Charged three-body system with arbitrary masses near conformal invariance

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 q3 (with mass m3) is captured by the first-excited state of a dimer [with individual masses and charges (m1, q1) and (m2, q2 =- q1)]. The approach leads to a universal mass-charge critical condition for the existence of three-body level condensation, (m1 -1 + m2 -1) / [(m1 + m2) -1 + m3 -1] > | q1 / (24 q3) |, 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. © 2009 The American Physical Society.