Low-Temperature Behavior of a Dilute Bose System of Hard Spheres. I. Equilibrium Properties

By a generalization of the method used in a previous paper the distribution of energy levels of a dilute Bose system of hard spheres is found. These energy levels are then used to compute the statistical properties for the system. A phase transition is found, and the transition point is calculated to the lowest order of a, the diameter of the hard spheres. Furthermore, the thermodynamical functions of the system in both the gas phase and the degenerate phase are obtained, provided (aλ)1 and ρa³1, where λ is the thermal wavelength and ρ is the particle density.