One reliable and convenient way of processing the cross sections in the resolved energy region is by
use of the generalized pole representation, whereby the Doppler-broadening calculation can be
carried out rigorously using the analyticalapproach. So far, its applicationsykmve been- limited’%o ‘-->-
,,, .. .
cases with resonance parameters specified by the Reich-Moore formalism. Although such an
approach, in principle, can be extended to all three remaining representations of resolved resonance
parameters specified by the ENDF data format, there is no computational tool for handling such a
task at present. Given that Breit-Wigner formalisms are probably the most widely used by any
evaluated nuclear data library to represent cross sections, a special effort has to be made to convert
the single level and multilevel Breit-Wigner resonance parameters to pole parameters. A
FORTRAN computer code BW2PR has been developed for this purpose. Extensive calculations
have been performed to demonstrate that the proposed method ensures the conservation of the
information contained originally in Breit-Wigner resonance parameters. This will make it possible
to apply the exact Doppler–broadening method to a larger collection of nuclides.
The case in point here is whether the same approach is also extendable to alternative cross section
formalisms other than that of the Reich-Moore also widely used in the existing data files. Three
other formalisms also in use are the single level Breit-Wigner (SLBW), multilevel Breit-Wigner
(MLBW), and Adler-Adler formalisms. Of the three, the Adler-Adler formalism is seldom used
because its applicability is limited to the s-wave resonances of few fissile isotopes in the low energy
region. In contrast, approximately 90% of W resonant isotopes in most nuclear data files are
specified by the SLBW or MLBW parameters. However,. for. the most. importan~ nuclides,. the .. ..
MLBW formalism is apparently prefened to the SLBW formalism that represents the limiting case
when the resonances are well isolated. In the JEF 2.2 library, SLBW resonance parameters are
almost systematically replaced by MLBW ones. The MLBW formalism is an enhancement in the
sense that it accounts for the interference effect between each resonance for the scattering and total
cross sections. That effect can be fully described by an additional interference cross section. The
fission and radiative capture cross sections are identically represented in the two Breit-Wigner
formalisms. Consequently, it will be seen that the conversion into pole parameters is formally
similar for those two formalisms except for the treatment of the so-mentioned interference cross
section.
Then, the scattering cross section can be directly computed as the difference between the total and
absorption cross sections. That interference cross section exhibits cross terms that expresses the
interference between the energy levels of a given (/, J) – state. Since there is no exponential factor
exp(–i2@g) in its expression, the interference cross section can be obviously expanded in terms of
pole parameters.
One first considers the rationalization of the following generic cross term that appears” in the
expression of the interference cross section:
fgJRe{l%~2
}=igJRe o
r+)(u) r
(u)]
A;(u) A,(u) )
‘Re{?i::’~u}
A code named BW2PR has been developed to implement the conversion of Breit-Wigner resonance
parameters to pole parameters. The code accomplishes several tasks that are described as follows.
i) Breit-Wigner resonance parameters for a given isotope are extracted from an ENDF-format based
file.
ii) Smooth cross section components are re-processed in order to force the tabulated data to follow a
linear-linear interpolation law consistent with a piecewise Doppler-broadening scheme. It will be
recalled that smooth cross section components provide the remedy for the lack of rigor in Breit-
Wigner formalisms.
iii) Resonant poles and residues are computed in extended precision using Eqs. (3), (7), (
and (13).
All those parameters are displayed in an output file.
iv) The code generates a binary fde storing the computed pole parameters and other relevant data to
be passed to the code POLEBRD (Hwang, 1998a) that performs an analytical and exact Dopplerbroadening
of any cross section described by the pole representation.
v) The code produces an output of pointwise cross sections at zero temperature obtained using the
generalized pole representation, and relative errors to compare the results with the directly
computed Breit-Wigner cross sections.
