Irreducible Cluster Integrals of Hard-Sphere Gases

Abstract

Three different methods of computing irreducible cluster integrals of hard‐sphere gases are developed and discussed. The first one employs integration in configuration space. The second one involves the multiple summation of infinite series of Weber—Schafheitlin‐type integrals. The third one is an extension of Nijboer—van Hove's modified Fourier transformation method. Of values of components of the fifth virial coefficient, Nos. 1, 2, 3, 4 have been obtained by the first method; Nos. 2, 5, 6, 7, 8 by the second method; and Nos. 1–10 also by a Monte Carlo method. The value of E/b⁴ is 0.1097. The value of the fifth virial coefficient for square‐mound potential has also been given.