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Charged-Particle Bound States in Periodic Boxes.

Hang Yu1, Sebastian König1, Dean Lee2

  • 1Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA.

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|December 10, 2023
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Summary

We calculated the binding energy for two-body systems with repulsive Coulomb interactions in finite volumes. Our method extracts asymptotic normalization coefficients for charged particle bound states, crucial for nuclear physics calculations.

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Area of Science:

  • Nuclear Physics
  • Quantum Mechanics
  • Computational Physics

Background:

  • Understanding the binding energy of two-body systems is fundamental in physics.
  • Repulsive Coulomb interactions complicate calculations, especially in confined systems.
  • Finite-volume methods are increasingly used in nuclear physics simulations.

Purpose of the Study:

  • To investigate the binding energy of a two-body system with repulsive Coulomb interaction in a finite periodic volume.
  • To derive the volume dependence of bound states with zero angular momentum.
  • To develop a method for extracting asymptotic normalization coefficients for charged-particle bound states.

Main Methods:

  • Defining a finite-volume Coulomb potential based on shortest separation.
  • Analyzing the problem in one and three-dimensional periodic boxes.
  • Deriving asymptotic behavior using Whittaker functions.
  • Benchmarking against numerical calculations.

Main Results:

  • Derived the asymptotic behavior of volume dependence for zero angular momentum bound states.
  • Developed a method to extract asymptotic normalization coefficients.
  • Validated results against numerical computations.

Conclusions:

  • The derived method is applicable for calculating atomic nuclei in finite volumes.
  • The method is particularly useful when finite-volume corrections involve charged clusters.
  • Provides a pathway for more accurate nuclear structure calculations in simulations.