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 sub-saturation 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 $e({\rho }_0)$ are needed. The value of $K({\rho }_0)$ comes out to be $211.9\pm 24.5$ MeV.