Mott–Bethe formula

The Mott–Bethe formula is used to calculate electron form factors from X-ray form factors. The equation uses the first Born approximation.

f B ( q , Z ) = m e 2 2 π ℏ 2 ϵ 0 ( Z − f x ( q , Z ) q 2 )

where f e ( q , Z ) is the electron scattering cross-section and f x ( q , Z ) is the x-ray scattering cross section. This is a function of 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 ℏ is Planck's constant, ϵ 0 is the vacuum permittivity.

The units of the scattering factor are P o t e n t i a l e l e c t r i c / d i s t a n c e 3