The atomic scattering factor depends on the electron density distribution of the atom, and describes how the incident radiation is scattered by the atom as a function of the angle of scattering and the wavelength of the radiation. It is defined as the complex amplitude of the scattered wave divided by the complex amplitude of the incident wave, both expressed in terms of their wave vectors. It depends upon the number and distribution of electron in an atom and wavelength and angle of scattering of radiation wave.
Let us consider a charge π(r)dπ in a small volume dπ at position (r, π). π(r) defines charge density at position vector r and π(r)dπ represents probability of finding the electron in a volume element dπ at vector r. The phase difference between the radiation scattered by element of charge π(r)dπ at (r, π) and radiation that would be scattered by same amount of charge located at the centre of atom is given by
Let amplitude of wave scattered from A in direction of vector k is Ae^i(kx -wt), where k is the distance coordinate along vector k' and k = 2π/π and w is angular frequency of the wave. The amplitude of scattered wave from volume element dπ in same direction will be proportional to amount of charge π(r)dπ in the volume element dπ and phase difference πr and is given by
f gives charge distribution in an atom. So, the atomic scattering factor is related to the electron density distribution or the atomic form factor, and provides important information about the interaction of radiation with atoms in a crystal or other sample.
The atomic scattering factor is an important tool in the field of crystallography, which is used to determine the structures of molecules and materials. By analyzing the diffraction pattern produced by a crystal, researchers can determine the positions of atoms in the crystal and their relative orientations.
This note is a part of the Physics Repository.