Semi-quantum approach for fast atom diffraction: solving the rainbow   divergence
  In this work we introduce a distorted wave method, based on the Initial Value Representation (IVR) approach of the quantum evolution operator, in order to improve the semiclassical description of rainbow effects in diffraction patterns produced by grazing scattering of fast atoms from crystal surfaces. The proposed theory, named Surface Initial Value Representation (SIVR) approximation, is applied to He atoms colliding with a LiF(001) surface along low indexed crystallographic channels. For this collision system the SIVR approach provides a very good representation of the quantum interference structures of experimental projectile distributions, even in the angular region around classical rainbow angles where common semiclassical methods diverge. 
M.S. Gravielle and J.E. Miraglia
physics.atom-ph