CoH 3 : The Hauser-Feshbach Code
29
the CC method, and the Engelbrecht-Weidenmüller transformation is invoked to
diagonalize the S-matrix [13].
Pre-equilibrium Reaction The two-component exciton model [14, 15] is used to
calculate the pre-equilibrium process. The quantum mechanical pre-equilibrium
models, such as FKK (Feshbach-Kerman-Koonin) [16, 17] or NWY (NishiokaWeidenmüller-Yoshida) [18, 19], are also available, yet provided as external codes.
See Ref. [20], for example.
Prompt Fission Neutron Spectrum For fissioning nuclei, the prompt fission
neutron spectrum is calculated with the Madland–Nix model [21] including prefission neutron emissions.
Direct/Semidirect (DSD) Neutron Capture The direct/semidirect (DSD) neutron
capture process is calculated with the DSD model [22–26]. A standard option
is to use the spherical Woods–Saxon potential for calculating the single-particle
wavefunctions. In the deformed nucleus case, two mean-field models can be
used [27]; FRDM (Finite-Range Droplet Model) [28, 29] and HF-BCS (HartreeFock BCS) [30].
3 Transmission Coefficients for the Excited States
CoH 3 is designed to combine tightly the CC optical model and the statistical HF
theory, in which the generalized transmission coefficients for the excited states are
calculated from the CC S-matrix [31]. This is especially important for calculating
nuclear reaction process on a deformed nucleus, such as actinides. The transmission
coefficient for the n-th excited state with orbital angular momentum l and spin j is
calculated as
T
(n)
lj =
J J
c
g J c
1 −
c
|S
J J
cc |
2
c∈n
,
(1)
where c labels the channel, and g J c is the spin factor. Here the flux going into the
directly coupled channels is eliminated from the total absorption probability, such
that the sum of T
(n)
ij gives a correct compound formation cross section from the n-th
level. In contrast to this, other HF codes often replace T
(n)
lj by the one for the ground
state T
(0)
lj , and shift the energy by the level excitation energy E
(n)
x ,
T
(n)
lj (E) T
(0)
lj
E − E
(n)
x
.
(2)
This approximation has never been validated. The calculated neutron transmission
coefficients of Eqs. (1) and (2) are compared in Fig. 1. These are for the first excited
29
the CC method, and the Engelbrecht-Weidenmüller transformation is invoked to
diagonalize the S-matrix [13].
Pre-equilibrium Reaction The two-component exciton model [14, 15] is used to
calculate the pre-equilibrium process. The quantum mechanical pre-equilibrium
models, such as FKK (Feshbach-Kerman-Koonin) [16, 17] or NWY (NishiokaWeidenmüller-Yoshida) [18, 19], are also available, yet provided as external codes.
See Ref. [20], for example.
Prompt Fission Neutron Spectrum For fissioning nuclei, the prompt fission
neutron spectrum is calculated with the Madland–Nix model [21] including prefission neutron emissions.
Direct/Semidirect (DSD) Neutron Capture The direct/semidirect (DSD) neutron
capture process is calculated with the DSD model [22–26]. A standard option
is to use the spherical Woods–Saxon potential for calculating the single-particle
wavefunctions. In the deformed nucleus case, two mean-field models can be
used [27]; FRDM (Finite-Range Droplet Model) [28, 29] and HF-BCS (HartreeFock BCS) [30].
3 Transmission Coefficients for the Excited States
CoH 3 is designed to combine tightly the CC optical model and the statistical HF
theory, in which the generalized transmission coefficients for the excited states are
calculated from the CC S-matrix [31]. This is especially important for calculating
nuclear reaction process on a deformed nucleus, such as actinides. The transmission
coefficient for the n-th excited state with orbital angular momentum l and spin j is
calculated as
T
(n)
lj =
J J
c
g J c
1 −
c
|S
J J
cc |
2
c∈n
,
(1)
where c labels the channel, and g J c is the spin factor. Here the flux going into the
directly coupled channels is eliminated from the total absorption probability, such
that the sum of T
(n)
ij gives a correct compound formation cross section from the n-th
level. In contrast to this, other HF codes often replace T
(n)
lj by the one for the ground
state T
(0)
lj , and shift the energy by the level excitation energy E
(n)
x ,
T
(n)
lj (E) T
(0)
lj
E − E
(n)
x
.
(2)
This approximation has never been validated. The calculated neutron transmission
coefficients of Eqs. (1) and (2) are compared in Fig. 1. These are for the first excited