Irreducible Cluster Integrals of Hard-Sphere Gases. II

It is shown that a class of irreducible clusters of hard-sphere gases can be evaluated by a multiple-series method by changing the integration variable from position vectors to bond vectors and from bond vectors to face vectors using bond—face transformation. The class includes graphs which were intractable so far, for example, Nos. 9 and 10 clusters of the fifth virial coefficient. The value of the fifth virial coefficient E of the hard-sphere gases is recalculated and is found to be 0.11040±0.00006, which has maximum accuracy among values so far obtained.