Incompressibility of asymmetric nuclear matter

Abstract

The incompressibility $K_{s}at(\delta )$ of isospin asymmetric nuclear matter at its saturation density. Our results show that in the expansion of $K_{s}at(\delta )$ in powers of isospin asymmetry $\delta$, i.e., $K_{s}at(\delta )$=K_{0}+K_{sat,2}δ^{2}+K_{sat,4}δ^{4}+O(δ^{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 $L$andthecurvatureparameter$K_{\mathrm{sym}}$ofthesymmetryenergyandthethird-orderderivativeparameter$J_0$oftheenergyofsymmetricnuclearmatteratsaturationdensity,andwefindthehigherorder$J_0$contributionto{K}_{sat,2}generallycannotbeneglected.Also,wehavefoundalinearcorrelationbetween{K}_{sym}and$L$aswellasbetween$J_{0}/K_{0}$and$K_{0}$.Usingthesecorrelationstogetherwiththeempiricalconstraintson$K_{0}$and$L$,thenuclearsymmetryenergy$E_sym(ρ_{0})$ 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.

11 pages, 3 figures. Conribution to The International Workshop on Nuclear Dynamics in Heavy-Ion Reactions and the Symmetry Energy (IWND2009), Shanghai, China, 22-25 August, 2009

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