Phase transitions of dense neutron matter with generalized Skyrme interaction to superfluid states with triplet pairing in strong magnetic field

Abstract

A generalized non-relativistic Fermi-liquid approach was used to find analytical formulas for temperatures Tc1(n, H) and Tc2(n, H) (which are functions nonlinear of density n and linear of magnetic field H) of phase transitions in spatially uniform dense pure neutron matter from normal to superfluid states with spin-triplet p-wave pairing (similar to anisotropic superfluid phases 3He-A1 and 3He-A2) in steady and homogeneous strong magnetic field (but |μn| H ≪ Ec < ∊F(n), where μn is the magnetic dipole moment of a neutron, Ec is the cutoff energy and ∊F(n) is the Fermi energy in neutron matter). General formulas for Tc1, 2 (n, H) (valid for arbitrary parameterization of the effective Skyrme interaction in neutron matter) are specified here for generalized BSk18 parameterization of the Skyrme forces (with additional terms dependent on density n) on the interval 0.3 n0 < n < nc (BSk18) ≍ 2.7952 · n0, where n0 = 0.17 fm−3 is nuclear density and at critical density nc(BSk18) triplet superfluidity disappears, Tc0(n, cH = 0) = 0. Expressions for phase transition temperatures Tc0(n)<0.09MeV (at Ec = 10MeV) and Tc1, 2(n, H) are realistic non-monotone functions of density n for BSk18 parameterization of the Skyrme forces (contrary to their monotone increase for all previous BSk parameterizations). Phase transitions to superfluid states of such type might occur in liquid outer core of magnetars (strongly magnetized neutron stars).