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Computational Implementation of the R—Matrix Method in Atomic and Molecular Collision Problems

In: Supercomputational Science

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  • K. A. Berrington

    (Queen’s University Belfast, Department of Applied Mathematics and Theoretical Physics)

Abstract

Whilst working on a contract for the Manhatten Project, Wigner and Eisenbud (1947) published a new theoretical method for interpreting resonances which had been observed in nuclear reactions. These resonances could be explained in terms of a compound nucleus interaction, in which the colliding nuclei “stick” temporarily in a compound state; the total wavefunction can therefore be expanded in a set of such states, and a many—body problem solved using nuclear structure techniques. This reaction zone was labelled the “internal region” of configuration space and delineated by a sphere of radius r = a around the scattering centre. In the “external region” however, where the colliding or separating nuclei are further apart, the system reduces to a two—body problem, the interaction being a simple function of the radial separation r. In order to connect the two regions, Wigner and Eisenbud introduced a matrix, which they called curly R, to relate the wavefunction to its derivative on the boundary r = a. Thus was R—matrix theory born.

Suggested Citation

  • K. A. Berrington, 1990. "Computational Implementation of the R—Matrix Method in Atomic and Molecular Collision Problems," Springer Books, in: R. G. Evans & S. Wilson (ed.), Supercomputational Science, pages 147-154, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4684-5820-6_12
    DOI: 10.1007/978-1-4684-5820-6_12
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