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