Dynamical Diffraction Theory by Optical Potential Methods

Abstract

In the past twenty years, there has been a renewed and steadily increasing interest in dynamical diffraction of X-rays and electrons, which is due partly to the availability of large, perfect crystals and to the development of the electron microscope. New branches have evolved, such as low-energy-electron-diffraction (LEED), channeling of high energy electrons, and positrons or dynamical scattering of Mossbauer quanta. Also, the dynamical theory has made considerable progress. This chapter discusses the conventional form of the dynamical theory. It presents the basic principles in a short, but self-contained way and emphasizes some new methods such as the band structure for complex wave vectors and the t-matrix method. Moreover, it develops at the same time the theory for electron, neutron, and X-ray diffraction by a finite crystal—that is, the matching of the wave fields, the calculations of diffracted intensities, the discussions of Laue and Bragg cases, etc. This chapter discusses the theory for the coherent wave, which is known as the optical potential method in nuclear physics. It explicitly derives the corrections to the potential coefficients due to inelastic waves, thermal motion, and statistically distributed defects, both for electron and X-ray diffraction.