Physics – Nuclear Physics – Nuclear Theory
Scientific paper
1995-03-20
Phys.Rev. A51 (1995) 3852-3867
Physics
Nuclear Physics
Nuclear Theory
35 pages, no figures, revtex
Scientific paper
10.1103/PhysRevA.51.3852
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 $\Delta_{\alpha} \rightarrow 0$ as $C_{1}\Delta_{\alpha} + o\,(\Delta_{\alpha})$. From this we derive for the Fourier transform of its on-shell restriction for $\rho_{\alpha} \rightarrow \infty$ 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 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}.
Alt Erwin O.
Mukhamedzhanov M.-A. A.
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