LAUSR

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 $${{\boldsymbol{T}}}_{{\bf{c}}}^{{\bf{n}}{\bf{n}}}$$Tcnn of the neutron superfluidity at Yp = 0 agrees well with Monte Carlo data at low densities and takes a maximum value $${{\boldsymbol{T}}}_{{\bf{c}}}^{{\bf{n}}{\bf{n}}}$$Tcnn= 1.68 MeV at $${\boldsymbol{\rho }}{\boldsymbol{/}}{{\boldsymbol{\rho }}}_{{\bf{0}}}{\boldsymbol{=}}{\bf{0.14}}$$ρ/ρ0=0.14 with ρ0 = 0.17 fm−3. Also, the critical temperature $${{\boldsymbol{T}}}_{{\bf{c}}}^{{\bf{n}}{\bf{n}}}$$Tcnn of the proton superconductivity for Yp ≤ 0.2 is substantially suppressed at low densities due to np-pairing fluctuations, and starts to dominate over $${{\boldsymbol{T}}}_{{\bf{c}}}^{{\bf{n}}{\bf{n}}}$$Tcnn only above $${\boldsymbol{\rho }}{\boldsymbol{/}}{{\boldsymbol{\rho }}}_{{\bf{0}}}{\boldsymbol{=}}{\bf{0.70}}$$ρ/ρ0=0.70(0.77) for Yp = 0.1(0.2), and (iii) the deuteron condensation temperature $${{\boldsymbol{T}}}_{{\bf{c}}}^{{\bf{d}}}$$Tcd is suppressed at Yp ≤ 0.2 due to a large mismatch of the two Fermi surfaces.