Non-local potentials with LS terms in algebraic scattering theory

Research output: Contribution to journalArticle

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Abstract

The group theoretical analysis of Coulomb scattering based on the SO(3, 1) group is revisited. Using matrix-valued differential operators, modifying the angular momentum and the Runge-Lenz vector used hitherto for the realization of the so(3, 1) (Lorentz) algebra, we obtain a three-dimensional solvable two-channel scattering problem. The interaction term besides the Coulomb potential contains a non-local potential of LS-type. Using the momentum representation the S-matrix can be calculated analytically. By employing a canonical transformation, another solvable three-dimensional scattering problem is found, in agreement with the expectations of algebraic scattering theory. The potential in this case is of Pöschl-Teller type with an LS term. It is also pointed out that our matrix-valued realization of the so(3, 1) algebra can be cast to an instructive form with the help of su(2) gauge fields. An interesting connection between gauge transformations and supersymmetry transformations of supersymmetric quantum mechanics is also observed. These results enable us to construct other solvable scattering problems by using su(2) gauge transformations.

Original languageEnglish
Pages (from-to)7243-7257
Number of pages15
JournalJournal of Physics A: Mathematical and General
Volume30
Issue number20
DOIs
Publication statusPublished - Oct 21 1997

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Algebraic Theory
Scattering Theory
Scattering Problems
Gauge Transformation
Scattering
Gages
Term
scattering
Supersymmetric Quantum Mechanics
Three-dimensional
Algebra
Canonical Transformation
Coulomb Potential
Gauge Field
Supersymmetry
Angular Momentum
algebra
matrices
Differential operator
Theoretical Analysis

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Non-local potentials with LS terms in algebraic scattering theory. / Lévay, P.

In: Journal of Physics A: Mathematical and General, Vol. 30, No. 20, 21.10.1997, p. 7243-7257.

Research output: Contribution to journalArticle

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