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

We present an experimental and theoretical study of symmetric ${\text{Xe}}^{54+}+\text{Xe}$ collisions at 50, 30, and 15 MeV/u, corresponding to strong perturbations with $v_K\mathrm{/}{v}_{\text{p}}$ = 1.20, 1.55, and 2.20, respectively ($v_K$: classical $K$-shell orbital velocity, $v_{\text{p}}$: projectile velocity), as well as ${\text{Xe}}^{53+}+\text{Xe}$ 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, $K{\alpha }_{2,1}^{\mathrm{s}}$ and $K{\alpha }_{2,1}^{\mathrm{h}\mathrm{s}}$, 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.