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

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.