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 some universal relations between them. 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 $m^{*}/m\simeq 0.4$ when the other properties of the saturation point are set near their generally accepted values. Then, we show that a more elaborated interaction (for instance, an effective two-body density-dependent term on top of the pure two-body term) is needed to reach the accepted value $m^{*}/m\simeq 0.7–0.8$.

Figure 1

The parameter $t_3$ plotted as a function of $\alpha$ for various sets of isoscalar bulk properties. In each case, one of the four bulk properties $K_{\infty }$, $m^{*}/m$, $E/A$, or ${\rho }_{\mathrm{sat}}$ is varied, keeping constant the three others (see text). The green triangle marks the ${\mathrm{SLy}5}^{*}$ parametrization [15].