Charged three-body system with arbitrary masses near conformal invariance
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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)]>vertical bar q(1)/(24q(3))vertical bar, 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.