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

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 $m^*/m \simeq 0.7-0.8$.