# Mott–Bethe formula

${\displaystyle f^{B}(q,Z)={\frac {me^{2}}{2\pi \hbar ^{2}\epsilon _{0}}}{\Bigg (}{\frac {Z-f_{x}(q,Z)}{q^{2}}}{\Bigg )}}$
where ${\displaystyle f_{e}(q,Z)}$ is the electron scattering cross-section and ${\displaystyle f_{x}(q,Z)}$ is the x-ray scattering cross section. This is a function of ${\displaystyle q}$, the scattering vector of momentum transfer cross section in reciprocal space (in units of inverse distance), and Z is the atomic number of the atom. In the equation ${\displaystyle \hbar }$ is Planck's constant, ${\displaystyle \epsilon _{0}}$ is the vacuum permittivity.
The units of the scattering factor are ${\displaystyle \mathrm {Potential_{electric}} /\mathrm {distance} ^{3}}$