  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.
