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We investigate the high-temperature effect on the nuclear matter thatconsists of mixture of nucleons and all nuclei in the dense and hot stellarenvironment. The individual nuclei are described within the compressibleliquid-drop model that is based on Skyrme interactions for bulk energies andthat takes into account modifications of the surface and Coulomb energies atfinite temperatures and densities. The free-energy density is minimized withrespect to the individual equilibrium densities of all heavy nuclei and thenuclear composition. We find that their optimized equilibrium densities becomesmaller and smaller at high temperatures because of the increase of thermalcontributions to bulk free energies and the reduction of surface energies. Theneutron-rich nuclei become unstable and disappear one after another at sometemperatures. The calculations are performed for two sets of model parametersleading to different values of the slope parameter in the nuclear symmetryenergy. It is found that the larger slope parameter reduces the equilibriumdensities and the melting temperatures. We also compare the new model with someother approaches and find that the mass fractions of heavy nuclei in theprevious calculations that omit vaporization are underestimated at $T \lesssim10$MeV and overestimated at $T\gtrsim10$~MeV. The further sophistication ofcalculations of nuclear vaporization and of light clusters would be required toconstruct the equation of state for explosive astrophysical phenomena.

Equilibrium nuclear ensembles taking into account vaporization of hot nuclei in dense stellar matter