Padé-Approximant Calculation of the Nonretarded van der Waals Coefficients for Two and Three Helium Atoms

Abstract

The long-range (nonretarded) van der Waals coefficients for two and three helium atoms are determined by an integration over imaginary frequencies of helium dynamic polarizabilities. An analytic form for the dynamic polarizability as a function of frequency is generated by the Padé-approximant method from accurate numerical values calculated by Schwartz. The coefficient $C_{\mathrm{AB}}$ of the van der Waals energy (the $-C_{\mathrm{AB}}{R_{\mathrm{AB}}}^{-6\mathrm{}}$ term) between two He atoms is calculated to be 1.460 a.u., and the coefficient $D_{\mathrm{ABC}}$ of the nonadditive contribution [the $D_{\mathrm{ABC}}(3\mathrm{} {cos\theta }_A{cos\theta }_B{cos\theta }_C+1) {R_{\mathrm{AB}}}^{-3\mathrm{}}{R_{\mathrm{BC}}}^{-3\mathrm{}}{R_{\mathrm{CA}}}^{-3\mathrm{}}$ term] between three He atoms is calculated to be 1.481 a.u.