Resonance Absorption of Neutrons In Lumps with Nonuniform Temperature Distributions

An extension of the methods for computing resonance integrals given by Chernick and Vernon (8) and Nordheim et al. (9) to the case of nonuniform temperature distributions in the absorber is given. Formally, the procedure is quite similar to the previous work and utilizes the same approximations: absorbed neutrons are broken into two groups according to whether their previous collisions were in the absorber or in the moderator; both the narrow resonance (NR) and infinite mass (NRIA) approximations are developed. The effect of nonuniform temperature distribution is to modify the escape probabilities required. The present calculation requires escape probabilities for lumps which contain nonuniform sources and/or cross sections. Methods of computing these escape probabilities are presented.