### 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 language | English |
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Pages (from-to) | 7243-7257 |

Number of pages | 15 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 30 |

Issue number | 20 |

DOIs | |

Publication status | Published - Oct 21 1997 |

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### 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.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 30, no. 20, pp. 7243-7257. https://doi.org/10.1088/0305-4470/30/20/023

}

TY - JOUR

T1 - Non-local potentials with LS terms in algebraic scattering theory

AU - Lévay, P.

PY - 1997/10/21

Y1 - 1997/10/21

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0039560006&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/30/20/023

DO - 10.1088/0305-4470/30/20/023

M3 - Article

AN - SCOPUS:0039560006

VL - 30

SP - 7243

EP - 7257

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 20

ER -