Level density of the $sd$-nuclei $-$ statistical shell-model predictions

TL;DR

This paper employs the configuration-interaction shell model and the moments method to predict nuclear level densities in $sd$-shell nuclei, providing data useful for nuclear structure studies and astrophysical applications.

Contribution

It introduces a statistical moments method for calculating level densities in $sd$-shell nuclei, avoiding large-scale diagonalizations and fitting a phenomenological model for practical use.

Findings

Level densities computed for all $sd$-shell nuclei and spins.

The moments method results agree with traditional shell-model calculations.

Fitted parameters for the Constant Temperature model for nuclear reactions.

Abstract

Accurate knowledge of the nuclear level density is important both from a theoretical viewpoint as a powerful instrument for studying nuclear structure and for numerous applications. For example, astrophysical reactions responsible for the nucleosynthesis in the universe can be understood only if we know the nuclear level density. We use the configuration-interaction nuclear shell model to predict nuclear level density for all nuclei in the $sd$-shell, both total and for individual spins (only with positive parity). To avoid the diagonalization in large model spaces we use the moments method based on statistical properties of nuclear many-body systems. In the cases where the diagonalization is possible, the results of the moments method practically coincide with those from the shell-model calculations. Using the computed level densities, we fit the parameters of the Constant Temperature phenomenological model, which can be used by practitioners in their studies of nuclear reactions at excitation energies appropriate for the $sd$-shell nuclei.