Abstract: 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 \textasciigrave \textasciigrave 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 \textasciigrave P1 -> nS0\textbackslash \textdollar n S\_0 \textbackslash rightarrow n<\^>\textbackslash \textbackslash prime \textbackslash P\_1 \textbackslash rightarrow n S\_0\textbackslash \textdollar , nS1/2 -> n \textasciigrave P1/2 -> nS1/2\textbackslash \textdollar n S\_\textbackslash 1/2\textbackslash \textbackslash rightarrow n<\^>\textbackslash \textbackslash prime \textbackslash P\_\textbackslash 1/2\textbackslash \textbackslash rightarrow n S\_\textbackslash 1/2\textbackslash \textbackslash \textdollar , and nS1/2 -> n \textasciigrave P3/2 -> nS1/2\textbackslash \textdollar n S\_\textbackslash 1/2\textbackslash \textbackslash rightarrow n<\^>\textbackslash \textbackslash prime \textbackslash P\_\textbackslash 3/2\textbackslash \textbackslash rightarrow n S\_\textbackslash 1/2\textbackslash \textbackslash \textdollar 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: 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 1s - 2p1/2 and 1s - 2p3/2 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.