Diatomic transition operators: Results of L2 basis expansions

Abstract

We study several expansion methods for two-atom transition operators T in terms of square-integrable functions. Methods were chosen such that (i) they apply to general potentials of interest in atomic systems; (ii) their numerical accuracy can be systematically improved; and (iii) they provide T operators useful in the solution of three- and many-atom problems. We describe the Hilbert–Schmidt and unitary pole expansion in terms of variationally calculated Weinberg states, and an implementation of the Schwinger variational method for diatomic potentials. Results are presented for the lowest 1Σ and 3Σ potentials of H2, and include partially and completely off-energy-shell T matrix elements for several angular momenta, energies and wave numbers, calculated within the variational, Hilbert–Schmidt, and unitary pole expansions.