The computation of fourth virial coefficients for pairwise-additive spherically symmetric interaction potentials

✍ Scribed by C.H.J. Johnson

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 705 KB
• Volume: 6
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(73)90052-0

✦ Synopsis

A method is given for computing the fourth virial coefficient D(fl for a pairwise additive spherically symmetric interaction potential. Taking one of the four interacting particles as origin and using the appropriate co-ordinate transformations in the usual way the ninefold integrals defining D(fl are reduced to sixfold integrals which are then formally reduced to triple integrals by expanding out those Ursell-Mayer functions in the integrals not involving the origin particle as infinite series in Legendre polynomials P 5(cos 0), where 0 is the angle between the radius vectors of the interacting particles. The coefficients in these expansions are integrals of highly oscillatory functions, especially for large s, and are evaluated using the Chebyshev polynomial expansion for the Ursell-Mayer functions, thus making explicit use of the oscillatory behaviour ofP5(cos 0). The triple integrals are evaluated using a nonproduct integration formula of the seventh degree employed earlier in the computation of the third virial coefficient. The values of D(T) computed by the present method have the same qualitative behaviour as the literature values but appear to be more accurate, particularly at lower temperatures.