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The asymptotic behavior of the optical potential, describing elasticscattering of a charged particle $\alpha$ off a bound state of two charged, orone charged and one neutral, particles at small momentum transfer$\Delta_{\alpha}$ or equivalently at large intercluster distance$\rho_{\alpha}$, is investigated within the framework of the exact three-bodytheory. For the three-charged-particle Green function that occurs in the exactexpression for the optical potential, a recently derived expression, which isappropriate for the asymptotic region under consideration, is used. We findthat for arbitrary values of the energy parameter the non-static part of theoptical potential behaves for $\Delta_{\alpha} \rightarrow 0$ as$C_{1}\Delta_{\alpha} + o\,(\Delta_{\alpha})$. From this we derive for theFourier transform of its on-shell restriction for $\rho_{\alpha} \rightarrow\infty$ the behavior $-a/2\rho_{\alpha}^4 + o\,(1/\rho_{\alpha}^4)$, i.e.,dipole or quadrupole terms do not occur in the coordinate-space asymptotics.This result corroborates the standard one, which is obtained by perturbativemethods. The general, energy-dependent expression for the dynamicpolarisability $C_{1}$ is derived; on the energy shell it reduces to theconventional polarisability $a$ which is independent of the energy. Weemphasize that the present derivation is {\em non-perturbative}, i.e., it doesnot make use of adiabatic or similar approximations, and is valid for energies{\em below as well as above the three-body dissociation threshold}.Comment: 35 pages, no figures, revte

Long-range behavior of the optical potential for the elastic scattering of charged composite particles