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 (ρ) with a low proton fraction (Yp ≤ 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 phase shifts of neutron-neutron (nn), proton-proton (pp) and neutron-proton (np) interactions up to k = 2 fm−1 are described by multi-rank separable potentials. We show that the critical temperature Tcnn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{T}}}_{{\bf{c}}}^{{\bf{n}}{\bf{n}}}$$\end{document} of the neutron superfluidity at Yp = 0 agrees well with Monte Carlo data at low densities and takes a maximum value Tcnn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{T}}}_{{\bf{c}}}^{{\bf{n}}{\bf{n}}}$$\end{document}= 1.68 MeV at ρ/ρ0=0.14\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\rho }}{\boldsymbol{/}}{{\boldsymbol{\rho }}}_{{\bf{0}}}{\boldsymbol{=}}{\bf{0.14}}$$\end{document} with ρ0 = 0.17 fm−3. Also, the critical temperature Tcnn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{T}}}_{{\bf{c}}}^{{\bf{n}}{\bf{n}}}$$\end{document} of the proton superconductivity for Yp ≤ 0.2 is substantially suppressed at low densities due to np-pairing fluctuations, and starts to dominate over Tcnn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{T}}}_{{\bf{c}}}^{{\bf{n}}{\bf{n}}}$$\end{document} only above ρ/ρ0=0.70\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\rho }}{\boldsymbol{/}}{{\boldsymbol{\rho }}}_{{\bf{0}}}{\boldsymbol{=}}{\bf{0.70}}$$\end{document}(0.77) for Yp = 0.1(0.2), and (iii) the deuteron condensation temperature Tcd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{T}}}_{{\bf{c}}}^{{\bf{d}}}$$\end{document} is suppressed at Yp ≤ 0.2 due to a large mismatch of the two Fermi surfaces.