Supernova equations of state including full nuclear ensemble with in-medium effects

Abstract: We construct new equations of state for baryons at sub-nuclear densities for the use in core-collapse supernova simulations. The abundance of various nuclei is obtained together with thermodynamic quantities. The formulation is an extension of the previous model, in which we adopted the relativistic mean field theory with the TM1 parameter set for nucleons, the quantum approach for $d$, $t$, $h$ and $\alpha$ as well as the liquid drop model for the other nuclei under the nuclear statistical equilibrium. We reformulate the model of the light nuclei other than $d$, $t$, $h$ and $\alpha$ based on the quasi-particle description. Furthermore, we modify the model so that the temperature dependences of surface and shell energies of heavy nuclei could be taken into account. The pasta phases for heavy nuclei and the Pauli- and self-energy shifts for $d$, $t$, $h$ and $\alpha$ are taken into account in the same way as in the previous model. We find that nuclear composition is considerably affected by the modifications in this work, whereas thermodynamical quantities are not changed much. In particular, the washout of shell effect has a great impact on the mass distribution above $T \sim 1$ MeV. This improvement may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores.