A microscopic statistical model based on the relativistic density functional theory (RDFT) is developed to calculate the nuclear level density (NLD). The approach employs self-consistent single-particle levels obtained from RDFT as input, incorporates pairing correlations within a finite-temperature Bardeen-Cooper-Schrieffer theory, and accounts for rotational and vibrational collective enhancement effects. The spin cut-off parameter is calculated from the single-particle levels, thereby naturally retaining the shell effects and the structural characteristics of different nuclei. Using the shape-coexisting nucleus ${}^{98}\mathrm{Sr}$ as a representative example, the microscopic origin of the deformation effect on the NLD is investigated. In addition, the calculated NLDs are systematically compared with those from various phenomenological and microscopic models, as well as with available experimental data. The results indicate that although certain discrepancies exist among different models, they exhibit consistent overall evolutionary trends. Meanwhile, the RDFT-based microscopic statistical approach is capable of providing a reasonable description of the experimental NLDs as well as the $s$- and $p$-wave neutron resonance spacings.

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• Level densities
• Nuclear structure & decays
• Nuclear mass ranges
• Nuclear density functional theory