Skyrme interaction to second order in nuclear matter

TL;DR

This paper calculates nuclear matter properties using the Skyrme interaction up to second order, revealing inaccuracies in previous results and emphasizing the importance of density-dependent terms for realistic modeling.

Contribution

It provides a corrected second-order calculation of nuclear matter properties with Skyrme interaction, highlighting the necessity of density-dependent terms for accurate saturation behavior.

Findings

Published second-order contributions are often incorrect.

Interference terms affect asymmetry energies only.

Density-dependent term is crucial for realistic saturation curve.

Abstract

Based on the phenomenological Skyrme interaction various density-dependent nuclear matter quantities are calculated up to second order in many-body perturbation theory. The spin-orbit term as well as two tensor terms contribute at second order to the energy per particle. The simultaneous calculation of the isotropic Fermi-liquid parameters provides a rigorous check through the validity of the Landau relations. It is found that published results for these second order contributions are incorrect in most cases. In particular, interference terms between $s$-wave and $p$-wave components of the interaction can contribute only to (isospin or spin) asymmetry energies. Even with nine adjustable parameters, one does not obtain a good description of the empirical nuclear matter saturation curve in the low density region $0<\rho<2\rho_0$. The reason for this feature is the too strong density-dependence $\rho^{8/3}$ of several second-order contributions. The inclusion of the density-dependent term ${1\over 6}t_3 \rho^{1/6}$ is therefore indispensable for a realistic description of nuclear matter in the Skyrme framework.