Supported by the National Science Foundation and Indiana Universit

Adams, G.S.

Bacher, A.D.

Emery, G.T.

Jones, W.P.

Kailas, S.

Love, W.G.

Miller, D.W.

Nann, H.

Olmer, C.

Petrovich, F.

Schwandt, P.

English

IUScholarWorks

STUDIES OF EXCITED STATES IN 208~b BY INELASTIC PROTON SCATTERING 
AT 135 AND 100 MeV 
G.S. Adams,* A.D. Bacher, G.T. Emery, W.P. Jones, S. Kailas, D.W. Miller 
H. Nann, C. Olmer, and P. Schwandt 
Indiana University Cyclotron Faci Zity, Bloomington, Indiana 4 7405 
W.G. Love 
University of Georgia, Athens, Georgia 30602 
F. Petrovich 
Florida State University, Tallahassee, Florida 32306 
Differential cross sections have been measured for energies. At higher beam energies it is found that 
the reaction 208~b(p,p') 208~b at 135 MeV leading to deformed spin-orbit contributions play a much more 
the following excited states in 208~b: 3-(2.615 MeV), important role, that differences in the ratios of the 
5-(3.198 MeV), 5-(3.709 MeV), 2+(4.086 MeV), 4+(4.323 central and spin-orbit coupling parameters are needed 
MeV), 6+(4.424 MeV), 8+(4.608 MeV) , 10+(4.882 + .015 for different states of the same spin and parity, and 
+ 
MeV), 10 (5.071 & .007 MeV), 12+(6.076 + .023 MeV), that for the states of highest J the collective model 
12-(6.415 + .013 MeV), 14-(6.727 + .015 MeV), and fails to provide a satisfactory description of the 
12-(7.037 + .007 MeV). A sample spectrum is shown differential cross sections. On the other hand, for 
in Fig. 1. The data on the natural-parity states, the states of J 2 6, the deduced central coupling 
together with a collective-model analysis, have been parameters are in good agreement with those found at 
1 presented in a paper in Physics Letters . Collective lower bombarding energy. The collective model cal- 
model analyses have been performed earlier for (p,pl) culations are compared with the data in Fig. 2, and the 
excitation of several of these states at lower incident derived coupling parameters are listed in Table I. 
Excitation (MeV) In a second paper, also to appear in Physics 
m C l  , TiO , GiO , 5 y  , 4F , SiO ,  
~etters~, a microscopic interpretation of the data on 
208 Pb (p,p') 
- 135 MeV 
the same natural-parity states is presented. A 
distorted-wave impulse approximation is used, with 
- - 
transition densities taken from electron inelastic 
3 
scattering results. The t-matrix interaction of Love , 
derived from free nucleon-nucleon scattering at the 
same energy, is used, and exchange is included in the 
knock-on approximation. The results of the calculations 
are in good agreement with the data, even in those 
high-J cases where the collective model fails, and it 
3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0  is especially noteworthy that the sharp reduction in 
Channel 
the central-force contributions to the higher-spin 
Figure I .  Inelastic proton spectrum a t  0 ab = 45'. states (and the resulting relative importance of the 
The peaks of in teres t  are labelled by the ir  spins and 
parities.  spin-orbit terms in the t-matrix) comes about naturally 
Fi-qure 2. Cornparison of experimental cross sections 
with collective model calculations for excitation of 
low-lying normal parity levels i n  2 0 8 ~ b  by 1.35 MeV 
protons. C + LS and C are cross sections with and 
without DSO contributions. 6 and B L ,  pre central and 
DSO deformation parameters. $or the ' loI  excitation 
(Q= -4.88 MeV) where BC has been determzned to  be 0, 
