密度相关协变密度泛函中介质平衡约束下的统一核物质物态方程
Unified nuclear matter EOSs constrained by the in-medium balance in density-dependent covariant density functionals
摘要：
考虑到电荷屏蔽效应，我们在T-F近似的框架下提出了一种新的数值计算方法，该方法可以自洽地计算核物质在很大密度范围内的性质.假设球形和圆柱形近似的Wigner-Seitz细胞，观察到典型的核物质结构（液滴，棒，板，管，气泡，和均匀）。然后我们研究了质子分数固定和$β$平衡下的核物质的能级结构和微观结构，其中采用了两个协变密度泛函DD-LZ 1和DD-ME 2.尽管DD-LZ 1得到的对称能斜率$L$较小，但曲率参数$K_\mathrm{sym}$远大于DD-ME 2，这是由于有限核中费米能级附近赝自旋对称性的恢复所导致的介子-核子耦合的特殊密度依赖行为.因此，这两种泛函预言了中子星不同的质量-半径关系。得到了非均匀核物质的不同微观结构，这些结构可能影响中子星性质和演化中的各种物理过程。
英文摘要：
Considering the effects of charge screening, we propose a new numerical recipe within the framework of Thomas-Fermi approximation, where the properties of nuclear matter throughout a vast density range can be obtained self-consistently. Assuming spherical and cylindrical approximations for the Wigner-Seitz cell, typical nuclear matter structures (droplet, rod, slab, tube, bubble, and uniform) are observed. We then investigate the EOSs and microscopic structures of nuclear matter with both fixed proton fractions and $β$-equilibration, where two covariant density functionals DD-LZ1 and DD-ME2 are adopted. Despite the smaller slope $L$ of symmetry energy obtained with the functional DD-LZ1, the curvature parameter $K_\mathrm{sym}$ is much larger than that of DD-ME2, which is attributed to the peculiar density-dependent behavior of meson-nucleon couplings guided by the restoration of pseudo-spin symmetry around the Fermi levels in finite nuclei. Consequently, different mass-radius relations of neutron stars are predicted by the two functionals. Different microscopic structures of nonuniform nuclear matter are obtained as well, which are expected to affect various physical processes in neutron star properties and evolutions.
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