Structure of Bound States with Coulomb plus Short-range Interaction

TL;DR

This paper investigates how Coulomb and short-range interactions influence the structure, binding energies, and wave functions of bound states, revealing Coulomb effects on energy shifts and asymptotic behavior.

Contribution

It provides new insights into the impact of Coulomb forces on bound state properties and modifies the understanding of near-threshold mass scaling for weakly bound states.

Findings

Coulomb-induced shifts correlate with wave function distribution

Coulomb repulsion alters asymptotic wave function behavior

Near-threshold mass scaling is modified by Coulomb effects

Abstract

We study the structure of bound states appearing in systems governed by the Coulomb and short-range interactions. We analyze the binding energies and wave functions of the bound states generated by the Coulomb plus short-range potential. We demonstrate that Coulomb-induced shifts of the binding energy are closely correlated with the spatial distribution of the wave function. Furthermore, we show that the asymptotic behavior of wave functions of weakly bound states is qualitatively altered by Coulomb repulsion, leading to a modification of the near-threshold mass scaling that is otherwise universal for short-range interactions.