Title: Inference of Parameters for Back-shifted Fermi Gas Model using Feedback Neural Network Show Chinese title

Title: 利用反馈神经网络推断背移位费米气体模型的参数

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. Show Chinese abstract

Abstract: 背移费米气体模型被广泛用于计算核能级密度（NLD），因为它可以通过调整参数有效地重现实验数据。然而，对于缺乏实验数据的核素选择参数是一项挑战。在这项研究中，利用前馈神经网络（FNN）学习了289个核素在中子分离能 $a(S_{n})$ 和能量位移 $\varDelta$ 处的能级密度参数。同时，通过FNN提供了近3000个核素的参数。使用这些参数，计算了 $s$ 和 $p$ 波长下的中子共振间距、能级累积数和核能级密度。还将FNN的结果与拟合实验数据得出的参数（局部参数）以及系统研究得到的参数（全局参数）的计算结果以及实验数据进行了比较。结果显示，FNN得出的参数在再现实验数据方面表现与局部参数相当。此外，对于外推核素，FNN得出的参数仍然能够对实验数据提供稳健描述。