Fine structure of Rydberg states. V.n=5and6FandGstates ofHe4

We have made 17 new high-precision measurements of the $\mathrm{nF}-\mathrm{nG}$ intervals ($n=5,6\mathrm{}$) of neutral ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ using the microwave-optical method. The rms one-standard-deviation experimental uncertainty for the transitions reported here is 188 kHz (14 ppm). The new measurements agree with the predictions of a least-squares fit to previous experimental data, and are up to 40 times more precise. The $\mathrm{nF}-\mathrm{nG}$ manifold is now known experimentally to better than 1 MHz for all values of the quantum numbers. The precision of the experimental measurement exceeds that of the best currently available theory by approximately three orders of magnitude.