  We construct new 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 thermodynamic quantities. A model free energy
is constructed, based on the relativistic mean field theory for nucleons and
the mass formula for nuclei with the proton number up to ~ 1000. The
formulation is an extension of the previous model, in which we adopted the
liquid drop model to all nuclei under the nuclear statistical equilibrium. We
reformulate the new liquid drop model so that the temperature dependences of
bulk energies could be taken into account. Furthermore, we extend the region in
the nuclear chart, in which shell affects are included, by using theoretical
mass data in addition to experimental ones. We also adopt a quantum theoretical
mass evaluation of light nuclei, which incorporates the Pauli- and self-energy
shifts that are not included in the ordinary liquid drop model. The pasta
phases for heavy nuclei are taken into account in the same way as in the
previous model. We find that the abundances of heavy nuclei are modified by the
shell effects of nuclei and temperature dependence of bulk energies. These
changes may have an important effect on the rates of electron captures and
coherent neutrino scatterings on nuclei in supernova cores. The abundances of
light nuclei are also modified by the new mass evaluation, which may affect the
heating and cooling rates of supernova cores and shocked envelopes.
