A new equation of state with abundances of all nuclei in core collapse simulations of massive stars

We construct the equations of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The abundance of various nuclei is obtained together with the ther-modynamic quantities. The formulation is the NSE description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with the atomic number up to ∼ 1000. We have also taken into account the pasta phase for heavy nuclei and the contribution of Pauli energies between free nucleons to binding energies to light nuclei. The experimental and theoretical mass data are employed to evaluate the shell effects of nuclei. We find that the abundance of heavy nuclei is different depending on shell effects of nuclei, which may have an important effect to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. The Pauli and self energy shifts also affect the abundance of light nuclei by comparing with ordinary nuclear statistical equilibrium results, which may affect the heating and cooling rates of supernova cores and shocked envelopes.