The Derivation of the Doppler Broadening Function using Frobenius Method

An analytical approximation of the Doppler broadening function ψ(ξ,x) is proposed. This approximation is based on the solution of the differential equation for ψ(ξ,x) using the methods of Frobenius and parameters variation. The analytical form derived for ψ(ξ,x) in terms of elementary functions is v...

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Bibliographic Details
Published inJournal of nuclear science and technology Vol. 43; no. 6; pp. 617 - 622
Main Authors PALMA, Daniel A. P., MARTINEZ, Aquilino S., SILVA, Fernando C.
Format Journal Article
LanguageEnglish
Published Tokyo Taylor & Francis Group 01.06.2006
Atomic Energy Society of Japan
Subjects
Applied sciences
cross section
Doppler broadening function
Energy
Energy. Thermal use of fuels
Exact sciences and technology
Fission nuclear power plants
Frobenius method
Installations for energy generation and conversion: thermal and electrical energy
Frobenius method
Numerical analysis
cross section
Differential equation
Measurement technique
Activation
Doppler broadening function
Doppler effect
Cross section (collision)
Nuclear reactor
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Summary:An analytical approximation of the Doppler broadening function ψ(ξ,x) is proposed. This approximation is based on the solution of the differential equation for ψ(ξ,x) using the methods of Frobenius and parameters variation. The analytical form derived for ψ(ξ,x) in terms of elementary functions is very simple and precise. It can be useful for applications related to the treatment of nuclear resonances, mainly for calculations of multigroup parameters and resonances self-protection factors, the latter being used to correct microscopic cross section measurements by the activation technique.
ISSN:0022-3131
1881-1248
DOI:10.1080/18811248.2006.9711141