Equation of state for a partially ionized gas. III.

The derivation of equations of state for fluid phases of a partially ionized gas or plasma is addressed from a fundamental point of view. The results of the Thomas-Fermi model always yield pressures which are less than or equal to that of an ideal Fermi gas. On the other hand, the spherical cellular model shows significant "overpressure" relative to the ideal Fermi gas in certain regions of low density and low temperature. This effect is studied in considerable detail. A nonthermodynamic region, more or less overlapping the regions of overpressure, is found. It is characterized by a negative specific heat at constant volume. An independent electron model within a Z -electron cell is employed. The inadequacy of the wave function in the low-density, low-temperature nonthermodynamic region is shown to be the cause of this overpressure. Numerical examples of the theory for several elements (Li, N, Al, K, and Er) are reported. These results reduce in various limits of temperature and density to the expected behavior, except in the aforementioned region.

Improved quantum hard-sphere ground-state equations of state.

The London ground-state energy formula as a function of number density for a system of identical boson hard spheres, corrected for the reduced mass of a pair of particles in a "sphere-of-influence" picture, and generalized to fermion hard-sphere systems with two and four intrinsic degrees of freedom, has a double-pole at the ultimate regular (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are constructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, extrapolated to intermediate densities via Padé and other approximants, but whose ultimate density is irregular or random closest close-packing as suggested in studies of a classical system of hard spheres. Results show substantially improved agreement with the best available Green-function Monte Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder, variational Fermi hypernetted chain, and so-called L -expansion data for two-component fermions.

Bose-Einstein condensation in the relativistic ideal Bose gas.

The Bose-Einstein condensation (BEC) critical temperature in a relativistic ideal Bose gas of identical bosons, with and without the antibosons expected to be pair-produced abundantly at sufficiently hot temperatures, is exactly calculated for all boson number densities, all boson point rest masses, and all temperatures. The Helmholtz free energy at the critical BEC temperature is lower with antibosons, thus implying that omitting antibosons always leads to the computation of a metastable state.

Equation of state for a partially ionized gas. II.

The derivation of equations of state for fluid phases of a partially ionized gas or plasma is addressed from a fundamental point of view. A spherical cellular model is deduced for the hot curve limit (or ideal Fermi gas). Next the Coulomb interactions are added to the spherical cellular model for general ionic charge Z. Then an independent electron model within a Z electron cell plus several many-body effects are employed. Numerical examples of the theory for several elements (H, Li, N, Na, K, Ni, Rb, Pd, Cs, and Er) are reported. These results reduce in various limits of temperature and density to the expected behavior. They display electron, localization-delocalization phase transitions of liquid-gas character. In the higher Z elements, a second possible critical point has been found. The critical pressure, electron density and temperature for the lower-density critical points seem to obey power laws as a function of Z.