The entrainment matrix of a superfluid nucleon mixture at finite temperatures

TL;DR

This paper derives and solves equations for the entrainment matrix in superfluid nucleon mixtures at finite temperatures, accounting for temperature-dependent energy gaps and pairing states, with practical formulas provided.

Contribution

It presents an analytic solution near the critical temperature and numerical solutions with fitting formulas for the entrainment matrix in superfluid nucleon mixtures.

Findings

Analytic solution near the neutron superfluid transition temperature.

Numerical solutions for arbitrary temperatures.

Practical formulas for the entrainment matrix using Landau parameters.

Abstract

It is considered a closed system of non-linear equations for the entrainment matrix of a non-relativistic mixture of superfluid nucleons at arbitrary temperatures below the onset of neutron superfluidity, which takes into account the essential dependence of the superfluid energy gap in the nucleon spectra on the velocities of superfluid flows. It is assumed that the protons condense into the isotropic $^1$S$_0$ state, and the neutrons are paired into the spin-triplet $^3$P$_2$ state. It is derived an analytic solution to the non-linear equations for the entrainment matrix under temperatures just below the critical value for the neutron superfluidity onset. In general case of an arbitrary temperature of the superfluid mixture the non-linear equations are solved numerically and fitted by simple formulas convenient for a practical use with an arbitrary set of the Landau parameters.