Imperfect Bose Gas with Hard-Sphere Interaction

Abstract

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 $\frac{a}{\lambda }$, where $a$ is the hard-sphere diameter and $\lambda$ the thermal wavelength. The approximate equation of state for the gas phase is thereby obtained by calculating all the virial coefficients to order ${\left(\frac{a}{\lambda }\right)}^2$.