Inference of Parameters for Back-shifted Fermi Gas Model using Feedback Neural Network

Abstract

The back-shifted Fermi gas model is widely employed for calculating nuclear level density (NLD) as it can effectively reproduce experimental data by adjusting parameters. However, selecting parameters for nuclei lacking experimental data poses a challenge. In this study, the feedforward neural network (FNN) was utilized to learn the level density parameters at neutron separation energy $a(S_{n})$ and the energy shift $\varDelta$ for 289 nuclei. Simultaneously, parameters for nearly 3000 nuclei are provided through the FNN. Using these parameters, calculations were performed for neutron resonance spacing in $s$ and $p$ waves, cumulative number of levels, and NLD. The FNN results were also compared with the calculated outcomes of the parameters from fitting experimental data (local parameters) and those obtained from systematic studies (global parameters), as well as the experimental data. The results indicate that parameters from the FNN achieve performance comparable to local parameters in reproducing experimental data. Moreover, for extrapolated nuclei, parameters from the FNN still offer a robust description of experimental data.