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Modification of the Porter-Thomas Distribution by Rank-One Interaction.

E Bogomolny1

  • 1CNRS, Université Paris-Sud, UMR 8626, Laboratoire de Physique Théorique et Modèles Statistiques, 91405 Orsay, France.

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Summary
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Deviations in nuclear physics resonance data challenge the Porter-Thomas distribution. A new model incorporating rank-one interactions provides an analytical solution, explaining experimental results and modifying the distribution.

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Area of Science:

  • Nuclear physics
  • Statistical physics
  • Quantum mechanics

Background:

  • The Porter-Thomas (PT) distribution is a foundational statistical model for nuclear resonance widths.
  • Recent experimental data reveal significant deviations from the standard PT distribution.
  • Existing random matrix ensembles alone do not fully account for these observed discrepancies.

Purpose of the Study:

  • To analytically solve a nuclear resonance model that includes rank-one interactions.
  • To explicitly determine the modifications to the Porter-Thomas distribution caused by these interactions.
  • To provide a theoretical framework that reconciles experimental observations with statistical nuclear physics.

Main Methods:

  • Analytical solution of a statistical nuclear resonance model.
  • Inclusion of a rank-one interaction coupling resonances to decay channels.
  • Comparison of derived formulas with numerical simulations.

Main Results:

  • Development of simple, analytically derived formulas describing modified resonance width distributions.
  • Demonstrated good agreement between the analytical results and numerical simulations.
  • The modified distribution accounts for deviations observed in recent experimental data.

Conclusions:

  • The standard Porter-Thomas distribution requires modification to accurately describe nuclear resonance phenomena.
  • A rank-one interaction is crucial for a realistic model of nuclear resonances.
  • The derived analytical framework offers a potential explanation for experimental anomalies in nuclear physics.