Charged three-body system with arbitrary masses near conformal invariance

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, $(m_1^{-1}+m_2^{-1})/[(m_1+m_2{)}^{-1}+m_3^{-1}]>|q_1/(24q_3)|$, 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.

5 pages, 1 figure, to appear in Physical Review A

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Cited by in corpus (1)

• Geometric scaling in the spectrum of an electron captured by a stationary finite dipole