Single and double $K$-shell vacancy production in slow Xe$^\textrm{54+,53+}$-Xe collisions

We present an experimental and theoretical study of symmetric $\textrm{Xe}^{54+}+\textrm{Xe}$ collisions at 50, 30, and 15 MeV/u, corresponding to strong perturbations with $v_K/v_\text{p}$ = 1.20, 1.55, and 2.20, respectively ($v_K$: classical $K$-shell orbital velocity, $v_\text{p}$: projectile velocity), as well as $\textrm{Xe}^{53+}+\textrm{Xe}$ collisions at 15 MeV/u. For each of these systems, x-ray spectra were measured under a forward angle of $35^\circ$ with respect to the projectile beam. Target satellite and hypersatellite radiation, $Kα_{2,1}^\mathrm{s}$ and $Kα_{2,1}^\mathrm{hs}$, respectively, were analyzed and used to derive cross section ratios for double-to-single target $K$-shell vacancy production. We compare our experimental results to relativistic time-dependent two-center calculations.