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

Abstract

The asymptotic behavior of the optical potential, describing elastic scattering of a charged particle $\alpha$ off a bound state of two charged, or one 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-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 ${\Delta }_{\alpha }\to 0$ as $C_1{\Delta }_{\alpha }+o({\Delta }_{\alpha })$. From this we derive for the Fourier transform of its on-shell restriction for ${\rho }_{\alpha }\to \infty$ 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 perturbative methods. The general, energy-dependent expression for the dynamic polarisability $C_1$ 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 {\em non-perturbative}, i.e., it does not make use of adiabatic or similar approximations, and is valid for energies {\em below as well as above the three-body dissociation threshold}.

Comments: 35 pages, no figures, revtex