Combined linear polarization and angular distribution measurements of x-rays for precise determination of multipole-mixing in characteristic transitions of high-Z systems

By applying novel-type position sensitive x-ray detectors as Compton polarimeters we recently performed a study of the linear polarization of Lyman-${\alpha }_1$ radiation following radiative electron capture into initially bare uranium ions. It was found that a model-independent determination of the ratio of the E1 and M2 transition amplitudes, and consequently of the corresponding transition rates, is feasible by combining the linear polarization data with a measurement of the angular distribution of the emitted radiation. In this work a detailed description of the underlying experimental technique for combined measurements of the linear polarization and the angular distribution of characteristic transitions in high-Z ions is presented. Special emphasis is given to the application of two, two-dimensional position-sensitive x-ray detectors for Compton polarimetry of hard x-rays. Moreover, we demonstrate the polarimeter efficiency of such detector systems can be significantly improved if events, where the charge is spread over neighboring segments, are reconstructed to be used in the polarization analysis. (paper)