Higher-orderCndispersion coefficients for the alkali-metal atoms

Abstract

The van der Waals coefficients, from ${C}_{11}$ through to ${C}_{16}$ resulting from second-, third-, and fourth-order perturbation theory are estimated for the alkali-metal (Li, Na, K, and Rb) atoms. The dispersion coefficients are also computed for all possible combinations of the alkali-metal atoms and hydrogen. The parameters are determined from sum rules after diagonalizing a semiempirical fixed core Hamiltonian in a large basis. Comparisons of the radial dependence of the ${C}_{n}∕{r}^{n}$ potentials give guidance as to the radial regions in which the various higher-order terms can be neglected. It is seen that including terms up to ${C}_{10}∕{r}^{10}$ results in a dispersion interaction that is accurate to better than 1% whenever the inter-nuclear spacing is larger than $20{a}_{0}$. This level of accuracy is mainly achieved due to the fortuitous cancellation between the repulsive $({C}_{11},{C}_{13},{C}_{15})$ and attractive $({C}_{12},{C}_{14},{C}_{16})$ dispersion forces.