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

The asymptotic behavior of the optical potential, describing elastic scattering of a charged particle α off a bound state of two charged, or one charged and one neutral, particles at small momentum transfer ∆ α or equivalently at large intercluster distance ρ α , is investigated within the framework of the exact three-body theory. For the three-charged-particle Green function that occurs in the exact expression for the optical potential, a recently derived expression, which is appropriate for the asymptotic region under consideration, is used. We find that for arbitrary values of the energy parameter the non-static part of the optical potential behaves for ∆ α → 0 as C 1 ∆ α + o (∆ α). From this we derive for the Fourier transform of its on-shell restriction for ρ α → ∞ the behavior −a/2ρ 4 α + o (1/ρ 4 α), i.e., dipole or quadrupole terms do not occur in the coordinate-space asymptotics. This result corroborates the standard one, which is obtained by perturbative methods. The general, energy-dependent expression for the dynamic po-larisability C 1 is derived; on the energy shell it reduces to the conventional polarisability a which is independent of the energy. We emphasize that the present derivation is non-perturbative, i.e., it does not make use of adiabatic or similar approximations, and is valid for energies below as well as above 1 the three-body dissociation threshold.