Multigroup importance function calculation method in the MCU code

The calculation of neutron kinetics functionals, including the effective fraction of delayed neutrons ( β eff ) and the prompt neutron generation time (Λ), by the Monte Carlo method is known to be challenging due to the complexities involved in calculating the adjoint function. In the context of the Monte Carlo method, it is optimal to represent the importance function as the asymptotic number of descendants of a neutron placed at a given point in phase space. In practice, it is possible to consider only a finite number of generations. This limitation forms the basis of the Iterated Fission Probability (IFP) method. However, this approach is associated with several disadvantages, including the convergence of the adjoint source through a given number of generations, the appearance of statistical noise, and high memory consumption. In this paper, we present a methodology for calculating the multigroup importance function using the matrix method implemented in the MCU code. The computational model is partitioned into a finite number of tally objects and energy groups. During the modeling process, the elements of the fission matrix are tallied, and the neutron importance function for each energy group of each object is calculated at the post-processing stage. The methodology was validated by calculating β eff and Λ for 6 ICSBEP Handbook experiments. The one- and 14-group approximation of the importance function yielded almost identical results, with a negligible difference (less than 1%), due to the minor change in importance in the energy range where most neutrons are generated.