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 $\left(\frac{a}{\lambda }\right)\ll 1$ and $\rho a^3\ll 1$, where $\lambda$ is the thermal wavelength and $\rho$ is the particle density.