The probability distribution of transmutation events and its application for solving burnup problems

摘要

In reality, numerous possible transmutation events can transform a nucleus into one or more daughter nuclei. However, only one of these events is finally selected to occur. Primarily, such a selection is related to the probabilities of these transmutation events, and the distribution of these probabilities has never been discussed. This paper concerns the general statistical model that describes the random selection of transmutation events at the nucleus level. We derive the discrete probability distribution function of transmutation events experienced by nuclei. It motivates us to explore the feasibility of using the proposed distribution to produce the approximate solution to ~(241)Pu and ~(238)U depletion problems, thus, verifying the distribution correctness at the same time. The results indicate that the proposed calculation reproduces the reference nuclides concentrations with acceptable accuracies.