# Solution of Nuclide Burnup Equations Using Transition-Probabilities

*Nuclear Science and Engineering*, 102 (1): 54-63 May 1989

## Abstract

A new approach to the solution of burnup equations is developed that takes into account
the dependence of the reaction constants on time as well as nonlinear and feedback effects. With the
help of the transition probabilities for the simplified problem, the burnup differential equation is
reduced to the equivalent integral equation, which is solved by iterations. The solution is made easy
to understand with the help of diagrams constructed following the suggested rules. It is strictly proved
that any nuclide transmutation network can be broken into independent depletion chains if the burnup
equations are linear in concentrations. The theory is illustrated by examples of the time dependence
of reaction constants.

#### Keywords: nuclide burnup equations, reaction constants

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