Irreducible Cluster Integrals of Hard-Sphere Gases

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.