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arXiv 0905.4323nucl-thastro-ph.SRnucl-ex
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同位旋非对称核物质不可压缩性的高阶效应

Higher-order effects on the incompressibility of isospin asymmetric nuclear matter

Lie-Wen Chen, Bao-Jun Cai, Che Ming Ko, Bao-An Li, Chun Shen, Jun Xu

备注：
61 pages, 12 figures, 6 Tables. Title changed a little and results of several Skyrme interactions updated. Accepted version to appear in PRC
发表信息：
Phys.Rev.C80:014322,2009
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摘要：

本文利用正常核密度ρ_0下定义的11个特征参数，在同位旋不对称性δ =（rho_n-rho_p）/rho下，精确地给出了不对称核物质的饱和密度、饱和密度下的结合能和不可压缩性的四阶解析表达式。本文利用修正的Gogny（MDI）相互作用和63种常用Skyrme相互作用的SHF方法，系统地研究了非对称核物质饱和性质的同位旋依赖性，特别是饱和密度下的不可压缩性$K_{sat}(δ)=K_{0}+K_{sat,2}δ^{2}+K_{sat,4}δ^{4}+O(δ^{6})$.我们的研究结果表明，高阶$K_{sat,4}$参数的幅度一般是小的相比，$K_{\sat,2}$参数。后者本质上表征了饱和密度下不可压缩性的同位旋依赖性，可以表示为$K_{sat,2}=K_{sym}-6L-\frac{J_{0}}{K_{0}}L$。此外，我们构造了一个唯象修正的类Skyrme（MSL）模型，该模型能合理地描述对称核物质的一般性质和由MDI模型和SHF方法预测的对称能。结果表明，高阶$J_{0}$对$K_{sat,2}$的贡献一般不能忽略。此外，还发现$K_{sym}$和$L$之间以及$J_{0}/K_{0}$和$K_{0}$之间存在很好的线性相关性。这些相关性与$K_{0}$，$L$，$E_{sym}(ρ_{0})$和核子有效质量的经验约束一起导致$K_{sat,2}=-370\pm 120$ MeV的估计。

英文摘要：

Analytical expressions for the saturation density as well as the binding energy and incompressibility at the saturation density of asymmetric nuclear matter are given exactly up to 4th-order in the isospin asymmetry delta =(rho_n - rho_p)/rho using 11 characteristic parameters defined at the normal nuclear density rho_0. Using an isospin- and momentum-dependent modified Gogny (MDI) interaction and the 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 $K_{sat}(δ)=K_{0}+K_{sat,2}δ^{2}+K_{sat,4}δ^{4}+O(δ^{6})$ at the saturation density. Our results show that the magnitude of the high-order $K_{sat,4}$ parameter is generally small compared to that of the $K_{\sat,2}$ parameter. The latter essentially characterizes the isospin dependence of the incompressibility at the saturation density and can be expressed as $K_{sat,2}=K_{sym}-6L-\frac{J_{0}}{K_{0}}L$, Furthermore, we have constructed a phenomenological modified Skyrme-like (MSL) model which 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 high-order $J_{0}$ contribution to $K_{sat,2}$ generally cannot be neglected. In addition, it is found that there exists a nicely linear correlation between $K_{sym}$ and $L$ as well as between $J_{0}/K_{0}$ and $K_{0}$. These correlations together with the empirical constraints on $K_{0}$, $L$, $E_{sym}(ρ_{0})$ and the nucleon effective mass lead to an estimate of $K_{sat,2}=-370\pm 120$ MeV.

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