Fermi-liquid theory of superfluid asymmetric nuclear matter

Influence of asymmetry on superfluidity of nuclear matter with triplet-singlet pairing of nucleons (in spin and isospin spaces) is considered within the framework of a Fermi-liquid theory. Solutions of self-consistent equations for the critical temperature and the energy gap at $T=0$ are obtained with the use of Skyrme effective nucleon interaction. It is shown that if the chemical potentials of protons and neutrons are determined in the approximation of ideal Fermi-gas, then the energy gap for some values of density and asymmetry parameter of nuclear matter demonstrates double-valued behavior. However, accounting for the feedback of pairing correlations through the normal distribution functions of nucleons, two-valued behavior of the energy gap turns into universal one-valued behavior. At $T=0$ superfluidity arises and disappears as a result of a first order phase transition in density.