Connection between Pair Density and Pressure for a Bose Gas Consisting of Rigid Spherical Atoms

It is shown that, for a Bose gas of rigid spherical atoms of radius $a$, the pressure $p$ is given by the pair-density $g\left(r\right)\mathrm{}$ and the energy per atom $u$ by the formula $\frac{p}{\rho T}=\frac{2}{3}\frac{u}{T}+\frac{2}{3}\pi a^3·\frac{1}{2}\mathrm{mT}·g^{\prime \prime }\mathrm{}\left(a\right).$