中文摘要：

在相对论平均场理论框架下研究非均匀核物质,自洽的Thomas-Fermi近似是一种有效的方法。这种方法假设了非均匀核物质是由原子核及核外中子气和质子气构成。在温度T、质子分支比Yp以及重子密度ρB确定的情况下,通过改变Wigner-Seitz原胞半径,对系统的每重子自由能进行最小化,从而得到热力学稳定态,原胞内的重子分布也可以自洽地得到。由自洽的Thomas-Fermi近似得到的结果可以与之前工作所得到的结果进行详细比较,之前的工作所采用的是参数化的Thomas-Fermi近似方法。

英文摘要：

Background： The self-consistent Thomas-Fermi approximation has been widely used in atomic and nuclear physics. Many properties of nuclei can be described by the Thomas-Fermi approximation in good agreement with experimental data. Purpose： We studied the non-uniform nuclear matter using the self-consistent Thomas-Fermi approximation with a relativistic mean-field model. Methods： The non-uniform matter was assumed to be composed of a lattice of heavy nuclei surrounded by dripped nucleons. We determined the thermodynamically favored state by minimizing the free energy density with respect to the radius of the Wigner-Seitz cell, while the nucleon distribution in the cell was determined self-consistently in the Thomas-Fermi approximation. Results： A detailed comparison is made between the present results and previous calculations in the Thomas-Fermi approximation with a parameterized nucleon distribution that has been adopted in the widely-used-Shen-EOS （equation of state）. Conclusion： It has been found that there is no obvious difference in nucleon distributions at lower densities, while the difference becomes noticeable near the transition density to uniform matter. For thermodynamical quantities, such as the free energy and entropy per baryon, the results of both methods generally agree well with each other.