Electron–positive-ion scattering near reaction thresholds: Effect of long-range polarization forces

Abstract

A multichannel version of effective-range theory is developed, applicable to electron scattering by positive ions. The formalism allows for the inclusion of the effect of long-range inverse-power-law interactions arising from target distortion in the field of the projectile. A perturbation theory is described for the construction of asymptotic states accounting for the combined effect of Coulomb and polarization forces. The explicit extraction of threshold branch-point singularities leaves modified reaction-matrix elements that vary slowly with energy, thereby permitting the smooth extrapolation of scattering parameters through reaction thresholds. A systematic procedure is made available to determine the effect of long-range forces on quantum defects and resonance level shifts; it is applied here, as an illustration, in first order. The theory provides an extension, to a wider class of scattering systems and long-range interactions, of an analysis of threshold behavior in electron-ion reactions given some time ago [M. Gailitis, Sov. Phys. JETP 17, 1328 (1963)].