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Coulomb excitation of hydrogen atoms by vortex protons is theoretically investigated within the framework of the non--relativistic first--Born approximation and the density matrix approach. Special attention is paid to the magnetic sublevel population of excited atoms and, consequently, to the angular distribution of the fluorescence radiation. We argue that both these properties are sensitive to the projection of the orbital angular momentum (OAM), carried by the projectile ions. In order to illustrate the OAM--effect, detailed calculations have been performed for the $1s \to 2p$ excitation and the subsequent $2p \to 1s$ radiative decay of a hydrogen target, interacting with incident Laguerre--Gaussian vortex protons. The calculation results suggest that Coulomb excitation can be employed for the diagnostics of vortex ion beam at accelerator and storage ring facilities., Comment: 15 pages, 4 figures

We present a theoretical study of photoexcitation of highly charged ions from their ground states, a process which can be realized at the Gamma Factory at CERN. Special attention is paid to the question of how the excitation rates are affected by the mixing of opposite-parity ionic levels, which is induced both by an external electric field and the weak interaction between electrons and the nucleus. In order to reinvestigate this "Stark-plus-weak-interaction" mixing, well-known in neutral atomic systems, we employ relativistic Dirac theory. Based on the developed approach, detailed calculations are performed for the ${\rm 1s}_{1/2} \to {\rm 2s}_{1/2}$ and ${\rm 1s}^2 \; {\rm 2s}_{1/2} \to {\rm 1s}^2 \; {\rm 3s}_{1/2}$ (M1 + parity-violating-E1) transitions in hydrogen- and lithium-like ions, respectively. In particular, we focus on the difference between the excitation rates obtained for the right- and left-circularly polarized incident light. This difference arises due to the parity violating mixing of ionic levels and is usually characterized in terms of the circular-dichroism parameter. We argue that future measurements of circular dichroism, performed with highly charged ions in the SPS or LHC rings, may provide valuable information on the electron-nucleus weak-interaction coupling., Comment: 14 pages, 6 figures

We present a theoretical investigation of the radiative recombination of twisted Bessel electrons with initially hydrogen-like (finally helium-like) heavy ions. In our study, we focus especially on the linear polarization of x-ray photons emitted in the electron capture into the ground $1s^2_{1/2}$ ionic state. Particular emphasis is placed on the question of how this polarization is affected if incident hydrogen-like ions are themselves spin-polarized. To explore such a "polarization transfer" we apply the density matrix theory and derive the Stokes parameters of recombination x-rays for the realistic case of collisions between macroscopic electron and ion beams. Based on the developed general approach two scenarios are discussed that are of interest for the planned experiments at ion storage rings. First, we demonstrate how the use of twisted electrons can empower the known method for the diagnostics of spin-polarized ion beams, based on the rotation of the linear polarization of recombination light. In the second scenario we show how the internal structure of ions beams with inhomogeneous intensity and spin patterns can be probed by the capture of Bessel electrons, carrying different values of angular momentum.

Modern spectroscopic experiments in few-electron atoms reached the level of precision at which an accurate description of quantum electrodynamics (QED) effects is mandatory. In many cases, theoretical treatment of QED effects has to be performed without any expansion in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant). Such calculations involve multiple summations over the whole spectrum of the Dirac equation in the presence of the binding nuclear field, which can be evaluated in terms of the Dirac Green function. In this paper we describe the technique of numerical calculations of QED corrections with the Dirac Green function, developed in numerous investigations during the last two decades.

The thorium nucleus with mass number $A=229$ has attracted much interest because its extremely low lying first excited isomeric state at about $8$eV opens the possibility for the development of a nuclear clock. However, neither the exact energy of this nuclear isomer nor properties, such as nuclear magnetic dipole and electric quadrupole moment are known to a high precision so far. The latter can be determined by investigating the hyperfine structure of thorium atoms or ions. Due to its electronic structure and the long lifetime of the nuclear isomeric state, Th$^{2+}$ is especially suitable for such kind of studies. In this letter we present a combined experimental and theoretical investigation of the hyperfine structure of the $^{229}$Th$^{2+}$ ion in the nuclear ground and isomeric state. A very good agreement between theory and experiment is found for the nuclear ground state. Moreover, we use our calculations to confirm the recently presented experimental value for the nuclear magnetic dipole moment of the thorium nuclear isomer, which was in contradiction to previous theoretical studies.