Nuclear level density studied in odd-mass nuclei in the framework of the projected shell model

In a recent article [Phys. Rev. C 108, 034309 (2023)], we proposed a projected shell model method for the calculation of nuclear level density (NLD) in deformed even-even nuclei. The current article presents the subsequent study of NLDs in odd-mass nuclei as well as a comparative analysis between our calculated NLDs in adjacent even-even and odd-$A$ systems. Since one nucleon in the odd-mass system remains blocked from participating in the pair formation, resulting in a weakened pairing (assessed by a smaller BCS pairing gap $\mathrm{\ensuremath{\Delta}}$), pronounced differences between the NLDs in an odd-mass (both even-odd and odd-even) nucleus and its immediate even-even neighbor have been found. In general, the structure-dominated variations, which were found to be prominent in the even-even NLD at low energies, are greatly suppressed in the odd-mass systems. Specifically, from excitation energy as low as 2 MeV, the calculated densities of odd-parity and even-parity levels in odd-mass nuclei show an equal division signaling faster attainment of the statistical behavior. Nuclear level-spin distributions of both parities have been seen to adopt a regular Gaussian shape earlier than that found in the even-even system. Moreover, the pleasant property of our shell-model results, that each of our calculated levels is an eigenstate of angular momentum, allows us to extract the values of the energy-dependent dispersion $\ensuremath{\sigma}$ of Ericson's spin-distribution formula and plot $\ensuremath{\rho}(E,I,\ensuremath{\pi})$, the energy-, spin-, and parity-dependent level density.