions Excited in the 207-Pb(p,p') Reaction at 135 MeV and 61 MeV

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Core Polarization Amplitudes for Single-Neutron-Hole Transitions Excited in the 207-Pb(p,p') Reaction at 135 MeV and 61 MeV

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