Abundance distribution of heavy nuclides up to a subnuclear density and the equation of state for gravitationally collapsing stars

Abstract

With the use of the empirical equations for the binding and internal energies of heavy nuclides with density dependence, the abundance distribution of neutron-excess nuclides which appear up to some subnuclear density along the collapsing trajectory of a stellar core is calculated with an assumption of the β-equilibrium condition. Free nucleons are simply assumed to be non-interacting, degenerate fermions. Using the abundance distribution thus derived, the quantities affecting the hydrodynamics of the core, such as the average mass number and the mass fraction of heavy nuclides, the mass fraction of free neutrons, the number of electrons per baryon, the average excitation energy per nucleus, and the entropy, the pressure and the adiabatic index of the system are then calculated. It is found that we can obtain fairly reliable values of these physical quantities by introducing only the magic and near-magic number nuclides in the calculation, and that the results are hardly affected by the difference of the semi-empirical nuclear mass formula we use to derive the binding energies of unknown nuclides and the formula of the grand partition function of these nuclides.