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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]

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]

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]

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 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]