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, the momentum transfer is given by

where the last identity expresses momentum conservation is a better measure for the typical distance resolution of the reaction than the momenta themselves.

Wave mechanics and optics

and is a vectorial quantity. The difference in momentum of the scattered wave from the incident wave is called momentum transfer. The wave number k is the absolute of the wave vector and is related to the wavelength. Momentum transfer is given in wavenumber units in reciprocal space.

Diffraction

The momentum transfer plays an important role in the evaluation of neutron, X-ray, and electron diffraction for the investigation of condensed matter. Laue-Bragg diffraction occurs on the atomic crystal lattice, conserves the wave energy and thus is called elastic scattering, where the wave numbers, respectively, are equal and just the direction changes by a reciprocal lattice. As momentum is conserved, the transfer of momentum occurs to crystal momentum.

The presentation in reciprocal space is generic and does not depend on the type of radiation and wavelength used but only on the sample system, which allows to compare results obtained from many different methods. Some established communities such as powder diffraction-space is

.

See also

References