Long-range dispersion interactions. III: Method for two homonuclear atoms

The Cn parameters are the dispersion coefficients while R is the distance between the two nuclei. The procedures for determining the dispersion coefficients for identical atoms in two spherically symmetric states are known and there has been a lot of activity in calculating the van der Waals coefficients for such atoms 3–9 . When one of the atoms is in a state with nonzero angular momentum the situation becomes more complicated. In the first case, the dispersion coefficient depends on the angular momentum projection of the state. In the second case, there is a possibility of excitation transfer between the two atoms leading to what is usually termed the resonant van der Waals interaction. This results in additional terms appearing in the interaction potentials, e.g., the existence of a term inversely proportional to R3 when one of the atoms is in a P state and the other is in an S state. The purpose of the present paper is to describe a procedure for the calculation of the Cn dispersion parameters for homonuclear atoms in arbitrary states. An examination of some earlier work on this topic gives one the impression that the theoretical formalisms for systems involving nonzero angular momentum were developed in an ad hoc fashion with expressions for different configurations derived on a case by case basis 5,10–14 . Previously, the most sophisticated treatments were the tensorial approaches developed by Ovsiannikov 15 and Santra and Greene 16 . The present study describes a general procedure which makes use of previous results derived to describe the dispersion interaction between two heteronuclear atoms 17 . Once the formalism is presented, it is applied to the calculation of the dispersion interaction for a number of alkali-metal and alkaline-earth metals atoms.