Effect of long-range interactions on low-energy scattering parameters: Variational formulation

A systematic treatment is presented of near-threshold electron-atom scattering based on a variational principle. Results obtained here extend the modified effective-range theory derived some time ago (in which long-range polarization forces are taken into account) by providing a prescription, based on a minimum principle, for calculating the effective-ran parameters. With the aid of perturbation-theory methods introduced recently for obtaining asymptotic solutions of the wave equation for scattering by a superposition of long-range power-law potentials [see M. J. Cavagnero, Phys. Rev. A 50, 2841 (1994)], higher-order corrections to the modified effective-range expansion in powers of the polarizability parameters are readily obtained. Explicit examples are provided. The theory is developed for both single-channel and multichannel scattering.