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We construct new equations of state for baryons at sub-nuclear densities forthe use in core-collapse simulations of massive stars. The abundance of variousnuclei is obtained together with thermodynamic quantities. A model free energyis constructed, based on the relativistic mean field theory for nucleons andthe mass formula for nuclei with the proton number up to ~ 1000. Theformulation is an extension of the previous model, in which we adopted theliquid drop model to all nuclei under the nuclear statistical equilibrium. Wereformulate the new liquid drop model so that the temperature dependences ofbulk energies could be taken into account. Furthermore, we extend the region inthe nuclear chart, in which shell affects are included, by using theoreticalmass data in addition to experimental ones. We also adopt a quantum theoreticalmass evaluation of light nuclei, which incorporates the Pauli- and self-energyshifts that are not included in the ordinary liquid drop model. The pastaphases for heavy nuclei are taken into account in the same way as in theprevious model. We find that the abundances of heavy nuclei are modified by theshell effects of nuclei and temperature dependence of bulk energies. Thesechanges may have an important effect on the rates of electron captures andcoherent neutrino scatterings on nuclei in supernova cores. The abundances oflight nuclei are also modified by the new mass evaluation, which may affect theheating and cooling rates of supernova cores and shocked envelopes.

New equations of state based on the liquid drop model of heavy nuclei and quantum approach to light nuclei for core-collapse supernova simulations