Charged three-body system with arbitrary masses near conformal invariance

TL;DR

This paper analyzes a three-body Coulomb system near conformal invariance, deriving universal conditions for level condensation and energy ratios, relevant for experiments involving charged particles like excitons or matter-antimatter dimers.

Contribution

It introduces a universal mass-charge critical condition for three-body level condensation in Coulomb systems near conformal invariance.

Findings

Derived a universal critical condition for three-body level condensation.

Established ratio between energy levels in the system.

Applicable to experimental setups with charged three-body systems.

Abstract

Within an adiabatic approximation to the three-body Coulomb system, we study the strength of the leading order conformaly invariant attractive dipole interaction produced when a slow charged particle $q_3$ (with mass $m_3$) is captured by the first excited state of a dimer [with individual masses and charges $(m_1,q_1$) and ($m_2,q_2=-q_1$)]. The approach leads to a universal mass-charge critical condition for the existence of three-body level condensation, ${(m_1^{-1}+m_2^{-1})}/ {[(m_1+m_2)^{-1}+m_3^{-1}]}>|{q_1}/(24 q_3)|$, as well as the ratio between the geometrically scaled energy levels. The resulting expressions can be relevant in the analysis of recent experimental setups with charged three-body systems, such as the interactions of excitons, or other matter-antimatter dimers, with a slow charged particle.