Second-order equation of state with the full Skyrme interaction: toward new effective interactions for beyond mean-field models

TL;DR

This paper develops a regularization strategy for second-order energy calculations in nuclear matter using the full Skyrme interaction, addressing divergences and enabling applications to finite nuclei.

Contribution

It extends a divergence treatment method to the full Skyrme interaction, facilitating beyond mean-field models in nuclear physics.

Findings

The divergence scales as Λ^5 due to velocity-dependent terms.

The cutoff regularization works for symmetric and asymmetric nuclear matter.

This approach enables future applications to finite nuclei.

Abstract

In a quantum Fermi system the energy per particle calculated at the second order beyond the mean-field approximation diverges if a zero-range interaction is employed. We have previously analyzed this problem in symmetric nuclear matter by using a simplified nuclear Skyrme interaction, and proposed a strategy to treat such a divergence. In the present work, we extend the same strategy to the case of the full nuclear Skyrme interaction. Moreover we show that, in spite of the strong divergence ($\sim$ $\Lambda^5$, where $\Lambda$ is the momentum cutoff) related to the velocity-dependent terms of the interaction, the adopted cutoff regularization can be always simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratio. This paves the way to applications to finite nuclei.