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Part II. Presents information on a study which investigated the degeneracy in quantum statistics. Generalization of the Joyce-Dixon theory to Bose-Einstein and Fermi-Dirac particles; Conclusions.

In quantum statistics there are four categories of quantum degeneracy: nondegenerate, weak, intermediate, and strong. These are associated with the Fermi-Dirac and Bose-Einstein integrals, which are difficult to evaluate over the entire range of the activity parameter r defined as the particle density divided by the quantum concentration. In this paper (I), four classical systems with r&Le; 1, and four weakly degenerate systems with r ≲ 1 are examined. In the former, the Maxwell-Boltzmann distribution is sufficient. In the latter, the treatment of Landau and Lifschitz is extended. Physically realistic systems, like electrons in intrinsic and impurity semiconductors, and noble gases at different pressures and temperatures, are investigated. The neutrino and neutral pion systems are illustrative, albeit esoteric. Expressions for the quantum concentration for different dimensions and particle velocities are useful in predicting the onset of degeneracy. In the companion paper (II), intermediate and strong degeneracies are studied for r ≥ 1. [ABSTRACT FROM AUTHOR]

The methods developed in the first paper of this series (I) [J. Math. Phys. 27, 302 (1986)] are used to calculate the pressure in several cases of physical interest: conduction electrons inside and outside a heated tungsten cathode; helium atoms in liquid helium II and He vapor; electrons in a white dwarf star, and photons in a cavity. The latter two cases involve ultrarelativistic particles whose energy ε=pc. The formulation in I is extended to include particle speeds comparable to c. The grand potential is used to establish two useful, exact relationships between pressure and energy density: P=2u/3 and P=u/3, valid for v

The mathematical methods used to average a function of energy over the Maxwell-Boltzmann (MB), Bose-Einstein (BE), and Fermi-Dirac(FD) statistics are compared. Blankenbecler's method converts the FD integrals into a series of differentiations which converge rapidly if the Fermi energy is large compared to kT. The BE integrals may be obtained from the corresponding MB integral by setting the chemical potential equal to zero and multiplying by a slowly converging numerical series. In each case a single integral of general form is used to calculate familiar quantities like chemical potential, energy, and heat capacity. [ABSTRACT FROM AUTHOR]