Multi-Level Correction to Breit-Wigner Single-Level Formula

Abstract

A formula for neutron cross sections of heavy nuclei is derived on the basis of the Wigner-Eisenbud theory. The derived formula is the same as the single-level one introduced by Breit and Wigner except for the inclusion of additional interference parameters (u, v) which represent the contribution of the interference effect between resonances. The present formula is therefore applicable to reactor calculations without much modifications of the existing resonance integral codes.

The present formula has been applied to the analyses of the ²³⁵U and ²³³U fission cross sections and the ²³⁸U total cross sections in the resolved resonance region. By the use of least squares fits of the experimental data, the interference parameters (u, v) are obtained for resonance levels of these nuclei in their typical resonance regions. It is shown that the present formula well represents the experimental data.

In the unresolved resonance region, both the single-level resonance parameters and the present interference parameters are generated by using a random sampling method. The contributions of the interference between the resonances, to the Doppler effect are also evaluated for the fission cross sections of ²³⁵U and ²³⁹Pu in the unresolved resonance energy region of 1 to 2 keV.

KEYWORDS:

• single-level formula
• interference effects
• resonance
• interference parameters
• least squares fits
• Doppler effect
• uranium 235
• uranium 233
• uranium 238
• Breit-Wigner formula
• multi-level analysis
• total cross sections