CNUCTRAN: A program for computing final nuclide concentrations using a direct simulation approach

It is essential to precisely determine the evolving concentrations of radioactive nuclides within transmutation problems. It is also a crucial aspect of nuclear physics with widespread applications in nuclear waste management and energy production. This paper introduces CNUCTRAN, a novel computer program that employs a probabilistic approach to estimate nuclide concentrations in transmutation problems. CNUCTRAN directly simulates nuclei transformations arising from various nuclear reactions, diverging from the traditional deterministic methods that solve the Bateman equation using matrix exponential approximation. This approach effectively addresses numerical challenges associated with solving the Bateman equations, therefore, circumventing the need for matrix exponential approximations that risk producing nonphysical concentrations. Our sample calculations using CNUCTRAN shows that the concentration predictions of CNUCTRAN have a relative error of less than 0.001% compared to the state-of-the-art method, CRAM, in different test cases. This makes CNUCTRAN a valuable alternative tool for transmutation analysis.

Program summary

Program Title: CNUCTRAN

CPC Library link to program files: https://doi.org/10.17632/b484w2vx52.1

Developer's repository link: https://github.com/rabieomar92/cnuctran/releases

Licensing provisions: MIT

Programming language: C++

Nature of problem: CNUCTRAN simulates the transmutation of various nuclides such as decays, fissions, and neutron induced reactions using a direct simulation approach. It has the capability of predicting the final concentration of a large system of nuclides altogether after a specified time step, $t_f$.

Solution method: CNUCTRAN works based on the novel probabilistic method such that it does not compute the final nuclide concentrations by solving Bateman equations. Instead, it statistically tracks nuclide transformations into one another in a transmutation problem. The technique encapsulates various possible nuclide transformations into a sparse transfer matrix, $T$, whose elements are made up of various nuclear reaction probabilities. Next, $T$ serves as a matrix operator acting on the initial nuclide concentrations, $y\left(0\right)$, producing the final nuclide concentrations, y.