Diffraction and channeling

A review of the scattering of fast charged particles by crystal lattices in terms of both classical and quantum mechanics is presented and a contrast and comparison of the two approaches is made. The anomalous transmission and absorption phenomena of the Borrmann effect of diffraction are analogs of channeling and blocking, which appear as classical mechanical effects in a mass independent limit. For conditions which correspond to localization of a wave packet in the crystal, accompanied by the elimination of observable diffraction effects, all features of the quantal model become analogous features of the classical model. The patterns seen in reflection, and in transmission with either thin or thick crystals, are then dominated by mass independent critical angles, commensurate with the disappearance of Planck's quantum of action and with the appearance of the laws of geometrical optics. An experimental study of the transmission of low energy protons through single crystals of gold is described and the different effects obtained for thin and thick specimens, analogous to those obtained in diffraction, are discussed. A consequence of the replacement of the extinction distance and the Bragg angle by a continuum of values for the orbital wavelength and critical angle respectively is that of a new phenomenon, referred to as quasi-channeling, which violates continuum potential concepts. It is proposed that quasi-channeling can give rise, in the best circumstances, to an oscillatory Rutherford scattering yield with depth in the `shadow' behind a crystal surface, analogous to the Pendellösung effects of diffraction, and to an additional yield due to scattering in the wake of point or clustered crystal defects.