atomic scattering factor

The atomic scattering factor is the scattering amplitude by an atom for an incident electron. This factor is used to calculate the crystal structure factor, which is needed to obtain the diffraction intensity from a crystal.
An incident electron is scattered by the electrostatic potential created by an atomic nucleus and surrounding electrons. The scattering amplitude increases with increasing the atomic number* and monotonically decreases with increasing the scattering angle (Fig. 1). The unit of the atomic scattering factor for an incident electron is [Potential] x [Volume]. The angular dependence of the scattering amplitude has been obtained for all the elements and is given with the numerical values (Ref.1). Expressions of the scattering amplitudes using a mathematical function are also available. The value of the atomic scattering factor at zero angle scattering for the incident electron beam is the total electrostatic potential (value), which is finite, for the neutral atom. For an ionized atom, the atomic scattering factor rapidly increases with decreasing the scattering angle. This means that the scattering (diffraction) intensity of the electron beam changes sensitively against ionization.
It is noted that, when the incident beam is an X-ray, it is scattered only by electrons, and that the value of the atomic scattering factor for a neutral atom at zero scattering angle is the number of electrons of the atom Z. Thus, the units of the atomic scattering factors for X-rays are dimensionless.

Fig. 1. Scattering angle dependence (sinθ/λ) of the four atomic scattering factors for an incident electron. (Ref. 1) *: For light elements, the scattering amplitudes are not always in the order of atomic number in the regions where the scattering angle is small.

Ref.1: International Tables for Crystallography (2006). Vol. C. ch. 4.3, pp. 259-429
https://doi.org/10.1107/97809553602060000593

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