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Concept
Scattering amplitude
Summary
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.
Official source
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