Combining Semi-Classical and Quantum Mechanical Methodologies for Nuclear Cross-section Calculations Between 1 Mev and 5 Gev Page: 2 of 4
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higher energy. One of the reasons for limiting the upper en-
ergy to 150 MeV is that it is the pion threshold, above which
more difficulties in calculations and evaluations arise. Refer-
ence 3 and the present paper complement each other.
Lillie and Gallmeier) have developed a coupled neutron
and photon library, HIL02k, for neutron energies up to 2 GeV.
Of particular interest to the present work is that there exist dis-
continuities at 150 MeV in many cross sections between this
library and LA150. The present model promises a smooth
transition across 150 MeV for all partial reaction cross sec-
Chadwick et al.,') in developing the LA150 library, used a
global set of optical model parameters for both neutrons and
protons between 30-50 MeV and 150 MeV. Koning et al.'>
evaluated cross section data for the Fe and Ni isotopes with an
upper energy of 200 MeV. They developed valuable optical
model parameters for these elements for both neutrons and
protons covering the the energy range from 1 MeV to 200
MeV. Shen') determined a set of optical model parameters si-
multaneously for Fe and Pb isotopes up to 300 MeV. All these
developments are for applications in studying accelerator-
driven systems. The set of global optical parameters of Ref. 4
has been adopted as one of the default sets in TNG and used in
the present work. Those in Refs. 6 and 7 will be considered in
II. Model Approximations
We have validated TNG for incident energies below 40
MeV and will assume for the present paper it is satisfactory up
to this energy. Above 40 MeV TNG needs a direct reaction
component that we plan to adopt from the INC model in CEM.
We also need the INC model to account for pion production
for incident energies above 150 MeV. Therefore, the present
effort is for incident energies above 40 MeV. We present first
our approximation for incident energies between 40 and 80
MeV, and then for incident energies from 80 MeV to 5 GeV.
CEM and TNG are run for the same incident energy if it is
between 40 MeV and 80 MeV. From CEM we write into a file
the excitation spectra (cross sections as a function of excita-
tion energy) below an excitation energy of 40 MeV in all
residual nuclides. These nuclides are no longer followed in
CEM. TNG reads this CEM file and continues the decay pro-
cess. Because CEM is Monte Carlo, the CEM file is converted
into TNG group structure first. Then the excitation spectra
calculated in TNG after the first particle emission are com-
bined with those from CEM (see paragraph below for the
combination method), while replacing the part of TNG spectra
having excitation energies above 40 MeV to small values.
These small values are arbitrarily fixed as 0.001 mb per group
(group width of 1-2 MeV) because this part of TNG is already
accounted for in CEM. Now we have spin and parity distribu-
tions calculated by TNG and can proceed with the H-F model
to calculate the emission of the next particle.
From the second particle on, TNG and CEM excitation
spectra are summed (not combined, see next paragraph). Our
first approximation is that the CEM output have the same
spin and parity distributions as calculated by TNG in the ex-
citation energy range below 40 MeV. This is an approxima-
tion because the INC model in CEM has a direct reaction
component whose spin and parity distributions may be differ-
ent than those calculated in TNG. The combined code is re-
ferred to hereafter as CETNG (Cascade Exciton TNG), used
for incident energies above 40 MeV. Thus, from here on,
excitation spectra from CEM, TNG, and CETNG have com-
pletely different definitions.
The CEM and TNG excitation spectra in the residual nu-
clide after the first particle emission (also called the binary
reaction) are calculations from two different models for the
same quantities. We combine them in CETNG by using a
weight (40/E)2 for TNG and 1-(40/E)2 for CEM where E is
the incident energy. The combined excitation spectra in
CETNG deexcite and produce new excitation spectra (in a
daughter nucleus) that are referred to as CETNG excitation
spectra. The weights are intended to smooth all calculated
results across the 40-MeV incident energy between TNG
(used below 40 MeV) and CETNG (used above 40 MeV).
The direct component from the INC model in CEM, that pro-
duces harder particle emission spectra than TNG, also phases
in smoothly in CETNG. Another advantage in using these
weights is that the first-chance alpha-particle emission is
extremely low in CEM, and keeping some TNG contribution
to CETNG reduces this problem. After the second particle
emission, CETNG excitation spectra and the new CEM input
are summed (not combined) because from this emission on,
the CEM part comes from the decay of nucleii having excita-
tion energies above 40 MeV while the CETNG part arises
from those below 40 MeV, hence the two components com-
plement each other.
The replacement (to 0.001 mb per group) mentioned
above for excitation energies above 40 MeV calculated in
CETNG is meant to trick CETNG to calculate spin and par-
ity distributions for daughter nucleii from mother nucleii
having excitation energies up to the incident energy (limited
to 80 MeV if the incident energy is greater than 80 MeV, as
A second approximation arises because TNG methodol-
ogy is not appropriate for incident energies above 80 MeV.
For CEM runs with incident energies greater than 80 MeV,
TNG is always run with a fixed incident energy of 80 MeV.
After emitting a few particles in the CETNG calculation, the
maximum excitation energy in the residual nuclide may drop
(due to the Q-value loss) below 40 MeV, a maximum excita-
tion energy not high enough to accomodate the CEM excita-
tion spectra in that residual nuclide. To prevent this from
happening, CETNG excitation spectra after each particle
emission are extended to 80 MeV before applying the
replacement method described above. The spin and parity
distributions for the extended energy region, from about 72
MeV to 80 MeV (assuming a Q-value of 8 MeV for emitting
one particle), are missing and are filled by the distributions
available in the next closest excitation energy. The widened
energy region, being twice as wide as the needed 40 MeV, is
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Fu, C.Y. Combining Semi-Classical and Quantum Mechanical Methodologies for Nuclear Cross-section Calculations Between 1 Mev and 5 Gev, article, August 15, 2001; Tennessee. (digital.library.unt.edu/ark:/67531/metadc725422/m1/2/: accessed February 20, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.