Abstract
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.
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