Extended combination rule for like-atom dipole dispersion coefficients

An extended combination rule is proposed to relate the dipole-dipole dispersion coefficient for the interaction of the like target species to the same coefficients for the interactions between the target and a set of partner species. The rule can be derived either by uniform discretization of the Casimir-Polder integral on a quadrature or by relating the dynamic dipole polarizabilities of the target species and the partner species. Both methods result in the same system of linear equations, whose solution also requires the knowledge of the dispersion coefficients for interaction between the partner species. The test examples indicate a high accuracy of the proposed rule for dispersion coefficients (better than 1% in the stringent test for the Yb atom interacting with a rare gas and alkaline-earth metal atoms). However, the combination rule does not warrant correct approximation of the dynamic polarizability of the target species.