Microscopic analysis of the nuclear level density in superheavy Hs nuclei in the ground state and at the saddle point

In this study, the nuclear level density (NLD) of superheavy even-even $^{266,268,270,272}\mathrm{Hs}$ nuclei was calculated using an accurate microscopic statistical approach that avoids common approximations. The approach employs a recursive partition-function method that uses realistic deformation-dependent single-particle level (SPL) spectra obtained from the deformed Woods-Saxon potential diagonalization as input. Calculations are performed at both the ground state and the saddle point (SP), which allows the detailed analysis of NLD behavior along the fission path and provides insight into the probability of survival of the synthesized superheavy Hs nuclei. The SPs were determined using the macroscopic-microscopic method and applying the imaginary water flow technique. The results are compared with those obtained using SPL schemes derived from self-consistent mean-field models and with the predictions of traditional Fermi gas models. The precise microscopic method used in this study provides a more realistic representation of NLD behavior in superheavy nuclei, which offers significant improvements over approximative methods.