# Atomic Form Factor

The atomic form factor is the scattering contribution from a single, isolated atom. The form factor is generally described as encoding the shape of a scattering object. The atomic form factor thus encodes the shape of an atom. More specifically, it is the Fourier transform of the atom's spatial distribution.

The interpretation of 'spatial distribution' depends on the kind of scattering. X-rays are scattered from an atom's electron cloud; thus the scattering amplitude scales with the atomic number (Z). The scattering interaction for each element is tabulated as the "atomic scattering factor". For neutrons, the scattering interaction instead occurs with the nucleus; which leads to a non-intuitive variation of the neutron scattering length across the periodic table. (Neutron scattering also has a magnetic scattering component, owing to nuclear spin.)

## Equation

In the most general case of an arbitrary distribution of scattering density, $\rho (\mathbf {r} )$ , the form factor is computed by integrating over all space:

$F(\mathbf {q} )=\int \rho (\mathbf {r} )e^{i\mathbf {q} \cdot \mathbf {r} }\mathrm {d} V$ Where q is the momentum transfer (in reciprocal-space), r is the spatial coordinate in realspace, and $\rho$ is the spatial distribution of the scattering object. (The equation is essentially a Fourier transform.)