Momentum transfer
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 formula_1, resulting in final momenta formula_2, the momentum transfer is given by where the last identity expresses momentum conservation. Momentum transfer is an important quantity because formula_4 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 formula_5 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 formula_6 and is related to the wavelength formula_7. Momentum transfer is given in wavenumber units in reciprocal space formula_8 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 final and incident particles, formula_9 and formula_10, respectively, are equal and just the direction changes by a reciprocal lattice vector formula_11 with the relation to the lattice spacing formula_12. 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 employ the diffraction angle formula_13 as the independent variable, which worked fine  in the early years when only a few characteristic wavelengths such as Cu-Kformula_14 were available. The relationship to formula_15-space is with formula_17 and basically states that larger formula_13 corresponds to larger formula_15.