Analytical derivation of expressions for the specific heat of superfluid Fermi liquids with anisotropic spin-triplet p-wave pairing at finite temperatures

Abstract

Analytical expressions for the specific heat of superfluid Fermi liquids (SFLs) with anisotropic spin-triplet p-wave pairing of the 3He-A type have been obtained based on a generalised Fermi-liquid approach both at the low temperatures of 0 < T ≪Tc0 (n) and near the temperature of the phase transition [Tc0 (n)] from a normal to a superfluid phase in the absence of a magnetic field. Apart from liquid 3He-A, we also study dense superfluid neutron matter (SNM) with anisotropic spin-triplet p-wave pairing (similar to 3He-A) at subnuclear (n < n0, where n0 = 0.17 fm–3 is the nuclear density) and supernuclear densities (n > n0) in view of generalised Skyrme forces (with additional terms depending on the density n). At 0 < T ≪Tc0 (n), we have obtained an asymptotic expansion for the specific heat CSNM(SFL)(T,n), in which, apart from the main term ∼ T 3 (known for 3He-A in the limit of T → 0) there is an additional correction term (∼ T5), which may reach several percent of the contribution from the main term to the decomposition of the specific heat of SNM (or SFLs). An analytical formula has also been derived for calculating the specific heat CSNM(SFL)(T,n) at temperatures near Tc0(n). The expressions obtained for the CSNM(T,n) functions (valid for an arbitrary parametrisation of the effective Skyrme interaction in neutron matter) have been defined for SNM with the generalised BSk21 parametrisation of Skyrme forces. In addition, dependency graphs were plotted for the specific heat CBSk21(t, y) in the reduced temperature range of 0 < t ≡ T/Tc0(n) ≪ 1 and at t ≲ 1 for dense SNM (at 0.1 ≤ y ≡ n/n0 ≤ 1.7). These results may be of interest for neutron star physics in connection with neutron star cooling (in the presence of neutron superfluidity with anisotropic spin-triplet p-wave Cooper pairing in the outer part of dense liquid neutron star cores).