Scattering amplitude

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 plane wave 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 scattering amplitude is a probability amplitude; the differential cross-section as a function of scattering angle is given as its modulus squared, The scattering length for X-rays is the Thomson scattering length or classical electron radius, r0. The nuclear neutron scattering process involves the coherent neutron scattering length, often described by b. 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.