Asymptotic Theory of Channeling in the Field of an Atomic Chain and an   Atomic Plane
  A rigorous theory of diffraction scattering from extended objects is proposed. The present theory is based on a multiple asymptotic expansion of an integral equation for the exact wave function in terms of the large parameters of the problem, which are the range of the potential and the momentum components of the incident particle. For small angles of incidence the density of positively charged particles on the axis of a chain is always lower than unit y and the density of negatively charged particles has a maximum for certain strength of the potential which can exceed considerably unity. The conditions of validity of the proposed approach are obtained. 
Gennady V. Kovalev
cond-mat.other