Charged-particle bound states in periodic boxes

TL;DR

This paper analyzes the finite-volume effects on the binding energy of charged two-body systems in periodic boxes, deriving asymptotic behaviors and providing methods to extract physical parameters relevant for nuclear physics calculations.

Contribution

It introduces a novel approach to define and analyze Coulomb interactions in finite periodic volumes, deriving asymptotic formulas and benchmarking them with numerical results.

Findings

Derived asymptotic volume dependence for Coulomb-bound states

Validated formulas with numerical calculations

Provided a method to extract normalization coefficients

Abstract

We consider the binding energy of a two-body system with a repulsive Coulomb interaction in a finite periodic volume. We define the finite-volume Coulomb potential as the usual Coulomb potential, except that the distance is defined as the shortest separation between the two bodies in the periodic volume. We investigate this problem in one and three-dimensional periodic boxes and derive the asymptotic behavior of the volume dependence for bound states with zero angular momentum in terms of Whittaker functions. We benchmark our results against numerical calculations and show how the method can be used to extract asymptotic normalization coefficients for charged-particle bound states. The results we derive here have immediate applications for calculations of atomic nuclei in finite periodic volumes for the case where the leading finite-volume correction is associated with two charged clusters.