Liquid-gas and superconducting phase transitions in finite symmetric nuclear matter

Real-time finite-temperature Green’s-function methods with a normal pair cutoff approximation and an abnormal pair cutoff approximation are applied to the calculation of liquid-gas and superconducting phase transitions of finite nuclear matter. Finite-size effects are found to lead to a sizable reduction of the critical temperature of the liquid-gas phase transition (6 MeV) as compared to the case of infinite nuclear matter. A critical number of nucleons $N_c$ as well as a critical volume $V_c$ are found. Under the condition N$N_c$ (or V$V_c$) the superconducting phase disappears. Dependence of the energy gap for the finite nuclear matter with different sizes is discussed.