Energy and Pressure of a Zero-Temperature Plasma.

The equation of state is considered for matter consisting of electrons and nuclei of atomic weight A and charge Z, at zero temperature and at densities much larger than that of the solid at zero pressure Corrections are evaluated to the energy and pressure of a degenerate Fermi gas of non-interacting electrons, due to the following effects: (1) classical Coulomb energy of an ion lattice with uniformly distributed electrons (this is the biggest correction); (2) Thomas-Fermi deviations from uniform charge distribution of the electrons; and (3) exchange energy and spin-spin interactions between the electrons. The corrections increase with decreasing density, and the approximations break down when the spacing between nuclei is greater than the mean radius of the free Thomas-Fermi atom, and the formulae are not applicable to the interior of planets At very high densities, where the electrons are extremely relativistic, the correction to the pressure is a multiplying constant factor which is 0.994, 0 986, and 0.960, respectively, for Z = 2, 6, and 26. It is shown that the nuclei form a lattice rather than a gas At very high densities, restrictions are found on possible values for A and Z due to inverse beta decays and pycnonuclear reactions For instance, C" changes to Ne24 at densities above 6 X 10' gm/cc.