The exploitation of polarization degrees of freedom of hadron beams and/or targets offers a wealth of observables that are not accessible with unpolarized particles.These observables can be used to test the conservation or violation of fundamental symmetries like parity, charge conjugation, time reversal or combinations thereof.This paper describes some of the physics that can be pursued with polarized hadron beams or polarized targets using the CRYRING and the Experimental Storage Ring (ESR) at GSI/FAIR in Darmstadt after the completion of the experimental program with the Cooler Synchrotron COSY at Forschungszentrum Jülich.

We present a theoretical study of elastic photon scattering by atomic targets. This process is of special interest since various channels from atomic and nuclear physics as well as quantum elctrodynamics (QED) contribute to it. In this work, we focus on Delbr\"uck scattering which proceeds via production of virtual $e^+e^-$ pairs. In particular, we explore whether and how the Delbr\"uck channel can be "seen" in present synchrotron experiments which employ strongly linearly polarized light in the energy range of a few hundred keV. In order to answer this question, detailed calculations have been performed for the scattering of 300 keV and 889.2 keV photons off helium-like tin ions. Based on these calculations, we argue that the Delbr\"uck scattering for the energies below the threshold for $e^+e^-$ pair creation leads to a shift in the angular distribution and the polarization of the scattered photons which can be observed by state-of-the-art solid-state detectors.

For decelerated bare lead ions at a low beam energy of 10 MeV/u, the x-ray emission associated with radiative recombination (RR) at threshold energies has been studied at the electron cooler of CRYRING@ESR at GSI, Darmstadt. In our experiment, we observed the full x-ray emission pattern by utilizing dedicated x-ray detection chambers installed at 0??? and 180??? observation geometry. Most remarkably, no line distortion effects due to delayed emission are present in the well-defined x-ray spectra, spanning a wide range of x-ray energies (from about 5 to 100 keV), which enables us to identify fine-structure resolved Lyman, Balmer, and Paschen x-ray lines along with the RR transitions into the K, L, and M shells of the ions. For comparison with theory, an elaborate theoretical model is established taking into account the initial population distribution via RR for all atomic levels up to Rydberg states with principal quantum number n = 165 in combination with time-dependent feeding transitions. Within the statistical accuracy, the experimental data are in very good agreement with the results of rigorous relativistic predictions. Most notably, this comparison sheds light on the contribution of prompt and delayed x-ray emission (up to 70 ns) to the observed x-ray spectra, originating in particular from yrast transitions into inner shells.