Shell effects in hot nuclei and their influence on nuclear composition in supernova matter

We calculate nuclear composition in supernova (SN) matter explicitly taking into account the temperature dependence of nuclear shell effects. The abundance of nuclei in SN matter is important in the dynamics of core-collapse supernovae and, in recently constructed equations of state (EOS) for SN matter, the composition of nuclei are calculated assuming nuclear statistical equilibrium wherein the nuclear internal free energies govern the composition. However, in these EOS, thermal effects on the shell energy are not explicitly taken into account. To address this shortfall, we calculate herein the shell energies of hot nuclei and examine their influence on the composition of SN matter. Following a simplified macroscopic-microscopic approach, we first calculate single-particle (SP) energies by using a spherical Woods-Saxon potential. Then we extract shell energies at finite temperatures using Strutinsky method with the Fermi distribution as the average occupation probability of the SP levels. The results show that at relatively low temperatures, shell effects are still important and magic nuclei are abundant. However, at temperatures above approximately 2 MeV, shell effects are almost negligible, and the mass fractions with shell energies including the thermal effect are close to those obtained from a simple liquid drop model at finite temperatures.