Fourth Virial Coefficient for the Square Well Potential

Abstract

The fourth virial coefficient $D$ and its components ${D}_{1}$, ${D}_{2}$, ${D}_{3}$ for molecules interacting with a square-well potential have been obtained as functions of the temperature by the use of Fourier transformation and the addition theorem of Bessel functions. Each component and their sum are nearly constant above the Boyle temperature and tend to negative infinity as temperature tend to zero. The total $D$ is expressed by $\frac{D}{{b}^{3}}=0.28642+1.5397f\ensuremath{-}23.554{f}^{2}+53.645{f}^{3}+69.859{f}^{4}\ensuremath{-}170.01{f}^{5}\ensuremath{-}14.777{f}^{6},$ where $f={e}^{\frac{\ensuremath{\epsilon}}{\mathrm{kT}}}\ensuremath{-}1$, and well width is equal to the hard core diameter. Corrections of the critical data and some related problems are discussed.