Improved resonance formulas for cross sections of fissile elements
The Adler--Adler cross-section formalism with energy-dependent parameters is a practical approximation to the R-matrix formalism, on the basis of the smallness of the s-wave neutron width in fissile elements. Attempts were made to represent experimental cross sections by the Adler--Adler formulas through an initial representation by the Reich--Moore approximation of R-matrix and a subsequent conversion of the Reich--Moore formulas to the Adler--Adler formulas. Adler and Adler foresaw difficulties in associating their formulas with approximate R-matrix theories such as those of Reich and Moore. Indeed, it is shown that, due to the nonunitarity of the Adler--Adler formalism on the one hand and the unitarity, by definition, of the Reich--Moore formalism on the other hand, the conversion from the latter to the former is ambiguous. Examples are shown to demonstrate that this ambiguity results in numerical inaccuracies, sometimes very large ones, for neutron widths that are not extremely small. Improved Adler--Adler-type formulas have been derived from the R-matrix formalism. In these formulas, the multipliers of the Breit--Wigner resonance lines exhibit more explicit energy dependence than their original counterparts, mainly in the form of additional terms in the formula for the total cross section. The conversion from Reich--Moore cross sections to the improved resonance formulas is shown to be much less ambiguous and to produce very accurate cross sections. In particular, the inaccuracies encountered with the Reich--Moore to Adler--Adler conversion are eliminated. A computer code, PEDRA, was written to perform the conversion from a given set of Reich--Moore parameters to the parameters required in the improved formulas. The numerical algorithm of this code is based on an adaptation with modifications of the numerical approach of de Saussure--Perez in the POLLA code, which converts Reich--Moore parameters to Adler--Adler parameters. 7 figures, 1 table.
- Research Organization:
- Argonne National Lab., IL
- OSTI ID:
- 6535402
- Journal Information:
- Nucl. Sci. Eng.; (United States), Journal Name: Nucl. Sci. Eng.; (United States) Vol. 67:2; ISSN NSENA
- Country of Publication:
- United States
- Language:
- English
Similar Records
Multilevel analysis of the low-energy /sup 239/Pu cross sections
TREND code for reconstruction of neutron reaction cross sections and calculation of the Doppler broadening in the region of resolved resonances
Related Subjects
A=220 & above
Theoretical-- Nuclear Reactions & Scattering-- (-1987)
653003 -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BARYON REACTIONS
BARYONS
CAPTURE
CROSS SECTIONS
ELEMENTARY PARTICLES
ENERGY DEPENDENCE
ENERGY RANGE
EPITHERMAL NEUTRONS
EV RANGE
EV RANGE 01-10
EV RANGE 10-100
FERMIONS
FISSILE MATERIALS
FISSIONABLE MATERIALS
HADRON REACTIONS
HADRONS
MATRICES
MILLI EV RANGE
NEUTRON REACTIONS
NEUTRONS
NUCLEAR REACTIONS
NUCLEON REACTIONS
NUCLEONS
PARTIAL WAVES
PLUTONIUM 239 TARGET
R MATRIX
REICH-MOORE FORMULA
RESONANCE
RESONANCE NEUTRONS
S WAVES
SCATTERING
TARGETS
URANIUM 235 TARGET