In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process. The latter is described by the wavefunction
where is the position vector; ; is the incoming plane wave with the wavenumber k along the z axis; is the outgoing spherical wave; θ is the scattering angle; and is the scattering amplitude. The dimension of the scattering amplitude is length.
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.
The scattering amplitude can be determined by the scattering length in the low-energy regime.