Probing phase of a scattering amplitude beyond the plane-wave approximation

TL;DR

This paper demonstrates that the phase of a scattering amplitude, typically ignored in plane-wave models, can influence observable outcomes when particles are described as wave packets, especially using novel beam states.

Contribution

It introduces methods to probe phase effects in scattering beyond plane-wave approximation, including impact-parameter collisions and vortex or Airy beams.

Findings

Phase effects can alter cross sections by more than 10^{-4} to 10^{-3} in electron-electron collisions.

Wave packet descriptions reveal phase dependencies absent in plane-wave models.

Proposed experimental setups can detect these phase effects in realistic beam conditions.

Abstract

Within a plane-wave approach, a number of scattering events in a collision is insensitive to a general phase of a transition amplitude, although this phase is extremely important for a number of problems, especially in hadronic physics. In reality the particles are better described as wave packets, and here we show that the observables grow dependent upon this phase if one lays aside the simplified plane-wave model. We discuss two methods for probing how the Coulomb- and hadronic phases change with a transferred momentum $t$, either by colliding two beams at a non-vanishing impact-parameter or by employing such novel states as the vortex particles carrying orbital angular momentum or the Airy beams. For electron-electron collision, the phase contribution to a cross section can reach the values higher than $10^{-4} -- 10^{-3}$ for well-focused beams with energies of hundreds of keV.