JAEA-Conf 2011-002 - 日本原子力研究開発機構

2-2. Pre-equilibrium reaction model
Pre-equilibrium emission plays an ever more important role in nucleon-induced reactions as the
incident energy increases above 10 MeV. Several theoretical models, semi-classical or quantum
mechanical, have been developed to account for emission of pre-equilibrium reactions over the last
many years. Among these, the semi-classical exciton model [3] proposed by J.J. Griffin in 1966 is
widely used in practical applications because of the reason that it is easy to carry out computationally.
In the exciton model, the nuclear state is characterized, at any moment during the reaction, by the
total energy E out and the total number of particles p above and holes h below the Fermi energy. The
feature of the exciton model is a time-dependent master equation which describes the probability of
transition to more or less complex particle-hose state so-called exciton states as well as transitions to
the particle emission. In the exciton model, the basic formula of differential cross section for the
emission of particle k with energy Ek can be expressed as
PE
max max
p
p
d
k CF
W(
p , h , p , h ) ( p , h , p , h ) P(
p , h , p , h )
k
dE
0 0
p ppp k
The expression for P(pπ, hπ, pν, hν) contains the adjustable transition matrix element M 2 for each
possible transition between neutron-proton exciton configurations. The matrix element is given by
M
2
C1A
3
A
p
JAEA-Conf 2011-002
7.
48C
2
5
4.
62
10
tot
E
( 10.
7C3)
n.
A
where C1, C2 and C3 are adjustable constants, which enable a fit to angle-integrated outgoing
neutron and proton spectra.
Semi-classical models, such as the exciton model, have some problems to express angular
distributions. Therefore the double-differential cross sections are obtained from the calculated energy
spectra using the kalbach systematic [4].
3. Results
The energy and energy-angle spectra of secondary particles are essential. We compare the
calculations of the nuclear reaction code TALYS with the existing experimental data of S. Matsuyama
et al. [5], A. Takahashi et al. [6] and N. Yabuta et al. [7]. The neutron spectra and angular distributions
calculated by TALYS code are illustrated in figure 3~6. Our calculations are obtained through
adjusting the transition rates with the energy-dependent matrix elements.
As shown in Figures 3 and 4, the angular distributions for outgoing neutrons spectra are in rather
good agreements with experimental data of N. Yabuta et al. at 14 and 18 MeV. In addition, the results
have similar experimental data at low angle than large angle. Figures 5 and 6 describe the angleintegrated
emission spectra for (n, xn) reactions at 14 and 18 MeV. These results agree well with the
experimental data at 14 MeV but show some discrepancies at 18 MeV.
p
3