Quasi-Coulomb series in a two-dimensional three-body system

TL;DR

This paper demonstrates that a specific three-body system in two dimensions exhibits a Coulomb-like energy series with a Gaussian cutoff under certain conditions involving particle masses and interactions.

Contribution

It introduces the concept of a quasi-Coulomb series in a two-dimensional three-body system with specific mass and potential conditions, extending understanding of bound state spectra.

Findings

Bound states form a Coulomb series with Gaussian cutoff

Series merges into pure Coulombic form as mass ratio decreases

Conditions include a light particle, two heavy bosons, and p-wave resonance

Abstract

We show that the bound states in a three-body system display a Coulomb series with a Gaussian cut-off provided: (i) the system consists of a light particle and two heavy bosonic ones, (ii) the heavy-light short-range potential has a resonance in the $p$-wave scattering amplitude, and (iii) all three particles move in two space dimensions. For a decreasing mass ratio this quasi-Coulomb series merges into a pure Coulombic one.