Radiative recombination of twisted electrons with bare nuclei: Going beyond the Born approximation

Abstract

We present a fully relativistic investigation of the radiative recombination of a twisted electron with a bare heavy nucleus. The twisted electron is described by the wave function which accounts for the interaction with the nucleus in all orders in αZ. We use this wave function to derive the probability of the radiative recombination with a single ion being shifted from the twisted electron propagation direction. We also consider more realistic experimental scenarios where the target is either localized (mesoscopic) or infinitely wide (macroscopic). The situation when the incident electron is a coherent superposition of two vortex states is considered as well. For the nonrelativistic case we present analytical expressions which support our numerical calculations. We study in details the influence of the electron twistedness on the polarization and angular distribution of the emitted photon.It is found that these properties of the outgoing photon might be very sensitive to the total angular momentum and kinematic properties of twisted beams. Therefore, the recombination of the twisted electrons can serve as a valuable tool for atomic investigations as well as for the diagnostics of the vortex electron beams.

Radiative recombination of twisted electrons with hydrogen-like heavy ions: Linear polarization of emitted photons

“…As seen from this expression, the elements of the density matrix are independent of the projection m j of the total angular momentum (TAM) of Bessel electrons and just sensitive to the ratio of (the absolute values of) their transverse to longitudinal momenta. This result is consistent with the common knowledge that the probabilities of atomic processes, involving twisted particles, are insensitive to the TAM if the integration over the impact parameter b is performed [28,36]. By inserting the density matrix ( 22) into Eqs.…”

“…Below we will assume that this electron is prepared in the twisted Bessel state |κm j p z m s , which is characterized by the well-defined projections p z and m j of the linear-and total angular momenta, as well as by the fixed absolute value of the transverse momentum κ = |p ⊥ |. Since the properties of the Bessel electrons, moving in the Coulomb field of an ion, have been thoroughly discussed in the literature [27][28][29], here we just briefly recall the basic expressions, required for the further analysis. The wave function of an electron in the Bessel state can be written as the superposition of the plane-wave continuum solutions ψ pms (r) of the Dirac equation:…”

“…In particular, both the probability density distribution of the electrons and their spin polarization varies with the distance from the center of the Bessel beam, see Refs. [27][28][29] for further details.…”

“…We can expect that OAM-effects will also play an important role in the fundamental process of the radiative recombination and can significantly modify the linear polarization of emitted photons. A first step towards such an analysis of the RR linear polarization has been done by Zaytsev and co-workers [28] who considered the capture of twisted electrons by bare ions. As mentioned above, however, much of today's interest is focused on the radiative recombination of initially hydrogen-like (finally heliumlike) ions, whose spin states can be studied based on the polarization-resolved measurements of K-RR radiation.…”

Twisted particles as a new tool to study micro world phenomena and processes

“…A series of studies of various processes of collisions with twisted electrons was carried out over the last decade. However, in all these studies, twisted electron beam interacted with either a single counter-propagating beam (Compton scattering [6], electron-electron scattering [7]) or a target consisting of atoms (radiative recombination [8][9], Mott scattering [10]). The process of twisted electron scattering on target molecules has been studied herein for the first time.…”