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The fine-structure intervals in the nϭ29 state of Si 2ϩ separating levels from Lϭ8 to Lϭ14 have been measured by microwave spectroscopy. A beam of Si 3ϩ ͑Na-like silicon͒ captures a single electron from an n ϭ10 Rydberg target, forming highly excited Rydberg states of Si 2ϩ near nϭ29. Specific L levels within n ϭ29 are selectively detected by excitation with a Doppler-tuned CO 2 laser, followed by Stark ionization. This allows the detection of microwave induced transitions between different L levels in the nϭ29 state, determining the fine-structure intervals. The fine-structure pattern can be used to deduce the dipole polarizability of the Si 3ϩ ion, which forms the core of the Rydberg system. The result ␣ d ϭ7.404(11) is in good agreement with calculations that are comparable in precision.

Fine structure intervals connecting n = 19 Rydberg levels of Si+ with L between 9 and 16 were measured precisely using the RESIS/microwave technique. The fine structure pattern conforms closely with that predicted by an effective potential model, and indicates a value of 11.666(4)a30 for the adiabatic dipole polarizability of the Mg-like ion, Si2+.

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The fine structure of high-angular-momentum n = 9 and 10 Rydberg states of barium has been measured precisely, using the resonant excitation Stark ionization spectroscopy method. Optical transitions corresponding to ͑n , nЈ͒ = ͑10, 30͒, ͑9,17͒, and ͑9,20͒ were induced with a Doppler-tuned CO 2 laser, determining the finestructure energies corresponding to all n = 9 and 10 levels with L ജ 6. The pattern of these fine-structure energies conforms closely with an effective potential model, by comparison with which the dipole and quadrupole polarizabilities of Ba + can be determined. Combining our data with earlier measurements made it possible to deduce, in addition, the portion of ␣ 2 due to the lowest excited D state of Ba + . Our best estimates of these three properties are ␣ 1 = 124.30͑16͒a 0 3 , ␣ 2 = 2462͑361͒a 0 5 , and ␣ 2 0 = 1828͑88͒a 0 5 .