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In particle physics, wave mechanics, and optics, momentum transfer is the amount of momentum that one particle gives to another particle. It is also called the scattering vector as it describes the transfer of wavevector in wave mechanics. In the simplest example of scattering of two colliding particles with initial momenta ${\displaystyle {\vec {p}}_{i1},{\vec {p}}_{i2}}$, resulting in final momenta ${\displaystyle {\vec {p}}_{f1},{\vec {p}}_{f2}}$, the momentum transfer is given by

${\displaystyle {\vec {q}}={\vec {p}}_{i1}-{\vec {p}}_{f1}={\vec {p}}_{f2}-{\vec {p}}_{i2}}$

where the last identity expresses momentum conservation. Momentum transfer is an important quantity because ${\displaystyle \Delta x=\hbar /|q|}$ is a better measure for the typical distance resolution of the reaction than the momenta themselves.

Wave mechanics and optics

A wave has a momentum ${\displaystyle p=\hbar k}$ and is a vectorial quantity. The difference of the momentum of the scattered wave to the incident wave is called momentum transfer. The wave number k is the absolute of the wave vector ${\displaystyle k=p/\hbar }$ and is related to the wavelength ${\displaystyle k=2\pi /\lambda }$. Momentum transfer is given in wavenumber units in reciprocal space ${\displaystyle Q=k_{f}-k_{i}}$

See also

• Atomic form factor – Measure of the scattering amplitude of a wave by an isolated atom
• Mandelstam variables – Variables used in scattering processes
• Momentum-transfer cross section – Concept in scattering theory
• Impulse (physics) – Integral of a comparatively larger force over a short time interval

References