Multipole polarizabilities of the helium atom and collision-induced polarizabilities of pairs containing He or H atoms

The transient, collision-induced changes in electric properties of ion–atom or atom–atom pairs at long range are determined by the polarizabilities and hyperpolarizabilities of each of the interacting species. Induction effects on moments of the charge distribution or static susceptibilities depend on the response at zero frequency, and dispersion effects depend on the polarizabilities (linear and nonlinear) at imaginary frequencies. In this paper, we give numerical results for four static multipole hyperpolarizabilities of the helium atom obtained from large-basis, ab initio calculations using many-body perturbation theory and coupled-cluster methods. We report and analyze the numerical results for the R−6 and R−8 terms in the dispersion contributions to the He–He, He–H, and H–H pair polarizability functions with a corrected formula for the contributions from the P-hyperpolarizability tensor. For both parallel and perpendicular components of the polarizability, the numerical results at order R−8 have contributions of similar magnitude arising from the terms containing the P and Q hyperpolarizabilities; these terms approximately cancel for Δα⊥, but reinforce for Δα∥. When R is near to or smaller than the van der Waals minimum distance, the dispersion series is damped by overlap, but the ratio of the undamped R−6 and R−8 terms gives a guide to the convergence behavior. For the pairs treated here, the R−6 and R−8 terms in Δα∥ become equally important between 5 and 8 bohr, but the R−6 term dominates the series for Δα⊥ down to separations of 3–4.5 bohr.