Two-body contributions to the effective mass in nuclear effective interactions

TL;DR

This paper analyzes how two-body interactions influence the effective mass in nuclear matter, demonstrating that additional interaction terms are necessary to match empirical effective mass values.

Contribution

It derives the two-body contributions to the effective mass in nuclear interactions and shows the necessity of including density-dependent terms for realistic values.

Findings

Two-body contributions alone yield an effective mass around 0.4.

Full interactions with density dependence are needed for effective mass around 0.7-0.8.

Two-body effects correctly describe the saturation mechanism.

Abstract

Starting from general expressions of well-chosen symmetric nuclear matter quantities derived for both zero- and finite-range effective theories, we derive the contributions to the effective mass. We first show that, independently of the range, the two-body contribution is enough to describe correctly the saturation mechanism but gives an effective mass value around $m^*/m \simeq 0.4$. Then, we show that the full interaction (by instance, an effective two-body density-dependent term on top of the pure two-body term) is needed to reach the accepted value $m^*/m \simeq 0.7-0.8$.