Three-body effect: Nonrelativistic 1/ρ⁵ polarization term in the effective potential between charged particles

It is well known that the effective potential describing the interaction of a charged particle with a charged or neutral system at large distances, but in the nonretardation region, is given by the sum of the Coulomb term, if the net charge of the system is not zero, a static dipole polarization potential -a/2ρ⁴, a term ∼1/ρ⁶ plus higher-order terms. In the retardation region a term ∼1/ρ⁵ appears which is a correction to the static dipole polarization potential. It is shown here within the three-body approach that the dynamic polarization of the bound state through the continuum causes a long-range nonretardated term ∼1/ρ⁵ which can also be considered as a correction to the static dipole polarization potential and which exists in the nonretardation region.