momentumtransfer

Momentum transfer is the amount of momentum exchanged between bodies during an interaction. In classical mechanics, it is the impulse imparted to a target, equal to the change in its momentum: Δp = p_f − p_i. For a simple two-body collision, the momentum transferred to the target is q = p_target,f − p_target,i, and by conservation of total momentum the projectile experiences an opposite impulse.

In scattering problems, the momentum transfer is often denoted by q or Δp and is defined as the difference between the incoming and outgoing momenta of a particle: q = p_f − p_i. In relativistic contexts, the four-momentum transfer q^μ is used, with Q^2 = −q^μ q_μ = −(p_f − p_i)^2. The momentum transfer is a central variable in determining differential cross sections and form factors, because it encodes the spatial resolution of the probe in processes such as elastic scattering, deep inelastic scattering, and electron–nucleus interactions.

Momentum transfer also appears in optics and condensed matter: photons transferring momentum to surfaces generate radiation pressure; in electron-phonon interactions momentum is exchanged between electrons and the crystal lattice. In experiments, q is obtained from kinematic measurements of the initial and final states, and is constrained by energy and momentum conservation.