Computational Implementation of the R—Matrix Method in Atomic and Molecular Collision Problems
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.
KeywordsCollision Cross Section External Region Hamiltonian Matrix Spin Integral Radial Integral
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