2018/03/24 by Karlovets, Dmitry
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Optics (physics.optics) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1803.09150
One of the reasons for the tremendous success of a plane-wave approximation in particle physics is that the non-paraxial corrections to such observables as energy, magnetic moment, scattering cross section, and so on are attenuated as λc2/σ⊥2 ≪ 1 where σ⊥ is a beam width and λc = ℏ/mc is a Compton wavelength. This amounts to less than 10-14 for modern electron accelerators and less than 10-6 for electron microscopes. Here we show that these corrections are |ℓ| times enhanced for vortex particles with high orbital angular momenta |ℓ|ℏ, which can already be as large as 103ℏ. We put forward the relativistic wave packets, both for vortex bosons and fermions, which transform correctly under the Lorentz boosts, are localized in a 3D space, and represent a non-paraxial generalization of the Laguerre-Gaussian beams. We demonstrate that it is √(|ℓ|) λc ≫ λc that defines a paraxial scale for such packets, in contrast to those with a non-singular phase (say, the Airy beams). With current technology, the non-paraxial corrections can reach the relative values of 10-3, yield a proportional increase of an invariant mass of the electron packet, describe a spin-orbit coupling as well as the quantum coherence phenomena in particle and atomic collisions.