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

Brown, J.D.

Jacobs, W.W.

Jones, W.P.

Miller, D.W.

Nann, H.

Puttaswamy, N.G.

Radhakrishna, M.C.

Singh, P.P.

Stephenson, E.J.

English

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The 3s PROTON OCCUPANCY IN 206Pb 
M.C. Radhakrishnat, ~.~.~uttaswam~t, H.Nann, W.W. Jacobs, W.P. Jones, D.W. Miller, P.P. Singh and E.J. Stephenson 
Indiana University Cyclotron Facility, Bloomington, Indiana 47405 
J.D. Brown 
Princeton University, Princeton, New Jersey 08544 
-+ 
The experimental charge density difference Elastic scattering measurements of d + 206~b at 
between 206~b and 205~1 measured by electron scattering 79.4 MeV and 3~e+205~1 at EHe=78.4 MeV have also been 
has been interpreted by Cavedon et al. ,l as evidence made to obtain the appropriate optical potentials. 
for 30% quenching of the single-particle 3~112 Optical model analyses have been carried out using the 
strength. It is however expected that the code GOMFIL.~ Different shapes have been used for the 
fragmentation of the 3s112 strength in 2 0 5 ~ 1  plays an optical potential to obtain optimum fits to the elastic 
important role in the interpretation of the electron scattering data. Non-relativistic kinematics has been 
scattering data.2 We have therefore undertaken a study used throughout. The optical-model parameters are 
of the 206Pb(i,3He)205T1 reaction to extract listed in Tables I and 11. Analysis of the 
spectroscopic strengths for the transitions in 206Pb(i,3He)20 5 ~ 1  reaction data has been carried out 
205~l. to obtain the angular distributions of differential 
The 206Pb(:, 3He)205T1 reaction has been studied cross sections and analyzing powers for seventeen 
at Ed = 79.4 MeV using the QDDM magnetic spectrometer. transitions; spin-parity assignments have been made for 
Table I. Optical-Model Parameters for Deuteron Elastic Scattering from 206Pb at 79.4 MeV 1 set Type / v o a0 ws 
(MeV) (fm) (fm) (MeV) 
Table 11. Optical-Model Parameters for 3He Elastic Scattering from 205T1 at 78.4 MeV 
(MeV) 
Set 
(MeV) (MeV) 
27.37 
30.60 * 
I (fm) 
WS (Shallow) 
WS(deep) 
WS(shallow) 
(fm) (MeV) (fm) (fm) (MeV) (fm) (fm) (fm) (MeV.fm3) (mb) 
I all the transitions. Table 111 lists the excitation generate the distorted waves. The bound state wave 
i 
I 
I energies and spin-parity assignments as compared to the functions for the states in 2 0 5 ~ 1  have been generated 
I 
1 previous values .4 using the standard well-depth method and the parameters 
~ 
DWBA calculations have been carried out using the are listed in Table IV. The root-mean-square (RMS) 
~ 
exact finite range code FRUCK~ .5 The bound state form radii obtained from this method are 5.377 fm, 5.528 fm, 
~ 
factor for 3 ~ e  has been obtained from a fit to data on 5.490 fm, and 6.073 fm for the lowest 3~112, 2d312, 
elastic electron scattering. Different combinations 2d512, and 1hll12 orbits, respectively. These values 
of optical potentials both in entrance and exit are in good agreement with the RMS radii obtained from 
channels listed in Tables I and I1 have been used to Hartree-Fock (HF) calculations7 employing the Skyrme 
I Table 111. Energy Levels of 2 0 5 ~ 1  
Nuclear Data Sheets 
(Ref. 4) 
Our Experiment 
206Pb(a, 3He)205T1 
206 Pb (d. 3 ~ e )  2 0 5 ~ ~ ;  Ed = 79.4 MeV interaction SGII from Van Giai and ~ a ~ a w a . ~  The combi- 
Figure 1. Comparison of differential cross- 
section and analyzing-power measurements for the 
transitions to the 0.0-M~V (R= 0) , 0.202-MeV 
(R = 2), 0.618-MeV (A = 2), and 1.486-MeV (A = 5) 
states of 205~1 with exact finite range DWBA 
calculations. 
nation of potentials used here are D2 for deuterons and 
and H2 for 3~e. Non-locality parameters of 0.54 and 
0.25 have been used for deuterons and 3 ~ e  respectively 
As is evident from the figure the DWBA fits to the 
experimental data are quite good. The spectroscopic 
strengths for the 3s112 (R=O) transitions deduced from 
this experiment are listed in Table IV and are compared 
with the values from other related experiments. 
Our results yield a 3s112 proton occupation 
