Invariant expansion. IV. The exponentials of tensorial expressions

Abstract

The expansion of the exponential of a tensorial expression such as the interaction or pair correlation function between two nonspherical molecules 1, 2 is of the form ∑mnl λmnlΦmnl(12), where Φmnl(12) are invariant tensorial expressions that depend only on the orientation of 1 and 2. The generating function e−∑mnl λmnlΦmnl =∑pqt ipqt(λ) Φpqt defines a generalized Bessel function (GBF). We discuss integral representations and recurrence relations for the GBF. The first GBFs for dipolar and linear quadrupolar exponents, which are of interest in the theory of ionic solutions are computed explicitly.