Shell Structure and the Thomas-Fermi Equation of State

Abstract

The calculation of the electronic contribution to the equation of state of high-temperature, high-density matter by means of Thomas-Fermi theory is modified to include the effect of shell structure. Shell structure is included by accounting for the discrete nature of the energy levels of the bound states. The free states are treated by means of Thomas-Fermi theory. Comparisons are made between Thomas-Fermi (TF) theory and Thomas-Fermi shell (TFS) theory. The pressure and energy calculated by means of TFS theory vary about those calculated by means of TF theory, and for some temperatures and densities they are substantially different even at pressures far in excess of the 100-Mbar region where TF theory is generally thought to be applicable.