Polarization of Photons Scattered by Ultra‐Relativistic Ion Beams

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.