The S-state model for electron channeling in high-resolution electron microscopy

The S-state model which is well suited to describe the wave function in Fourier space for electron channeling in high-resolution electron microscopy is investigated. It was found that if the 1S eigenfunction is parameterized as a two dimensional (2D) quadratically normalized Gaussian function, the wave function in Fourier space can be expressed in closed analytical form. Using the s-state model it was proven that direct methods are still valid for electron microscopy even at thickness for which the electron scattering can be regarded as highly nonlinear. It has been proven that the Patterson function is still applicable for dynamic electron diffraction, as well as the inequalities orginally set up for x-ray diffraction.