Thermodynamical properties and Coulomb instabilities in hot nuclear systems with the Gogny interaction

The thermodynamical properties and Coulomb instability in hot nuclear system with Gogny interactions are studied by using the finite-temperature real-time Green's function method. The isotherms, critical temperature, limiting temperature, saturation density, and isothermal incompressibility for various temperatures and different asymmetric parameters are calculated. To illustrate the importance of the finite-range part and density-dependence part of the interaction, we have compared our results with that given by the Skyrme interaction and Brink-Boeker interaction.