Optical spectroscopy of complex open 4$d$-shell ions Sn${}^{7+}$-Sn${}^{10+}$

We analyze the complex level structure of ions with many-valence-electron open [Kr] 4$d^{\text{m}}$ sub-shells ($\text{m}$=7-4) with ab initio calculations based on configuration-interaction many-body perturbation theory (CI+MBPT). Charge-state-resolved optical and extreme ultraviolet (EUV) spectra of Sn${}^{7+}$-Sn${}^{10+}$ ions were obtained using an electron beam ion trap. Semi-empirical spectral fits carried out with the orthogonal parameters technique and Cowan code calculations lead to 90 identifications of magnetic-dipole transitions and the determination of 79 energy ground-configuration levels, questioning some earlier EUV-line assignments. Our results, the most complete data set available to date for these ground configurations, confirm the ab initio predictive power of CI+MBPT calculations for the these complex electronic systems.