Fine structure of Rydberg states. III. New measurements inD,F, andGstates ofHe4

We report further accurate measurements of fine structure in $D$, $F$, and $G$ Rydberg states of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ obtained using a microwave-optical resonance method and electron-bombardment excitation. Single-quantum electricdipole transitions $10{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}-10\mathrm{}{}_{}{}^{1,3}{}_{}{}^{}F_3^{}{}_{}{}^{}$, $11{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}-11\mathrm{}{}_{}{}^{1,3}{}_{}{}^{}F_3^{}{}_{}{}^{}$, $12{}_{}{}^3{}_{}{}^{}D_J^{}{}_{}{}^{}-12\mathrm{}{}_{}{}^{1,3}{}_{}{}^{}F_{J^{\prime }}^{}{}_{}{}^{}$, and $6{}_{}{}^1{}_{}{}^{}F_3^{}{}_{}{}^{}-6\mathrm{}{}_{}{}^1{}_{}{}^{}G_4^{}{}_{}{}^{}$, and two-quantum transitions $7{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}-7\mathrm{}{}_{}{}^{1,3}{}_{}{}^{}G_4^{}{}_{}{}^{}$, $9{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}-9\mathrm{}{}_{}{}^{1,3}{}_{}{}^{}G_4^{}{}_{}{}^{}$, $10{}_{}{}^3{}_{}{}^{}D_J^{}{}_{}{}^{}-10\mathrm{}{}_{}{}^{1,3}{}_{}{}^{}G_{J^{\prime }}^{}{}_{}{}^{}$, and $16{}_{}{}^1{}_{}{}^{}P-16\mathrm{}{}_{}{}^{1,3}{}_{}{}^{}F_3^{}{}_{}{}^{}$ were observed. Both electrostatic and relativistic fine-structure intervals were determined with uncertainties less than 1 MHz and are compared with theoretical results. The data constitute the first measurements of $G$-state fine structure in helium. Series formulas incorporating all our measurements are given for serveral resonance series, and we show that the entire series $n{}_{}{}^1{}_{}{}^{}F_3^{}{}_{}{}^{}-n{}_{}{}^1{}_{}{}^{}G_4^{}{}_{}{}^{}$ can be predicted to within 75 ppm.