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

Abstract

We investigate superfluid phase transitions of asymmetric nuclear matter at finite temperature ($T$) and density ($\rho$) with a low proton fraction ($Y_{\mathrm{p}}\le 0.2$) 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 $k=2$ ${\mathrm{fm}}^{-1}$ are described by multi-rank separable potentials. We show that (i) the critical temperature of the neutron superfluidity $T_{\mathrm{c}}^{\mathrm{nn}}$ at $Y_{\mathrm{p}}=0$ agrees well with Monte Carlo data at low densities and takes a maximum value $T_{\mathrm{c}}^{\mathrm{nn}}=1.68$ MeV at $\rho /{\rho }_0=0.14$ with ${\rho }_0=0.17$ fm${}^{-3}$, (ii) the critical temperature of the proton superconductivity $T_{\mathrm{c}}^{\mathrm{pp}}$ for $Y_{\mathrm{p}}\le 0.2$ is substantially suppressed at low densities due to np-pairing fluctuations and starts to dominate over $T_{\mathrm{c}}^{\mathrm{nn}}$ only above $\rho /{\rho }_0=0.70$ $(0.77)$ for $Y_p=0.1$ $(0.2)$, and (iii) the deuteron condensation temperature $T_{\mathrm{c}}^{\mathrm{d}}$ is suppressed at $Y_{\mathrm{p}}\le 0.2$ due to the large mismatch of the two Fermi surfaces.

23 pages, 12 figures

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