Nuclear state and level densities of actinides with the shell-model Monte Carlo

Abstract

Actinides are of great interest in astrophysics and technology applications since they can fission. However, the microscopic calculation of their statistical properties in the presence of correlations poses a major theoretical challenge. The configuration-interaction shell-model is a suitable framework to calculate these properties but the required large model spaces are beyond the reach of conventional diagonalization methods. The shell-model Monte Carlo (SMMC) method enables calculations in very large model spaces and was applied to nuclei as heavy as the lanthanides. Here, we extend the SMMC method to the actinides. Fifteen even-even and odd-mass actinides $^{232}$Th, $^{\textrm{234-239}}$U, $^{\textrm{240-243}}$Pu, $^{\textrm{246-248}}$Cm, and $^{250}$Cf are studied using a single-particle model space that is larger than one major shell each for protons and neutrons, with a total dimension of the many-particle space as large as $10^{32}$. We calculate nuclear state densities of these actinides and find they are strongly enhanced in comparison with mean-field densities. We use spin projection methods to calculate nuclear level densities and average $s$-wave neutron resonance spacings, both of which are found to be in good agreement with experiments.