J-matrix method: Application toS-wave electron-hydrogen scattering

Abstract

The method of the px eceding paper is here applied to s-wave electron-hydrogen collisions. A pseudo-state model is developed and applied to elastic and inelastic scattering above and below the ionization threshold where we compare with the results of Burke and Mitchell. Additional calculations show the effect of Kato correction, the effect of the closed-channel asymptotic forms, and include a comparison with the results of Schwartz.

Algebraic model for scattering in three-s-cluster systems. I. Theoretical background

“…The use of a basis of square integrable states reduces the Schrödinger equation to a matrix equation. This procedure is well-known for bound states, but is also applicable to continuum states when the appropriate boundary conditions are imposed on the expansion coefficients [1,2,[12][13][14]. Thus the Algebraic Model provides a unified approach to bound and continuous spectra based on familiar matrix techniques.…”

Algebraic model for quantum scattering: Reformulation, analysis, and numerical strategies

“…As applications to scattering problems, expressed in an L 2 basis, appeared, several algorithms were suggested to accelerate the convergence of the results within a restricted subset of the basis. For instance, Heller and Yamani [8] used "Kato correction", and Revai et al [9] introduced the "Lanczos factor". A more intuitive approximation was proposed by Fillipov et al [6].…”

Explicit demonstration of the convergence of the close-coupling method for a Coulomb three-body problem

“…A J-matrix calculation was carried out for the same model problem by Heller and Yamani [7]. In the J-matrix method one similarly makes use of L~e xpansions of the target and they also observed unphysical resonance features.…”