Mott–Bethe formula
The Mott–Bethe formula is used to calculate electron scattering form factors,, from X-ray scattering form factors,. Following the first Born approximation,
Here, is the magnitude of the scattering vector of momentum transfer cross section in reciprocal space, the atomic number of the atom, is Planck's constant, is the vacuum permittivity, and is the electron rest mass.
The units of the scattering factor are . The accuracy of this formula is best for large values of . For smaller values of, can be determined from tabulated values, such as those in the International Tables for Crystallography.
