2. Experimental method and data analysis

The measurements were performed at the internal gas-target of the ESR storage ring facility at GSI-Darmstadt. The detailed description of the experiment can be found elsewhere [4]. The absolute cross-sections for bremsstrahlung were determined by normalizing the bremsstrahlung intensity to that of the radiative electron capture to the L-shell of the projectile (L-REC) observed at 132^o. The theoretical L-REC cross-sections used for the normalization purpose were obtained from rigorous relativistic calculations [6]. The latter are known to describe very well the available experimental data for REC into high-Z projectiles. In particular, it has been demonstrated that this model yields good quantitative agreement with experimental sub-shell resolved angular distributions of L-REC for He-like uranium [5].

Simultaneously, the measured spectra were corrected for efficiency of the x-ray detectors, background radiation, as well as for the x-rays associated with radiative electron capture to L- and higher shells. The latter correction is essential in order to determine the overall shape of bremsstrahlung spectrum since REC into the M-, and higher shells partially overlaps with the end-point region of the primary bremsstrahlung. For this purpose, the spectra taken in coincidence with down-charged uranium ions were subtracted from the corresponding single spectra. We estimate that the overall uncertainty of the doubly differential cross sections does not exceed 30%.

For U $^{90+}\rightarrow$ N₂, Ar collisions bremsstrahlung occurs in the inverse scattering kinematics, i.e. the bound target electrons are inelastically scattered from the nucleus of the projectile giving rise to the emission of bremsstrahlung. In order to compare the experimental results with theoretical calculations (which are conventionally given in the rest frame of the scattering center), the latter have to be transformed to the laboratory reference frame (see e.g. [6]). In addition, we assume that the loosely bound target electrons can be treated as free particles, in high-energy collision. The initial electron momentum distribution of the target electron is, however, taken into account by folding the theoretical cross-sections with the Compton profile of the target electrons.