Distorted-wave reaction theory with long-range multipole potentials

A distorted-wave theory is developed in which the effect of long-range multipole potentials, having off-diagonal elements in channel space, is accounted far in the construction of asymptotic states. The theory may be applied to the scattering of an electron by a polarizable atomic system carrying a net positive charge and a permanent quadrupole moment. The current treatment is confined to such a system, though greater generality is possible. Asymptotic states are introduced in the form of a superposition of Coulomb wave functions with expansion coefficients determined by means of a modified perturbation theory. Analytic properties of the basis functions are preserved in this expansion and this allows, in the spirit of effective-range theory, for the determination of the energy dependence of the scattering matrix in the neighborhood of reaction thresholds. In particular, the Rydberg series of resonances that appears just below the energy for the opening of a new channel, well described by standard quantum-defect theory, is exhibited for the extended model scattering system considered here.