Long-Range Three-Body Dispersion Interactions

There is an increasing interest in producing alkali-metal homonuclear or heteronuclear trimers using the photo- association or magnetic-association techniques. Such trimers are formed near the zero-energy threshold and the constituent atoms typically have large internuclear separations where the dominant interactions are the long-range dispersion interactions. A general theoretical and computational framework is developed for the evaluation of long-range non-additive three-body dispersion interactions. The formalism allows for the possibility of one of the atoms to exist in an excited state. In the case of a homonuclear system such as Li($2s$)Li($2s$)Li($2p$), the long-range interaction will have a lower order $R$-dependence due to the possibility of particle interchange. The lowest order three-body dispersion coefficients are presented for systems involving the H, He, Li atoms and the Li$^+$, Be$^+$ and H$_2^+$ ions. The results of our calculations can be used as reference data for the long-range part of three-body potential energy curves for these systems.