the central only curve has been normalized t o  the peak 
experimental cross section i n  order t o  exhibit the 
difference i n  peak angle bebeen the C and LS con- 
tributions. 
'i 
\ .  
1 1 1 1 1 1  1 1 1 1 1 1  
0  1 0 2 0 3 0 4 0 5 0 6 0 7 0  0  1 0 2 0 3 0 4 0 5 0 6 0 ~  
(+,!dc%) 
Fiqure 3. The proton transition densities obtained 
from electron scatteri  for the J=2 t o  10 normal 
parity transitions i n  %8Pb and the moduligof the 
components of complex t-matrix interaction which 
cgntribute with no spin-transfer t o  the target. Both 
p and v are shown i n  momentum space. C and LS denote - 
&ntral and spin-orbit, respectively. Knockout exchange 
contributions are included i n  v. 
Table I. Detormation parameters (B)  for the 208~b(p,p') 208~b reaction 
E (MeV) 
Ex (ken J~ 135.2a'f) 61. 2b'g) 54~,g) 35ds B) 24. 5e'g) 
a) Present work. 
b) A. Scott, N.P. Mathur, and F..Petrovich, Nucl. Phys. A285, 222 (1977). 
c) M. Lewis, F. Bertrand, and C.B. Fulmer, Phys. Rev. C7, 1966 (1973). 
d) W.T. Wagner, G.M. Crawley, G.R. Hammerstein, and H. McManus, Phys. Rev. G, 757 (1975). 
e) J. Saudinos, G. Vallois, 0. Beer, M. Gendrot, and P. Lopato, Phys. Lett. 22, 492 (1966). 
f) BC is listed first with BLS given in parenthesis. 
g) Only BC is listed. The DSO contributions were not included in the calculations. 
as an effect associated with the short-range repul- and proton probes for a given transition strongly 
sion in the central t-matrix. A comparison of the suggests that this factor arises from nuclear structure 
momentum-transfer dependence of the transition den- effects, perhaps from effects such as ground state 
sities with that of the various relevant terms in the correlations. The 14- transition in 208~b, which 
t-matrix is shown in Fig. 3, and the quality of the corresponds to a stretched neutron particle-hole ex- 
agreement between the DWIA calculations and experi- citation, exhibits a similar behavior with a common re- 
ment is shown in Fig. 4. normalization factor of % 0.5 for both electron and 
A systematic comparison4 between the excitation proton inelastic scattering. However, it is already 
of stretched-spin states using both electron and apparent that the two 12- states require quite dif- 
proton inelastic scattering indicates that while the ferent renormalization factors from those observed with 
shapes of the angular distributions are well described (e,e'). One possible explanation for this anomaly is 
by the theory, an overall renormalization factor that the two 12- states observed are linear combinations 
(% 0.3 - 0.5) is required to reproduce the data. The of the two proton and neutron particle-hole configura- 
similar magnitude of this factor for both electron tions available. Such an explanation would require an 
amplitude mixing parameter of % 0.4. This observa- 
t i on ,  however, appears t o  be i ncons i s t en t  with an 
ana lys i s  of t he  ( e , e t )  d a t a  f o r  t he  same s t a t e s  which 
r equ i r e s  very l i t t l e  conf igura t ion  mixing. 
Since many of t he  exc i t ed  s t a t e s  of i n t e r e s t  
occur i n  a region of high l e v e l  dens i ty  i n  2 0 8 ~ b ,  and 
s i n c e  t he  minimum l i n e  width obtained i n  t he  135 MeV 
experiments was about 65 keV, t he  2 0 8 ~ b  experiments 
were repeated a t  a  bombarding energy of 100 MeV, where 
t he  l i n e  width could be reduced t o  about 40 keV. No 
q u a l i t a t i v e  d i f f e r ences  i n  t he  spec t r a  were observed, 
