A spline function approach to the numerical treatment of scattering and bound-state problems for nonlocal potentials

The Lippman-Schwinger equation for the reactance operator is converted into a system of linear equations. By using spline functions the principal-value singularity of the integral kernel can be treated analytically. Throughout this work recurrence relations suitable for automatic computation are der...

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Bibliographic Details
Published in:Computer physics communications 1980-01, Vol.20 (2), p.181-189
Main Author: Fiebig, H.R.
Format: Article
Language:English
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Summary:The Lippman-Schwinger equation for the reactance operator is converted into a system of linear equations. By using spline functions the principal-value singularity of the integral kernel can be treated analytically. Throughout this work recurrence relations suitable for automatic computation are derived, relying on the properties of normalized B-splines as given by de Boor. The algorithm developed is recommended for problems with a nonlocal interaction admitting partial wave decomposition. This case occurs, e.g. in the low-energy scattering of two composite nuclei when antisymmetrisation is taken into account. It is shown that addition of a repulsive Coulomb interaction requires no essential modifications of the method. Supplementary applications to bound-state energies and wave functions are given.
ISSN:0010-4655
1879-2944
DOI:10.1016/0010-4655(80)90001-6