Imperfect Bose Gas with Hard-Sphere Interaction

The method developed in the previous paper for the treatment of the quantum-mechanical N-body hard-sphere problem is applied to a calculation of the grand partition function of an imperfect Bose gas with hard-sphere interactions. The grand partition function is calculated to second order in an expansion in powers of aλ, where a is the hard-sphere diameter and λ the thermal wavelength. The approximate equation of state for the gas phase is thereby obtained by calculating all the virial coefficients to order (aλ)².The first-order energy levels obtained in the previous paper embody some interesting physical properties. A fictitious system with exactly such energy levels is considered. The partition function for such a system can be calculated exactly and the exact equation of state obtained. It is shown that there is a phase transition, which more closely resembles an ordinary gas-liquid transition than the Bose-Einstein condensation.