Heat capacity of low-density neutron matter: from quantum to classical regimes

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 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 ≤ T_sf. In the non-superfluid phase, T ≥ T_sf, the linear approximation is valid only at temperature T ≪ T_Fn (T_Fn 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_Fn, and the neutron number density n_n, can be easily implemented in neutron-star cooling simulations.