Judd, David Michael

A realistic equation of state is essential for accurate modeling of stellar core collapse. In this thesis, we present a derivation of the equation of state for stellar matter up to nuclear density. We begin with the lepton contribution to the equation of state. The thermodynamic equations of state for the leptons are derived from the grand potential. Two approximations for the lepton equations of state which obtain in different regimes are presented. A discussion of the computer programs that were developed to calculate the solutions to these equations is included, and the results are compared with those of similar programs. A formalism is introduced for treating the nuclear component of the equation of state. The energy per baryon of nuclei at zero temperature is derived using a compressible liquid drop model. Finite temperature effects are incorporated by (1) including the thermal excitation energy, and (2) by introducing a second phase (the drip phase) of like particles (neutrons, protons, and $\alpha$-particles) that coexist with the nuclei. Equilibrium conditions for the two phases and the nuclear mass number A are derived. Expressions for the nuclear thermodynamic quantities of interest are presented.