Incompressibility of asymmetric nuclear matter

The incompressibility $K_sat(\delta)$ of isospin asymmetric nuclear matter at its saturation density. Our results show that in the expansion of $K_sat(\delta)$ in powers of isospin asymmetry $\delta$, i.e., $K_sat(\delta )$=K_{0}+K_{sat,2}\delta^{2}+K_{sat,4}\delta^{4}+O(\delta^{6}), the magnitude of the 4th-order K_{sat,4} parameter is generally small. The 2nd-order K_{sat,2} parameter thus essentially characterizes the isospin dependence of the incompressibility of asymmetric nuclear matter at saturation density. Furthermore, the K_{sat,2} can be expressed as K_{sat,2}=K_{sym}-6L-J_{0}/{K_{0}L in terms of the slope parameter L$and the curvature parameter$K_{\mathrm{sym}}$of the symmetry energy and the third-order derivative parameter$J_0$of the energy of symmetric nuclear matter at saturation density, and we find the higher order$J_0$contribution to K_{sat,2} generally cannot be neglected. Also, we have found a linear correlation between K_{sym} and$L$as well as between$J_{0}/K_{0}$and$K_{0}$. Using these correlations together with the empirical constraints on$K_{0}$and$L$, the nuclear symmetry energy$E_sym(\rho_{0})$ at normal nuclear density, and the nucleon effective mass, we have obtained an estimated value of K_{sat,2}=-370 +- 120 MeV for the 2nd-order parameter in the isospin asymmetry expansion of the incompressibility of asymmetric nuclear matter at its saturation density.