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

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 $\alpha Z$. 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. This probability is utilized for the consideration of a more realistic experimental scenario where the target is 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.

Figure 1

The geometry of the RR process.

Figure 2

The normalized angular distribution (28) for the RR of the twisted electron into the $1s$ state of H-like ions. On the left, middle, and right panels the cases of the argon ($Z=18$), xenon ($Z=54$), and thorium ($Z=90$) ions are presented, respectively. The kinetic energy of the incident electron is 2 keV (for argon), 18 keV (for xenon), and 50 keV (for thorium).

Figure 3

The differential cross section (26) for the RR of the twisted electron into the $2p_{3/2}$ state of H-like ions. On the left, middle, and right panels the cases of the argon ($Z=18$), xenon ($Z=54$), and thorium ($Z=90$) ions are presented, respectively. The kinetic energy of the incident electron is 2 keV (for argon), 18 keV (for xenon), and 50 keV (for thorium).

Figure 4

The degree of the linear polarization (30) for the RR of the twisted electron with the bare nuclei. The results for the argon ($Z=18$) ion at 2 keV electron energy are presented in the first row. In the second row, the case of the thorium ($Z=90$) ion at the 50 keV electron energy is depicted. The recombinations into the $1s$ and $2p_{3/2}$ states are presented in the left and right columns, respectively. The black solid line corresponds to the conventional plane-wave-asymptotics case.

Figure 5

The azimuthal asymmetry parameter $\mathcal{A}$, defined by Eq. (38), for the radiative recombination of the 18 keV twisted electron into the $1s$ state of the xenon ($Z=54$) ion. It is assumed that $|c_1{c}_2|=1/2$ and $\mathrm{\Delta }\alpha =0$.