On the Use of Explicit Eigenfunctions in the Calculation of Multiplicity Moments in Nuclear Safeguards

Recent work [3] has shown the application of the particle transport equation to calculate the so-called multiplicity moments, which are very important in nuclear safeguards. In [3], a transformation was made from the integral formulation of the problem in a sphere to a slab geometry problem, where the Analytical Discrete Ordinates (ADO) method, a spectral method, was applied [1]. Numerical eigenfunctions were used, defined in terms of eigenvectors. In this work, we investigate the use of explicit expressions for the eigenfunctions that define the ADO solution. We are interested in precise formulations that require low computational time, as these results shall be used to solve inverse problems.

References

[1] L. B. Barichello. “Explicit formulations for radiative transfer problems”. In: Thermal measurements and inverse techniques (2011).

[2] L. B. Barichello, R. Garcia, and C. Siewert. “Particular solutions for the discrete-ordinates method”. In: JQSRT 64.3 (2000), pp. 219–226.

[3] L. B. Barichello and I. Pázsit. “Calculation of the multiplicity moments in nuclear safeguards with forward transport theory”. In: Annals of Nuclear Energy 212 (2025), p. 111046.

[4] I. Pázsit and L. Pál. “Multiplicity theory beyond the point model”. In: Annals of Nuclear Energy 154 (2021), p. 108119.