Inclusive quasifree electrofission cross section for
238
U
V. P. Likhachev,
1
J. D. T. Arruda-Neto,
1,2
W. R. Carvalho, Jr.,
1
A. Deppman,
1
I. G. Evseev,
3
F. Garcia,
4
M. S. Hussein,
1
L. F. R. Macedo,
1
A. Margaryan,
5
J. Mesa,
1
V. O. Nesterenko,
6
O. Rodriguez,
4
S. A. Pashchuk,
3
H. R. Schelin,
3
and M. S. Vaudeluci
1
1
Instituto de Fı ´sica, Universidade de Sa ˜ o Paulo, Sa ˜ o Paulo, Caixa Postal 66318, 05315-970, Sa ˜ o Paulo, Brazil
2
Universidade de Santo Amaro, Sao Paulo, Brazil
3
CEFET, Curitiba, PR, Brazil
4
Instituto Superior de Ciencias y Tecnologia Nucleares, Havana, Cuba
5
Yerevan Physics Institute, Yerevan, Armenia
6
Bogolubov Laboratory of Theoretical Physics, JINR, Dubna, Russia
Received 20 November 2002; published 30 July 2003
We present results from a joint theoretical and experimental study of inclusive quasifree electrofission of
238
U. The off-shell cross sections for the quasifree reaction stage have been calculated within the plane wave
impulse approximation with distortion corrections included in the effective momentum approximation. Proton
and neutron single-particle momentum distributions were calculated in the macroscopic-microscopic approach.
The fissility for proton and neutron single hole excited states of the residual nuclei
237
Pa and
237,238
U was
calculated within the compound nucleus model. Final state interaction corrections to residual nucleus excitation
energy were calculated using the imaginary part of the optical potential. The total inclusive electrofission cross
section was measured with high absolute precision, and all principal partial contributions are analyzed, in
particular, the quasifree one.
DOI: 10.1103/PhysRevC.68.014615 PACS numbers: 24.60.Dr, 24.75.+i, 21.60.Ev, 27.90.+b
I. INTRODUCTION
A new aspect of investigations of quasifree QF scatter-
ing of high-energy electrons has been opened with the study
of decay channels of single hole states in the residual
nucleus, created as a result of the QF process. Especially
interesting is to study fission following a QF process. In this
case we have essentially a single-particle process in the first
reaction stage, and essentially a collective process in the final
reaction stage. The collective degrees of freedom are excited
in the intermediate reaction stage due to the residual interac-
tion, and may allow to get unique information on both the
dissociation of well defined single hole configurations
which we can select by ( e , e ' p ) coincidence into complex
nuclear configurations, and the role of these single hole con-
figurations in nuclear fission. In particular, the limitations
associated with the predictions of the shell model based on
the mean field approximation and residual forces for heavy
deformed nuclei, such as
238
U, could be studied.
The unambiguous extraction of single hole contributions
is possible only in an exclusive experimental setup reaction
( e , e ' pf )]. This kind of experiment involves extremely thin
targets fission fragments have to leave the target with small
energy losses, high-energy resolution and coincidence be-
tween the final particles to separate the single hole states,
and it has never been performed. The estimation of expected
exclusive electrofission cross sections for single hole states
in the residual nucleus has been done in Ref. 1 through
both the macroscopic-microscopic approach for the descrip-
tion of the quasifree reaction stage, and the statistical theory
for calculation of the fissility.
Some integral properties of the quasifree electrofission
could be studied in more simple inclusive experiments: ( e , f )
and ( e , e ' f ), performed with high absolute precision, plus a
joint analysis with ( , f ) and ( e , e ' ) data. These works deal
with the total QF cross section, integrated over nucleon mo-
mentum distribution and summed over all shells.
The goal of the theoretical part of the present work is the
study of integral properties of the quasifree ( e , f )-cross sec-
tion for
238
U, based on the macroscopic-microscopic ap-
proach for the description of the quasifree reaction stage and
the statistical theory for calculation of the fissility.
The goals of the experimental part are the measurement of
the absolute electrofission cross section of
238
U with high
accuracy, and the extraction of the quasifree scattering con-
tribution through the joint analysis of ( , f ), ( e , e ' ), and
( e , f ) data in the framework of the distorted-wave Born ap-
proximation DWBA virtual photon formalism. The com-
parison of calculations with experimental data will provide a
check of the models used for the description of quasifree
fission for heavy deformed nuclei, as well as a check of the
consistency of ( , f ), ( e , e ' ), and ( e , f ) data used in the
analysis.
II. SINGLE-PARTICLE BOUND STATES
The single-particle bound state energies and momentum
distributions for
238
U were calculated in the framework of
the macroscopic-microscopic approach using the BARRIER
code 2. First, the equilibrium ground state deformation
parameters elongation and
4
hexadecapolar momen-
tum have been calculated by minimizing the total nuclear
energy, obtaining thus, =0.227 and
4
=0.059.
Single-particle states were calculated in cylindrical coor-
dinates for the axially symmetric Woods-Saxon potential 3,
V
WS
r , z , ,
4
=V r , z , ,
4
+V
so
r , z , ,
4
+V
Coul
r , z , ,
4
, 1
PHYSICAL REVIEW C 68, 014615 2003
0556-2813/2003/681/0146159/$20.00 ©2003 The American Physical Society 68 014615-1