  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.
