A general analytical solution for the variance-to-mean Feynman-alpha formulas for a two-group two-point, a two-group one-point and one-group two-point cases

Chernikova, D. and Ziguan, W. and Pázsit, I. and Pál, Lénárd (2014) A general analytical solution for the variance-to-mean Feynman-alpha formulas for a two-group two-point, a two-group one-point and one-group two-point cases. EUROPEAN PHYSICAL JOURNAL PLUS, 129. ISSN 2190-5444

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Abstract

This paper presents a full derivation of the variance- to-mean or Feynman-alpha formula in a two energy group- and two spatial region-treatment. The derivation is based on the Chapman - Kolmogorov equation with the inclusion of all possible neutron reactions and passage intensities be- tween the two regions. In addition, the two-group one-region and the two-region one-group Feynman-alpha formulas, treated earlier in the literature for special cases, are extended for fur- ther types and positions of detectors. We focus on the possi- bility of using these theories for accelerator-driven systems and applications in the safeguards domain, such as the dif- ferential self-interrogation method and the differential die- away method. This is due to the fact that the predictions from the models which are currently used do not fully de- scribe all the effects in the heavily reflected fast or thermal systems. Therefore, in conclusion a comparative study of the two-group two-region, the two-group one-region, the one- group two-region and the one-group one-region Feynman- alpha models is discussed.

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