Speaker
Description
A customary relativistic quantum scattering theory implies that all the particles in a reaction have definite momenta, that is, they are described by the delocalized plane waves. When the well-normalized wave packets are used instead (say, of Gaussian form), the scattering cross sections get corrections of the order of $\lambda_c^2/\sigma_{\perp}^2 \ll 1$ where $\lambda_c$ is a Compton wave length of a particle with a mass $m$ and $\sigma_{\perp}$ is a beam width. For modern electron accelerators, they do not exceed $10^{-16}$, whereas for the well-focused beams of electron microscopes they can reach $10^{-6}$. Here we show that these non-paraxial effects are enhanced when one collides non-Gaussian packets instead: the vortex beams with high orbital angular momentum $\ell \gg \hbar$, the quantum superpositions like the so-called Schrödinger cats, etc. Moderately relativistic vortex electrons with $\ell$ up to $10^3$ have been recently generated, they have large mean transverse momentum, which grows as $\sqrt{\ell}$, and, as a result, the non-paraxial effects in scattering are $\ell$ times enhanced for these beams and can reach $10^{-3}$. We calculate the non-paraxial corrections to the plane-wave cross section in a model-independent way, give examples from QED and QCD, study a contribution of a phase of a scattering amplitude, compare different models of the in-states, and show that for well-focused beams these effects can compete with the two-loop contributions to the basic QED processes like $e^-e^- \rightarrow e^-e^-, e^-\gamma \rightarrow e^-\gamma$, etc.
