Global optimization of nuclear level density parameters using Bayesian analysis

Nuclear level density (NLD) parameters for the constant temperature and back-shifted Fermi gas models were determined for 129 nuclei, spanning from ⁴³Sc to ²⁴³Pu. These parameters were extracted using a Bayesian optimization technique by fitting the experimentally measured NLD data obtained from the Oslo method and particle evaporation experiments. For each model, the extracted NLD parameters were further fitted using various functional forms, leading to the identification of optimal expressions based on fractional root-mean-square deviations. The resulting expressions reveal that the NLD parameters primarily depend on three key quantities: the mass number, shell correction energy, and deuteron pairing energy. The accuracy and reliability of these optimized formulations were assessed by comparing the predicted values with measured neutron resonance spacing data. This validation confirms their effectiveness in describing NLDs across the nuclear chart, capturing the signatures of nuclear magicity and deformation.