Momentum transfer

In scattering, the momentum transfer is a vector in the 3D reciprocal-space that denotes the change in momentum between the incoming and scattered rays. It thus describes the interaction between the radiation and the sample. This quantity is also frequently called the scattering vector, and is normally denoted by $\mathbf {q}$ or ${\vec {q}}$, in vectorial form, or simply by q when only the magnitude of the vector is relevant (for 1D scattering; e.g. TSAXS).

In the majority of scattering experiments (SAXS, WAXS, GISAXS, GIWAXS, etc.), the interaction is elastic, meaning that the energy (wavelength) of the incident and scattered photons are equal. In this case, the scattering vector is confined to the surface of the Ewald sphere. For inelastic scattering, the q-vector is off this surface.

Definitions

Some sources use Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \scripstyle s} instead of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \scripstyle q} to denote momentum transfer.

$q=2\pi s$

See Also

• Q value (conversion from q to d)