Abstract
We describe a novel iterative method for numerically solving the integro-differential equation used in electron-hydrogen scattering. An adaptive approach to the iteration is introduced. Converged solutions can be efficiently obtained for a wide range of initial conditions. We confirm the reliability of the present method by comparing the numerical data of elastic phase-shifts with previous calculations.
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References
Barnett, A. R. (1982). coulfg: Coulomb and Bessel functions and their derivatives, for real arguments, by Steed’s method. Comp. Phys. Commun., 27:147.
Dorn, A., Elliott, A., Lower, J., Mazevet, S. F., McEachran, R. P., McCarthy, I. E., and Weigold, E. (1998). The elastic scattering of spin-polarized electrons from xenon. J. Phys. B, 31:547.
Edmonds, A. R. (1957). Angular Momentum in Quantum Mechanics. Princeton University Press.
Furness, J. B. and McCarthy, I. E. (1973). Semiphenomenological optical model for electron scattering on atoms. J. Phys. B, 6:2280.
Ixaru, L., Vanden Berghe, G., De Meyer, H., and Van Daele, M. (1997a). Expfit4 — A FORTRAN program for the numerical solution of systems of non-linear second order initial value prolems. Comput. Phys. Commun., 100:71.
Ixaru, L., Vanden Berghe, G., De Meyer, H., and Van Daele, M. (1997b). Four-step exponential-fitted methods for nonlinear physical problems. Comput. Phys. Commun., 100:56.
Jones, S. and Madison, D. H. (1994). Asymptotically-correct distorted-wave calculations for low-energy electron-impact ionization of helium. J. Phys. B, 27:1423.
Rasch, J. (1996). (e,2e) processes with neutral atom targets. PhD thesis, University of Cambridge.
Riley, M. E. and Truhlar, D. G. (1976). Effects of the pauli principle on electron scattering by open-shell targets. J. Chem. Phys., 65:792.
Röder, J., Rasch, J., Jung, K., Whelan, C. T., Ehrhardt, H., Allan, R. J., and Walters, H. R. J. (1996). Coulomb three-body effects in low energy impact ionisation of H(1s). Phys. Rev. A, 53:225.
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© 2005 Kluwer Academic/Plenum Publishers, New York
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Kawano, S., Rasch, J., Roche, P.J.P., Whelan, C.T. (2005). A Study of Iterative Methods for Integro-Differential Equations of Electron-Atom Scattering. In: Whelan, C.T., Mason, N.J. (eds) Electron Scattering. Physics of Atoms and Molecules. Springer, Boston, MA. https://doi.org/10.1007/0-387-27567-3_8
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DOI: https://doi.org/10.1007/0-387-27567-3_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-306-48701-9
Online ISBN: 978-0-387-27567-3
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