# Superfluid Phase Transitions and Effects of Thermal Pairing Fluctuations in Asymmetric Nuclear Matter

## TL;DR

This paper studies superfluid phase transitions in asymmetric nuclear matter at finite temperature, revealing how proton fraction and pairing fluctuations influence critical temperatures for neutron and proton superfluidity relevant to neutron star interiors.

## Contribution

It extends a strong-coupling theory to four-component nuclear systems and provides detailed predictions of critical temperatures considering pairing fluctuations and asymmetry effects.

## Key findings

- Neutron superfluid critical temperature matches Monte Carlo data at low densities.
- Proton superconductivity is suppressed at low densities and dominates only at higher densities.
- Deuteron condensation is suppressed due to Fermi surface mismatch at low proton fractions.

## Abstract

We investigate superfluid phase transitions of asymmetric nuclear matter at finite temperature ($T$) and density ($\rho$) with a low proton fraction ($Y_{\rm p} \le 0.2$) which is relevant to the inner crust and outer core of neutron stars. A strong-coupling theory developed for two-component atomic Fermi gases is generalized to the four-component case and is applied to the system of spin-$1/2$ neutrons and protons. The empirical phase shifts of neutron-neutron (nn), proton-proton (pp) and neutron-proton (np) interactions up to $k = 2$ ${\rm fm}^{-1}$ are described by multi-rank separable potentials. We show that (i) the critical temperature of the neutron superfluidity $T_{\rm c}^{\rm nn}$ at $Y_{\rm p}=0$ agrees well with Monte Carlo data at low densities and takes a maximum value $T_{\rm c}^{\rm nn}=1.68$ MeV at $\rho/\rho_0 = 0.14$ with $\rho_0=0.17$ fm$^{-3}$, (ii) the critical temperature of the proton superconductivity $T_{\rm c}^{\rm pp}$ for $Y_{\rm p} \le 0.2$ is substantially suppressed at low densities due to np-pairing fluctuations and starts to dominate over $T_{\rm c}^{\rm nn}$ only above $\rho/\rho_0 = 0.70$ $(0.77)$ for $Y_p =0.1$ $(0.2)$, and (iii) the deuteron condensation temperature $T_{\rm c}^{\rm d}$ is suppressed at $Y_{\rm p}\le 0.2$ due to the large mismatch of the two Fermi surfaces.