Consistent nuclear model for compound and precompound reactions with conservation of angular momentum. [14. 6 MeV] Page: 1 of 5
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A CONSISTENT NUCLEAR MODEL FOR COMPOUND AND PRECOMPOUND REACT lO’.3
WITH CONSERVATION OF ANGULAR MOMENTUM
C. V. Fu
Oak Ridge National Laboratory
Oak Ridge, Tennessee 37830, USA
CO/i' f~ -
The exciton model is modified such that it automatically reduces to the usual
evaporation formula after ecuil ibrium has been reached. The result is further
modified to conser\e annular monen'um in a form compatible with the Hauser-Feshbacn
formula. This allows a consistent description of intermediate excitations from
vihich tertiary reaction cross sections can be calculated for transitions to discrete
residual levels with known spins and parities. Level densities used for the compound
component of reaction cross sections are derived from direct summation of the
particle-hole state densities used for the precompound component.
[Nuclear reactions ?7A1, l‘6,1‘sTi, 51V, 57’5zCr, .s" ,55Fe,
E = 14.6 MeV. Calculated a(n,xn), (n,xp), (n,xi), a(E ),
and precompound analysts.]
IjPtrqduction j !c(E)
Development of fusion energy calls for substan- 1 j
tial improvement in the knowledge of neutron cross
sections in the energy range from a few MeV to about
40 MeV. 1 In tin’s energy range, the multi-step Hauser-
Feshbach model with precompound effects is the most
versatile and is considered an indispensible theoreti-
cal tool for cross-section evaluations.'’ In analyzing
cross sections such as hydrogen and helium productions
from 14-MeV neutron-induced reactions, wo showed5 that
spin and parity effects are more important in the
second step of the calculation than in the first step.
However, it is not xtraighUorward to conserve anguljr
momentum even in the first step because the presently
j available models for precomoound reactions do not con-
■ serve or even recognize angular momentum. In addition
the compound and precompound components are generally
calculated in the first step from tvio physically dif- .
ferent models, thus lacking a common basis for
carrying out the calculation to the second step. j
In this paper we develop a model capable of cal- ;
culating the compound and precompound cross sections ;
consistently and conserving angular momentum in both
compound and precompound reactions. The model becomes,
that of Hauser-Feshbach" at low energies where the
precompound effects are negligible. Level densities
used for calculating the compound component are made
consistent with those used for the precompound com-
A full derivation of the formula given below has
been written up for publication elsewhere.5 Here we
only have enough space for a summary. We shall first
write down the final formula and then explain the
physical implications of the various components lead-
ing to its derivation.
The final formula is
l 9j I
Jtt j Si
T S ' i '
°Jit = ^b
p Ls'V 's'i'
I Db(p,E) wb(p~l,h,I,LT) +■ C(E)
Db(p.E) = /
Pb(I>U’) = Ip ub(p-l,h,I,U‘)
and the various components and notations are explained
The compound and precompound components are con-
sistent if the precompound model automatically reduces
to the compound model after equilibrium has been
‘reached. This is achieved by introducing a set of
master equations containing time-dependent particle-
type distributions. Defining P,(p,h,t), the occupation
probability, as the probabi1ity°that the system will be
found in a state with p particles and h holes of type b
i at time t, the master equations which describe the I
•approach of the nucleus to statistical equilibrium are
j given by i
;fpb(P-i.h-i,t) n_! , yp)
|LP(p-l,h-I,t)“ p P
P(p-1,h-l ,t) X+(p-l,h-l,E)
+ LP(p-H ,h+l ,t)
- Pb(p,h,t) [x+(p,h,E) + A_(p,h,E) + / maX Xb(p,h,c)dc]
P(P,h,t) = lb Pb(p,h,t)
The transition rates A+ and X are given by Ribansky 1
et al.5 which contain an empirical residual two-body !
matrix element determined by Kalbach.6 E is the total:
energy of the reacting system. j
In the first term in Eq. (11), P(p-l,h-l,t) i
X (p-l,h-l,E) represents the total transition rates
I from (p-l,h-l) states to (p,h) states. Among the p
particles in the (p,h) states, (p-1) of them retain the
I old particle-type distribution P.(p-1,h-l ,t)/P(p-l ,h-l,
i t), and the newly created particle may have a different
I particle-type distribution given by fb(p), which will
j be determined analytically. Thus the°compositions of
| particle types in the new (p,h) states are given by the
^quantity in the brackets. j
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Fu, C.Y. Consistent nuclear model for compound and precompound reactions with conservation of angular momentum. [14. 6 MeV], article, January 1, 1979; Tennessee. (digital.library.unt.edu/ark:/67531/metadc1093950/m1/1/: accessed June 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.