A 1. order formulation of a reaction rate variation for spatial and energy collapsing

In this paper we present an extension of the Generalized Perturbation Theory (GPT) which enables accounting for a perturbation due to spatial and/or energy collapsing in the evaluation of a reaction rate variation. The proposed methodology could be proficiently and effectively adopted to appreciate the precision of the discretized, less refined calculation against an asymptotic, continuous space and energy one or a discretized, more refined calculation. A specific advantage of the proposed methodology is to be able to assign to each spatial mesh the weight of its contribution to the reaction rate variation, opening the way to a better understanding of the physical consequences of the collapsing and to a quantitative method to optimize a spatial grid. (authors)