Using phenomenological equations of state, we study the chemical andmechanical instabilities in hot isospin-asymmetric nuclear matter. Bothinstabilities are found to depend strongly on the isospin asymmetry of thenuclear matter. For a chemically and mechanically stable asymmetric nuclearmatter, a lower neutron excess is found in the liquid phase than in the gasphase. Furthermore, the neutron excess in the mixed phase at densities betweenthat of the liquid and the gas phases is limited by certain maximum value.Also, for the nuclear equations of state considered here the boundary ofchemical instability in the pressure-density plane is found to be more extendedthan that of mechanical instability. However, locations of these boundariesdepend sensitively on both the bulk compressibility of nuclear matter and thedensity dependence of the symmetry energy.
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