increas ing  our l e v e l  of confidence i n  t h e  analyses a t  
135 MeV. Work has continued a t  100 MeV where t he  
improved r e so lu t ion  w i l l  enable t he  study of add i t i ona l  
i n e l a s t i c  t r a n s i t i o n s .  A complete s e t  of  analyzing 
power measurements, using the  IUCF polar ized  proton 
beam, has now been completed a t  100 MeV, covering the  
excitat ion-energy range 0-8 MeV and the  angular  range 
7.5' t o  75'. Analysis of these  d a t a  is  i n  progress.  
Of p a r t i c u l a r  i n t e r e s t  a r e  t he  analyzing powers f o r  
t he  e x c i t a t i o n  of  t he  two 12- s t a t e s  f o r  which ca l -  
cu l a t i ons  i n d i c a t e  a s e n s i t i v i t y  t o  t he  degree of con- 
f i g u r a t i o n  mixing. 
The th i rd-exci ted  s t a t e  i n  2 0 8 ~ b  a t  3.475 MeV, 
which is  a 4- s t a t e  with a well-known (pr imar i ly  neutron) 
par t ic le -hole  wave funct ion ,  is  weakly exci ted  i n  a l l  
i n e l a s t i c  s c a t t e r i n g  reac t ions .  This s t a t e  is  of in- 
t e r e s t  s i nce  i t s  weak e x c i t a t i o n  suggests  i t  may be a 
good case  i n  which t o  study poss ib l e  con t r ibu t ions  from 
two-step processes of t he  (p ,d ,p t )  type. Some recent  
d iscuss ions  of nuclear  c r i t i c a l  opalescence5 have led  t o  
predj-ct ions t h a t  t he  cross  s ec t ion  f o r  t h i s  s t a t e  should 
be enhanced, poss ib ly  by a l a r g e  f a c t o r ,  near a  momentum 
t r a n s f e r  of about 280 MeV/c. Cross s ec t ions  a r e  being 
ext rac ted  f o r  t he  ( p , p t )  e x c i t a t i o n  of t h i s  s t a t e  a t  
both 100 and 135 MeV. Our prel iminary analyses  show no 
Tynsi t ion Densities 4 
t Matrix Interaction 1 
Figure 4. The r e s u l t s  of  DWIA calculations for normal 
parity transi t ions  i n  2 0 8 ~ b .  Results with fC+LS) 
and without fC) the  spin-orbit in teract ion are shown 
separately. Note the decrease i n  the central contr+t- 
butions t o  the cross sections for transi t ions  with 
J a. 
evidence f o r  such an enhancement. 
1 )  G.S. Adams, A.D. Bacher, G.T. Emery, W.P. Jones, 
D.W. Mi l l e r ,  W.G. Love, and F. Petrovich,  t o  be 
published i n  Phys. Let t .  (1980). 
2)  F. Petrovich,  W.G. Love, G.S. Adams, A.D. Bacher, 
G.T. Emery, W.P. Jones, and D.W. Mi l l e r ,  t o  be 
published i n  Phys. Let t .  (1980). 
3) W.G. Love, A. Sco t t ,  F.T. Baker, W.P. Jones, and 
J . D .  Wiggins, Phys. Le t t .  z, 277 (1978); W.G. Love, 
in The (p,n)  Reaction and the Nucleon-Nucleon Force, 
ed. by C. Goodman. S. Austin, S. Bloom, J. Rapaport, 
Nucl. Phys. A326, 463 (1979); I.V. Kurchatov Atomic 
Energy Inst. Report IAE-3254 (Moscow, 1980). 
and G. Satchler (Plenum, New York, 1980), p. 23; 
F. Petrovich, ibid, p. 115. 6) A. Scott, N.P. Mathur and F. Petrovich, Nucl. 
Phys. A285, 222 (1977). 
4) R.A. Lindgren, W.J. Gerace, A.D. Bacher, W.G. Love, 
and F. Petrovich, Phys. Rev. Lett. 42, 1524 (1979). *Present address: MIT Bates Laboratory, Middleton, 
Massachusetts 01949 
5) S. Fayans, E.E. Saperstein, and S.V. Tolokonnikov, 


Studies of Excited States in 208-Pb by Inelastic Proton Scattering at 135 and 100 MeV

https://scholarworks.iu.edu/dspace/bitstream/2022/2853/1/iucf_1979_14-18.pdf

Studies of Excited States in 208-Pb by Inelastic Proton Scattering at 135 and 100 MeV

Abstract

Similar works

Full text

Available Versions

IUScholarWorks