Direct microscopic calculation of nuclear level densities in the shell model Monte Carlo approach

Nuclear level densities are required for estimating statistical nuclear reaction rates. The shell model Monte Carlo method is a powerful approach for microscopic calculation of state densities in very large model spaces. However, these state densities include the spin degeneracy of each energy level, whereas experiments often measure level densities, in which each level is counted only once. To enable the direct comparison of theory with experiments, we introduce a method to calculate directly the level density in the shell model Monte Carlo approach. The method employs a projection on the minimal absolute value of the magnetic quantum number. We apply the method to nuclei in the iron region and to the strongly deformed rare-earth nucleus Dy-162. We find very good agreement with experimental data obtained by various methods, including level counting at low energies, charged particle spectra and Oslo method data at intermediate energies, neutron and proton resonance data, and Ericson's fluctuation analysis at higher excitation energies. We also extract a thermal moment of inertia from the ratio between the state density and the level density, and observe that in even-even nuclei it exhibits a signature of a phase transition to a superconducting phase below a certain excitation energy.