number n(206)=1.34 in reasonable agreement with other 
results. If we use the ratio n(206)/n(208) = 0.84 from 
Ref. 9, we arrive at n(208)=1.6 which indicates 
depletion of the strength by only 20% in 208~b 
and 33% in 206~b. 
t~ermanent address : Department of Physics, Bangalore 
University, Bangalore 560001, India. 
1) J.M. Cavedon et al.. Phvs. Rev. Lett. 49. 978 
- .  
(1982) ; B. Frois et al., Nucl. Phys. A% 409C 
(1983). 
2) E.N.M. Quint et al., Phys. Rev. Lett. 57, 186 
(1986) and private communication. 
3) H. Leeb, Comuter code GOMFIL (unpublished). 
Table. IV. Spectroscopic Strengths for the 3s112 Hole States in 2 0 5 ~ 1  a
(MeV) 
Our Experi- Electron (e,e1p) (ds3He) 
ment Ed=79.4 MeV Scattering Ed=52 MeV 
(Ref. 10) (Ref. 2). (Ref. 9) 
aBound state parameters are ro=1.2675 fm, a0=0.81 fm, VSo=6:O MeV, 
r,o=l .l fm, and as0=0.65 fm (see Ref. 9) ; Vo is adjusted to match 
the separation energy of the excited state. 
7 8 
4) M.R. Schmorak, Nuclear Data Sheets 45, 145 (1985). 8) N. Van Giai and H. Sagawa, Phys. Lett. 106B, 379 
(1981) 
5) P.D. Kunz, Computer code DWUCK5 and extended as 
FRUCK2 by J. R. Comfort (unpublished). 9) P. Grabmayr et al., Phys. Lett. 164B, 15 (1985). 
6) P.D. Kunz, Private communication. 
7) B.A. Brown, Private communication. 
10) C.N. Papanicolas in Nuclear Structure at High Spin, 
Excitation, and Momentum Transfer, ed. H. Nann, 
A.I.P. Conf. Proc. No. 142, 110 (1986). 
RADIAL FORM-FACTOR FOR TRANSFER mACTIONS AND THE SHELL-MODEL POTENTIAL 
N.G. ~uttaswam~t and H. Nann 
Indiana University Cyclotron Facility, Bloomington, Indiana 47405 
M.H. Macfarlane 
Department of Physics and Nuclear Theory Center, Indiana University, Bloomington, Indiana 47405 
The radial form factors for single-nucleon and hence the spectroscopic factor (viz., the 
transfer reactions satisfy an inhomogeneous normalization factor of the transfer form-factor), are 
Schrodinger-like equation1 that incorporates both known to depend sensitively on the RMS radii. 
mean-field and many-body aspects of the interaction Attempts are being made to obtain SM potentials by 
responsible for transfer.  ust tern^ and Rae3 have making fits to more extensive data. The radial wave 
proposed an approximation scheme that retains the functions predicted by these potentials will be 
simplicity of a one-body Schrodinger equation while compared with those deduced from magnetic electron 
accounting for the main many-body corrections. The scattering13 and will also be tested by their 
method consists in introducing a shell-model (SM) application to single-nucleon transfer reactions at 
potential for the motion of the transferred nucleon in intermediate energies. 
the field of the core nucleus plus a surface-peaked 
t~ermanent address : Department of Physics, Bangalore 
potential to simulate the many-body corrections. The University, Bangalore -560 001, India 
strength of the surface term is varied to reproduce the 1) G.R. Satchler, Direct Nuclear Reactions, Clarendon 
Press, Oxford (1983), pp. 798-805. 
experimental separation energy of each final state. 
2) N. Austern, Nucl. Phys. A292, 190 (1977). 
Winfield et ale4 have recently applied this method to 
9 3) W.D.M. Rae, D.Phi1. thesis, Oxford 1976 
study ( ~ e ,  'OB) reactions. (unpublished). 
The SM potentials available in literature yield 4) J.S. Winfield et al., Nucl. Phys. A437, 65 (1985). 
varying predictions concerning the properties of 5) E. Rost, Phys. Lett. E, 184 (1968). 
single-nucleon orbits. As an example, the rootmean- 6) C.J. Batty and G.W. Greenlees, Nucl. Phys. A133, 
673 (1969). 
square (RMS) radii5-l2 of the neutron hole states in 
208 7) P. Mukherjee et al., Phys. Rev. Lett. 44, 1391 
Pb are tabulated in Table I; the RMS radii vary (1980). 
widely. The DWBA cross section for transfer reactions, 8) G. Bertsch, The Practitioner's Shell Model, 
North-Holland Publ. Co., Amsterdam (1972), p. 2. 


The 3s Proton Occupancy in 206-Pb

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The 3s Proton Occupancy in 206-Pb

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