论文标题
$ d $ dimensions中性物质状态的方程式
Equation of State of Neutron-Rich Matter in $d$-Dimensions
论文作者
论文摘要
在约束下，具有高度对称性和/或集体的核系统可以被视为在空间维度降低的空间中有效移动。我们首先得出核子特异能量$ e_0（ρ）$，压力$ p_0（ρ）$的分析表达式，不可压缩系数$ k_0（ρ）$和偏度系数$ j_0（ρ）$ symmetric nucleonic Matter（snm），quadratic Symmetratic symmetration symmetry $ e _ $ e _参数$ l（ρ）$和曲率系数$ k _ {\ rm {sym}}（ρ）$以及第四阶对称能量$ e _ {\ rm {\ rm {sym，4}}（sym，4}}（ρ）中子的中子$ d $ d $ d $ d $ d $ d $ d $ d $ D.根据普遍的Hugenholtz-Van Hove（HVH）定理，依赖ISOSPIN的单核子潜力。 $ d $ d中核物质的状态（EOS）方程可以与$ε$ - expansion在常规的3维（3D）空间中相关联，这是以前在治疗二阶相变和相关关键现象中成功使用的一种扰动方法，而最近在研究冷eos的eos eos eos eos。基于参考维度$ d _ {\ rm {f}} = d-ε$在$ d $ d中对核EOS的$ε$ - $ d的$ -1 \ 1 \ 1 \lyssimε\ Lessim1 $从$ 1 \ 1 \ sillsim d _ {flyssim d _ {\ rmm {f} \ rm {f} \ rmm {f} \ rmm {定理。此外，发现SNM的EOS（不考虑其潜在部分）在较低（较高）维度中降低（增强），特别表明许多核心系统往往更深，但在较低维度的空间中，在较高的密度下饱和。 $ε$ - expansion从3D和$ d $ d的空间之间的链接为中子富裕物质的EOS提供了新的视角。
Nuclear systems under constraints, with high degrees of symmetries and/or collectivities may be considered as moving effectively in spaces with reduced spatial dimensions. We first derive analytical expressions for the nucleon specific energy $E_0(ρ)$, pressure $P_0(ρ)$, incompressibility coefficient $K_0(ρ)$ and skewness coefficient $J_0(ρ)$ of symmetric nucleonic matter (SNM), the quadratic symmetry energy $E_{\rm{sym}}(ρ)$, its slope parameter $L(ρ)$ and curvature coefficient $K_{\rm{sym}}(ρ)$ as well as the fourth-order symmetry energy $E_{\rm{sym,4}}(ρ)$ of neutron-rich matter in general $d$ spatial dimensions (abbreviated as "$d$D") in terms of the isoscalar and isovector parts of the isospin-dependent single-nucleon potential according to the generalized Hugenholtz-Van Hove (HVH) theorem. The equation of state (EOS) of nuclear matter in $d$D can be linked to that in the conventional 3-dimensional (3D) space by the $ε$-expansion which is a perturbative approach successfully used previously in treating second-order phase transitions and related critical phenomena and more recently in studying the EOS of cold atoms. The $ε$-expansion of nuclear EOS in $d$D based on a reference dimension $d_{\rm{f}}=d-ε$ is shown to be effective with $-1\lesssimε\lesssim1$ starting from $1\lesssim d_{\rm{f}}\lesssim3$ in comparison with the exact expressions derived using the HVH theorem. Moreover, the EOS of SNM (with/without considering its potential part) is found to be reduced (enhanced) in lower (higher) dimensions, indicating in particular that the many-nucleon system tends to be deeper bounded but saturate at higher densities in spaces with lower dimensions. The links between the EOSs in 3D and $d$D spaces from the $ε$-expansion provide new perspectives to the EOS of neutron-rich matter.
