A self-consistent mean-field approach within the extended Thomas-Fermi approximation with Skyrme forces is applied to the calculations of the statistical level density in spherical nuclei. Landau's concept of quasiparticles with the nucleon effective mass and the correct description of the continuum states for the finite-depth potentials are taken into consideration. The $A$ dependence and the temperature dependence of the statistical inverse level-density parameter $K$ is obtained in a good agreement with experimental data.

• Received 18 January 2018

DOI:https://doi.org/10.1103/PhysRevC.97.064302