Supersymmetry between deep and shallow optical potentials for {sup 16}O+{sup 16}O scattering

Sparenberg, J; Baye, D

doi:10.1103/PhysRevC.54.1309

Title: Supersymmetry between deep and shallow optical potentials for {sup 16}O+{sup 16}O scattering

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Abstract

Pairs of supersymmetric transformations allow one to remove square-integrable solutions from a complex potential without modifying its complex phase shifts. This technique is applied to {sup 16}O+{sup 16}O scattering where deep and shallow optical potentials provide essentially similar fits of excitation functions over the 10{endash}35 MeV range in the center-of-mass system. After removing complex normalizable solutions from the deep optical potential of Kond{bar o} {ital et} {ital al}., the resulting potential resembles the shallow potential of Chatwin {ital et} {ital al}., except for the fact that it is singular at the origin. The transformation succeeds in removing bound states and also narrow resonances from the real part of the deep potential. Different theoretical aspects of scattering with complex potentials are also discussed such as the behavior of complex phase shifts in the vicinity of a resonant or normalizable state, and the Levinson theorem. In order to explain phase-shift behaviors, resonance locations are calculated by the complex rotation method, combined with numerical methods valid for determining square-integrable solutions of a Schr{umlt o}dinger equation involving a complex potential. In phase-equivalent pairs of supersymmetric transformations, the apparent contradiction between removing a square-integrable solution which corresponds to a pole of the scattering matrix, andmore »« less

Authors:

Sparenberg, J; Baye, D ^[1]

Physique Nucleaire Theorique et Physique Mathematique, C.P. 229, Universite Libre de Bruxelles, B-1050 Brussels (Belgium)

Publication Date:: Sun Sep 01 00:00:00 EDT 1996

OSTI Identifier:: 383341

Resource Type:: Journal Article

Journal Name:: Physical Review, C

Additional Journal Information:: Journal Volume: 54; Journal Issue: 3; Other Information: PBD: Sep 1996

Country of Publication:: United States

Language:: English

Subject:: 66 PHYSICS; OXYGEN 16; OXYGEN 16 REACTIONS; OPTICAL MODELS; SUPERSYMMETRY; POTENTIALS; EXCITATION FUNCTIONS; TRANSFORMATIONS; PHASE SHIFT; LEVINSON THEOREM; SCHROEDINGER EQUATION; S MATRIX

Citation Formats


                    Sparenberg, J, and Baye, D. Supersymmetry between deep and shallow optical potentials for {sup 16}O+{sup 16}O scattering.  United States: N. p., 1996. 
        Web.  doi:10.1103/PhysRevC.54.1309.

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                    Sparenberg, J, & Baye, D. Supersymmetry between deep and shallow optical potentials for {sup 16}O+{sup 16}O scattering.  United States.  https://doi.org/10.1103/PhysRevC.54.1309

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                    Sparenberg, J, and Baye, D. 1996.  
        "Supersymmetry between deep and shallow optical potentials for {sup 16}O+{sup 16}O scattering".  United States.  https://doi.org/10.1103/PhysRevC.54.1309.

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@article{osti_383341,

  title        = {Supersymmetry between deep and shallow optical potentials for {sup 16}O+{sup 16}O scattering},

  author       = {Sparenberg, J and Baye, D},

  abstractNote = {Pairs of supersymmetric transformations allow one to remove square-integrable solutions from a complex potential without modifying its complex phase shifts. This technique is applied to {sup 16}O+{sup 16}O scattering where deep and shallow optical potentials provide essentially similar fits of excitation functions over the 10{endash}35 MeV range in the center-of-mass system. After removing complex normalizable solutions from the deep optical potential of Kond{bar o} {ital et} {ital al}., the resulting potential resembles the shallow potential of Chatwin {ital et} {ital al}., except for the fact that it is singular at the origin. The transformation succeeds in removing bound states and also narrow resonances from the real part of the deep potential. Different theoretical aspects of scattering with complex potentials are also discussed such as the behavior of complex phase shifts in the vicinity of a resonant or normalizable state, and the Levinson theorem. In order to explain phase-shift behaviors, resonance locations are calculated by the complex rotation method, combined with numerical methods valid for determining square-integrable solutions of a Schr{umlt o}dinger equation involving a complex potential. In phase-equivalent pairs of supersymmetric transformations, the apparent contradiction between removing a square-integrable solution which corresponds to a pole of the scattering matrix, and keeping this {ital S} matrix unchanged is explained with the Jost function. {copyright} {ital 1996 The American Physical Society.}},

  doi          = {10.1103/PhysRevC.54.1309},

  url          = {https://www.osti.gov/biblio/383341},
  journal      = {Physical Review, C},
number       = 3,

  volume       = 54,

  place        = {United States},

  year         = {Sun Sep 01 00:00:00 EDT 1996},

  month        = {Sun Sep 01 00:00:00 EDT 1996}

}

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