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P-Matrix and J-Matrix Approaches: Coulomb Asymptotics in the Harmonic Oscillator Representation of Scattering Theory

✍ Scribed by J.M. Bang; A.I. Mazur; A.M. Shirokov; Yu.F. Smirnov; S.A. Zaytsev

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 420 KB
Volume: 280
Category: Article
ISSN: 0003-4916
DOI: 10.1006/aphy.1999.5992

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✦ Synopsis

The relation between the R-and P-matrix approaches and the harmonic oscillator representation of the quantum scattering theory (J-matrix method) is discussed. We construct a discrete analogue of the P-matrix that is shown to be equivalent to the usual P-matrix in the quasiclassical limit. A definition of the natural channel radius is introduced. As a result, it is shown to be possible to use a well-developed technique of R-and P-matrix theory for calculation of resonant states characteristics, scattering phase shifts, etc., in the approaches based on harmonic oscillator expansions, e.g., in nuclear shell-model calculations. The P-matrix is used also for formulation of the method of treating Coulomb asymptotics in the scattering theory in oscillator representation.

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