Classical and quantum evaluation in the low temperature limit of the Keesom integral for the interaction between permanent dipoles

In a previous paper on the Keesom effect, we presented a procedure for the evaluation of the average potential energy of interaction between two dipoles of strength μ a distance R apart in the limit of small temperature T. The resulting expansion in terms of the dimensionless T-dependent parameter a = −μ2/R3kT was then proved by us to be an asymptotic one. Here we reformulate our method in a simplified form, extending it to include the quantum effects which must be taken into account in the low-temperature regime. The resulting formulae show explicitly the transition from the quantum regime to the classical one as a function of temperature.