The energy levels of a nucleus and their spin distribution

The density of levels is an important ingredient in nuclear reactions, especially neutron capture reactions, which are needed to determine the abundance of elements. Experimentally, the density of levels is known mainly for nuclei close to stability. Historically, empirical models have been used to predict the density of levels with parameters that must be fitted to experimental data. These empirical models also rely on an empirical formula of the spin distribution of the density of levels to derive spin dependent densities of levels. Here, we present a methodology for calculating spin dependent densities of level based on the shell model. We also present calculations of the spin distribution of the density of levels.