Reassessing nuclear matter incompressibility and its density dependence

Experimental giant monopole resonance energies are now known to constrain nuclear incompressibility of symmetric nuclear matter $K$ and its density slope $M$ at a particular value of subsaturation density, the crossing density ${\rho }_c$. Consistent with these constraints, we propose a reasonable way to construct a plausible equation of state of symmetric nuclear matter in a broad density region around the saturation density ${\rho }_0$. Help of two additional empirical inputs, the value of ${\rho }_0$ and that of the energy per nucleon $e\left({\rho }_0\right)$ are needed. The value of $K\left({\rho }_0\right)$ comes out to be $211.9\pm 24.5$ MeV.

Figure 1

The sensitivity of the incompressibility $K_0$ at the saturation density $\left({\rho }_0\right)$ on the values of the incompressibility $K_c$ (green dash-dotted line), its density slope $M_c$ (red dashed line), the crossing density ${\rho }_c$ (blue dotted line), and the value of ${\rho }_0$ (black full line). The abscissa extends from $-1$ to +1. These endpoints refer to the scaled lower and upper limits of $K_c,M_c,{\rho }_c$, and ${\rho }_0$, respectively (see text).

Figure 2

The incompressibility and its different density derivative as defined in the text plotted as a function of $M_c$.

Figure 3

The nuclear EOS as a function of density. Panels (a) and (b) show the energy per nucleon and pressure, respectively, in a selected range around the saturation density.

Figure 4

The nuclear EOS as a function of density. Panels (a) and (b) show the incompressibility and its density derivative $M$, respectively, in a selected range around the saturation density.