Scattering amplitude

The scattering amplitude describes the amplitude of an outgoing, elementary, spherical wave relative to a plane, incoming wave scattered on a point size particle. Since the spherical wave amplitude varies with $frac\{1\}\{R\}$ (note, the intensity is the |square| of the amplitude), $R$ being the distance to the point scatterer, the unit of the scattering amplitude includes the unit of a length with respect to the units of the incoming wave. Therefore, the scattering amplitude is often also called scattering length.

X-rays

The scattering length for X-rays is the Thompson scattering length or classical electron radius, $r\_0$.

Neutrons

The nuclear neutron scattering process involves the coherent neutron scattering length, often described by $b$.

Quantum mechanical formalism

A quantum mechanical approach is given by the S matrix formalism.