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# 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.

## Scattering cross section

The scattering amplitude, f, relates to the scattering cross section, s by s = 4πf2.

## X-rays

The scattering length for X-rays is the Thompson scattering length or classical electron radius, r0.

## 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.