Higher-order effects on the incompressibility of isospin asymmetric nuclear matter
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abstract
Analytical expressions for the saturation density of asymmetric nuclear matter as well as its binding energy and incompressibility at saturation density are given up to fourth order in the isospin asymmetry =(n-p)/ using 11 characteristic parameters defined by the density derivatives of the binding energy per nucleon of symmetric nuclear matter, the symmetry energy Esym (), and the fourth-order symmetry energy Esym,4() at normal nuclear density 0. Using an isospin- and momentum-dependent modified Gogny interaction (MDI) and the Skyrme-Hartree-Fock (SHF) approach with 63 popular Skyrme interactions, we have systematically studied the isospin dependence of the saturation properties of asymmetric nuclear matter, particularly the incompressibility Ksat()=K0+Ksat,22+Ksat,44+O(6) at saturation density. Our results show that the magnitude of the higher order Ksat,4 parameter is generally small compared to that of the Ksat,2 parameter. The latter essentially characterizes the isospin dependence of the incompressibility at saturation density and can be expressed as Ksat,2=Ksym-6L-J0K0L, where L and Ksym represent, respectively, the slope and curvature parameters of the symmetry energy at 0 and J0 is the third-order derivative parameter of symmetric nuclear matter at 0. Furthermore, we have constructed a phenomenological modified Skyrme-like (MSL) model that can reasonably describe the general properties of symmetric nuclear matter and the symmetry energy predicted by both the MDI model and the SHF approach. The results indicate that the higher order J0 contribution to Ksat,2 generally cannot be neglected. In addition, it is found that there exists a nicely linear correlation between Ksym and L as well as between J0/K0 and K0. These correlations together with the empirical constraints on K0,L,Esym (0), and the nucleon effective mass lead to an estimate of Ksat,2=-370120 MeV. 2009 The American Physical Society.
