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The current status of the theoretical investigation of the bound-electron g factor in lithium-like and boron-like highly charged ions is reported. Some tension between the several theoretical values and measurements is discussed. Then, prospects for future investigations are briefly reviewed. [ABSTRACT FROM AUTHOR]

A theoretical investigation of the elastic resonant scattering of photons by ultra–relativistic and partially stripped ions is presented. Particular attention in the study is given to the angular distribution and polarization of scattered photons as "seen" in both the ion‐rest and laboratory reference frames. In order to evaluate these angular and polarization properties, the irreducible polarization tensor approach is combined with the density matrix theory. If, furthermore, the ion–photon coupling is treated within the electric dipole approximation, this framework enables one to obtain simple analytical expressions for both the emission pattern and the polarization Stokes parameters of the outgoing radiation. These (analytical) expressions for the nS0→n′P1→nS0$n S_0 \rightarrow n^{\prime } P_1 \rightarrow n S_0$, nS1/2→n′P1/2→nS1/2$n S_{1/2} \rightarrow n^{\prime } P_{1/2} \rightarrow n S_{1/2}$, and nS1/2→n′P3/2→nS1/2$n S_{1/2} \rightarrow n^{\prime } P_{3/2} \rightarrow n S_{1/2}$ transitions are displayed and analyzed , that are of interest for the Gamma Factory project and whose realization is currently under discussion at CERN. Based on the performed analysis, it is demonstrated that the resonantly scattered photons can be strongly (linearly or circularly) polarized, and that this polarization can be well controlled by adjusting either the emission angle and/or the polarization state of the incident radiation. Moreover, the potential of the photon scattering for measuring the spin‐polarization of ion beams is also discussed in detail. [ABSTRACT FROM AUTHOR]

For photon energies from several 10 keV up to a few MeV Compton polarimetry is an indispensable tool to gain insight into subtle details of fundamental atomic radiative processes. Within the SPARC collaboration several segmented semiconductor detectors are developed that are well suited for application as efficient Compton polarimeters. In this report, these recent developments are reviewed and it is discussed how Compton polarimetry can be employed at the upcoming Gamma Factory. [ABSTRACT FROM AUTHOR]

A theoretical investigation of the resonant elastic scattering of laser photons by ultra‐relativistic partially stripped ions, that is the core process of the Gamma Factory project, is presented. Special emphasis in the study is placed on the angular distribution and polarization of scattered photons as observed in the collider and ion‐rest reference frames. In order to describe these (angular and polarization) properties for arbitrary relativistic many‐electron ion, the general approach, based on the application of irreducible polarization tensors, is laid down. By making use of the polarization tensors, the scattering of both conventional plane‐wave‐ and twisted (or vortex) photons is explored in detail. For the former case, it is shown how the propagation directions and polarization states of incident and outgoing photons are related to each other for the nS0→n′P1→nS0$n S_{0} \rightarrow n^{\prime } P_{1} \rightarrow n S_{0}$, nS1/2→n′P1/2→nS1/2$n S_{1/2} \rightarrow n^{\prime } P_{1/2} \rightarrow n S_{1/2}$, and nS1/2→n′P3/2→nS1/2$n S_{1/2} \rightarrow n^{\prime } P_{3/2} \rightarrow n S_{1/2}$ resonant transitions. For the scattering of initially twisted light that carries non‐zero orbital angular momentum, the angular distribution of secondary photons is explored and the conditions under which they are also twisted are discussed. [ABSTRACT FROM AUTHOR]

A systematic investigation of the nuclear polarization effects in one- and few-electron heavy ions is presented. The nuclear polarization corrections in the zeroth and first orders in 1 /Z are evaluated to the binding energies, the hyperfine splitting, and the bound-electron g factor. It is shown that the nuclear polarization contributions can be substantially canceled simultaneously with the rigid nuclear corrections. This allows for new prospects for probing the QED effects in a strong electromagnetic field and the determination of fundamental constants. [ABSTRACT FROM AUTHOR]

Recent progress in quantum electrodynamics (QED) calculations of highly charged ions is reviewed. The theoretical predictions for the binding energies, the hyperfine splittings, and the g factors are presented and compared with available experimental data. Special attention is paid to tests of bound-state QED at strong field regime. Future prospects for tests of QED at the strongest electric and magnetic fields as well as for determination of the fine structure constant and the nuclear magnetic moments with heavy ions are discussed. [ABSTRACT FROM AUTHOR]

