Determination of the polarizability of Na-like silicon by study of the fine structure of high-LRydberg states ofSi2+

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The fine-structure intervals in the $n=29$ state of ${\mathrm{Si}}^{2+}$ separating levels from $L=8$ to $L=14$ have been measured by microwave spectroscopy. A beam of ${\mathrm{Si}}^{3+}$ (Na-like silicon) captures a single electron from an $n=10$ Rydberg target, forming highly excited Rydberg states of ${\mathrm{Si}}^{2+}$ near $n=29.$ Specific L levels within $n=29$ are selectively detected by excitation with a Doppler-tuned ${\mathrm{CO}}_{2}$ laser, followed by Stark ionization. This allows the detection of microwave induced transitions between different L levels in the $n=29$ state, determining the fine-structure intervals. The fine-structure pattern can be used to deduce the dipole polarizability of the ${\mathrm{Si}}^{3+}$ ion, which forms the core of the Rydberg system. The result ${\ensuremath{\alpha}}_{d}=7.404(11)$ is in good agreement with calculations that are comparable in precision.