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A rigorous theory of diffraction scattering from extended objects isproposed. The present theory is based on a multiple asymptotic expansion of anintegral equation for the exact wave function in terms of the large parametersof the problem, which are the range of the potential and the momentumcomponents of the incident particle. For small angles of incidence the densityof positively charged particles on the axis of a chain is always lower thanunit y and the density of negatively charged particles has a maximum forcertain strength of the potential which can exceed considerably unity. Theconditions of validity of the proposed approach are obtained.

Asymptotic Theory of Channeling in the Field of an Atomic Chain and an Atomic Plane