Liquid-gas and superconducting phase transitions of nuclear matter calculated with real time Green’s function methods and Skyrme interactions

Real-time finite temperature Green’s function methods with pair cutoff approximations are applied to the calculation of the equation of state of symmetric nuclear matter. The liquid-gas and the superconducting second-order phase transitions of nuclear matter are studied using, respectively, the normal and abnormal pair cutoff approximations. Several versions of the Skyrme effective interactions are employed. Significant differences are found between the pressure-density isotherms at finite temperature given by different Skyrme interactions, although they give quite similar ground state nuclear matter properties. The critical temperatures $k_B$ $T_c^{\mathrm{}\left(1\right)\mathrm{}}$ for the liquid-gas phase transition given by various Skyrme interactions range from ∼15 to ∼20 MeV. A strong dependence of $k_B$ $T_c^{\mathrm{}\left(1\right)\mathrm{}}$ on the combination 3$t_1$+5$t_2$, $t_1$ and $t_2$ being two parameters of the Skyrme interaction, is observed. For nuclear matter at normal density, nonvanishing energy gap is obtained only for the Skyrme interactions SkI and SkVI. The critical temperatures for the superconducting second-order phase transitions for these two cases are, respectively, 0.5 and 0.345 MeV. Dependence of the energy gap on the nuclear matter density is discussed.