E-catalog        

Библиогр.: 37 назв.

A plane-wave approximation in particle physics implies that a width of a massive wave packet σ⊥ is much larger than its Compton wavelength λc=ℏ/mc. For Gaussian beams or for packets with the non-singular phases (say, the Airy beams), corrections to this approximation are attenuated as λ2c/σ2⊥≪1 and usually negligible. Here we show that this situation drastically changes for particles with the phase vortices associated with an orbital angular momentum ℓℏ. For highly twisted beams with |ℓ|≫1, the non-paraxial corrections get |ℓ| times enhanced and |ℓ| can already be as large as 103. We describe 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 massive Laguerre-Gaussian beams. We compare such states with their paraxial counterpart paying specific attention to the relativistic effects and to the differences from the twisted photons. In particular, a Gouy phase is found to be Lorentz invariant and it generally depends on time rather than on a distance z. By calculating the electron packet's mean invariant mass, magnetic moment, etc., we demonstrate that the non-paraxial corrections can already reach the relative values of 10−3. These states and the non-paraxial effects can be relevant for the proper description of the spin-orbit phenomena in relativistic vortex beams, of scattering of the focused packets by atomic targets, of collision processes in particle and nuclear physics, and so forth.