Induction Forces. An Exact Treatment of Charge Overlap Effects through Third Order

Abstract

The interaction of a ground‐state atom or ion, consisting of a nucleus and a single electron, with a charge is considered in detail as a model for discussing induction forces through third order in the interaction potential. Expressions for all the angular components of the first‐order wavefunction and for all the individual nonexpanded second‐order induction energies are given in closed form. Exact numerical values for the total third‐order induction energy and its individual nonexpanded components, through terms varying as $R^{\text{−11}}$ at long range, are given in tabular form for the H–H⁺ interaction. The results are discussed with emphasis on the effects of charge overlap on induction forces through third order and on the complicated structure of the third‐order energy in terms of its individual nonexpanded induction energies. In the Appendix the Green function approach to the problem is discussed with the relevant Green functions being obtained as solutions of differential equations rather than by direct summation of their spectral expansions.