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Related Experiment Videos

Deep l-independent potentials from supersymmetric inversion

Sparenberg1

  • 1Physique Nucleaire Theorique et Physique Mathematique, C.P. 229, Universite Libre de Bruxelles, B-1050 Brussels, Belgium.

Physical Review Letters
|September 16, 2000
PubMed
Summary

Researchers constructed central potentials from elastic phase shifts, utilizing fixed-l inversion ambiguities to fit other partial waves. This method, applied to alpha-alpha and electron-Ne collisions, determines potential behavior and bound states.

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Area of Science:

  • Nuclear Physics
  • Atomic Physics
  • Quantum Mechanics
  • Scattering Theory

Background:

  • Determining central potentials from scattering data is crucial in various physics domains.
  • Elastic phase shifts provide key information about particle interactions.
  • Ambiguities in potential inversion methods can limit their applicability.

Purpose of the Study:

  • To develop a method for constructing central potentials independent of energy and angular momentum.
  • To exploit ambiguities in fixed-l inversion to fit phase shifts of other partial waves.
  • To apply the developed method to specific physical systems: alpha+alpha collisions and e(-)+Ne collisions.

Main Methods:

  • Construction of central potentials directly from elastic phase shifts.

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  • Utilizing the ambiguities inherent in fixed-l inversion techniques.
  • Employing supersymmetric transformations of the radial Schrödinger equation.

    • Main Results:

    • Successfully fitted phase shifts for other partial waves by exploiting inversion ambiguities.
    • Determined the energy and normalization constant of forbidden bound states.
    • Characterized the small-distance behavior of the constructed potentials.

    Conclusions:

    • The developed method provides a robust way to construct central potentials from elastic phase shifts.
    • Supersymmetric transformations offer a powerful tool for solving the radial Schrödinger equation in this context.
    • The method is applicable to both nuclear (alpha+alpha) and atomic (e(-)+Ne) physics problems.