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 ${\displaystyle {\vec {p}}_{i1},{\vec {p}}_{i2}}$, 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.