The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example of a single particle (electron or vacancy) excitation with respect to the redefined vacuum. Starting with simple one-electron QED diagrams, we deduce first- and second-order many-electron contributions: screened self-energy, screened vacuum polarization, one-photon exchange, and two-photon exchange. The redefined vacuum approach provides a straightforward and streamlined derivation and facilitates its application to any electronic configuration. Moreover, based on the gauge invariance of the one-electron diagrams, we can identify various gauge-invariant subsets within derived many-electron QED contributions. [ABSTRACT FROM AUTHOR]

Photoelectron angular distributions of the two-photon ionization of neutral atoms are theoretically investigated. Numerical calculations of two-photon ionization cross sections and asymmetry parameters are carried out within the independent-particle approximation and relativistic second-order perturbation theory. The dependence of the asymmetry parameters on the polarization and energy of the incident light as well as on the angular momentum properties of the ionized electron are investigated. While dynamic variations of the angular distributions at photon energies near intermediate level resonances are expected, we demonstrate that equally strong variations occur near the nonlinear Cooper minimum. The described phenomena is demonstrated on the example of two-photon ionization of magnesium atom. [ABSTRACT FROM AUTHOR]

Scattering of light on relativistic heavy ion beams is widely used for characterizing and tuning the properties of both the light and the ion beam. Its elastic component—Rayleigh scattering—is investigated in this work for photon energies close to certain electronic transitions because of its potential usage in the Gamma Factory initiative at CERN. The angle-differential cross-section, as well as the degree of polarization of the scattered light are investigated for the cases of 1 s − 2 p 1 / 2 and 1 s − 2 p 3 / 2 resonance transitions in H-like lead ions. In order to gauge the validity and uncertainty of frequently used approximations, we compare different methods. In particular, rigorous quantum electrodynamics calculations are compared with the resonant electric-dipole approximation evaluated within the relativistic and nonrelativistic formalisms. For better understanding of the origin of the approximation, the commonly used theoretical approach is explained here in detail. We find that in most cases, the nonrelativistic resonant electric-dipole approximation fails to describe the properties of the scattered light. At the same time, its relativistic variant agrees with the rigorous treatment within a level of 10% to 20%. These findings are essential for the design of an experimental setup exploiting the scattering process, as well as for the determination of the scattered light properties. [ABSTRACT FROM AUTHOR]

A recent measurement of the hyperfine splitting in the ground state of Li-like 208Bi80+ has established a "hyperfine puzzle"--the experimental result exhibits a 7s deviation from the theoretical prediction [J. Ullmann et al., Nat. Commun. 8, 15484 (2017); J. P. Karr, Nat. Phys. 13, 533 (2017)]. We provide evidence that the discrepancy is caused by an inaccurate value of the tabulated nuclear magnetic moment (µI) of 209Bi. We perform relativistic density functional theory and relativistic coupled cluster calculations of the shielding constant that should be used to extract the value of µI(209Bi) and combine it with nuclear magnetic resonance measurements of Bi(NO3)3 in nitric acid solutions and of the hexafluoridobismuthate(V) BiF-6 ion in acetonitrile. The result clearly reveals that µI(209Bi) is much smaller than the tabulated value used previously. Applying the new magnetic moment shifts the theoretical prediction into agreement with experiment and resolves the hyperfine puzzle. [ABSTRACT FROM AUTHOR]

A recent measurement of the hyperfine splitting in the ground state of Li-like ^{208}Bi^{80+} has established a "hyperfine puzzle"-the experimental result exhibits a 7σ deviation from the theoretical prediction [J. Ullmann et al., Nat. Commun. 8, 15484 (2017)NCAOBW2041-172310.1038/ncomms15484; J. P. Karr, Nat. Phys. 13, 533 (2017)NPAHAX1745-247310.1038/nphys4159]. We provide evidence that the discrepancy is caused by an inaccurate value of the tabulated nuclear magnetic moment (μ_{I}) of ^{209}Bi. We perform relativistic density functional theory and relativistic coupled cluster calculations of the shielding constant that should be used to extract the value of μ_{I}(^{209}Bi) and combine it with nuclear magnetic resonance measurements of Bi(NO_{3})_{3} in nitric acid solutions and of the hexafluoridobismuthate(V) BiF_{6}^{-} ion in acetonitrile. The result clearly reveals that μ_{I}(^{209}Bi) is much smaller than the tabulated value used previously. Applying the new magnetic moment shifts the theoretical prediction into agreement with experiment and resolves the hyperfine puzzle.