低密度中子物质的Heat capacity：从量子到经典
Heat capacity of low density neutron matter: from quantum to classical regimes
摘要：
在中子星壳的密度和温度范围内研究了中子物质的热容量，允许在低于某个临界温度$T_{sf}$的温度下过渡到超流相，并包括过渡到经典极限。有限温度Hartree-Fock-Bogoliubov方程（FTHFB）求解，并与现有的近似表达式进行比较。特别是，Levenfish和Yakovlev给出的公式被发现重现的数值结果与温度$T\leq T_{sf}$的高精度。在非超流相$T\geq T_{sf}$中，线性近似仅在温度为$T\ll T_{{\rm F} n}$（$T_{{\rm F} n}$是中子气体的费米温度）时才有效，而在中子星地壳的浅层很少出现这种情况。在量子和经典制度之间的非微扰插值建议在这里。热容，方便地参数化的$T_{sf}$，$T_{{\rm F} n}$，和中子数密度$n_n$，可以很容易地实现在中子星冷却模拟。
英文摘要：
The heat capacity of neutron matter is studied over the range of densities and temperatures prevailing in neutron-star crusts, allowing for the transition to a superfluid phase at temperatures below some critical temperature $T_{sf}$ and including the transition to the classical limit. Finite temperature Hartree-Fock-Bogoliubov equations (FTHFB) are solved and compared to existing approximate expressions. In particular, the formula given by Levenfish and Yakovlev is found to reproduce the numerical results with a high degree of accuracy for temperatures $T\leq T_{sf}$. In the non-superfluid phase, $T\geq T_{sf}$, the linear approximation is valid only at temperature $T\ll T_{{\rm F} n}$ ($T_{{\rm F} n}$ being the Fermi temperature of the neutron gas) which is rarely the case in the shallow layers of the neutron star's crust. A non-perturbative interpolation between the quantal and the classical regimes is proposed here. The heat capacity, conveniently parametrized solely in terms of $T_{sf}$, $T_{{\rm F} n}$, and the neutron number density $n_n$, can be easily implemented in neutron-star cooling simulations.
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