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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]