2s Hyperfine splitting

The frequency of the 1S hyperfine interval in atomic hydrogen is one of the best measured quantities in physics with about 13 digits known. The hyperfine interaction depends largely on the structure of the nucleus that can not be calculated from first principles with the required accuracy. Therefore the 1S hyperfine interval cannot be used directly to test quantum electrodynamics. However, if combined with 8 times the hyperfine splitting of the 2S state according to

{$ D_{21}=8f_{\rm HFS}(2S) - f_{\rm HFS}(1S) $}

an accurately calculable quantity is obtained. For this combination most of the difficult to calculate terms cancel thanks to the approximate scaling of the hyperfine structure with the inverse cube of the principle quantum number. The test of quantum electrodynamics via the above difference is limited by the experimental value for the 2S hyperfine interval. Traditionally this has been measured within the radio frequency domain so that uncertainties in the optical frequencies would cancel out. Meanwhile our spectrometer is sufficiently accurate to improve on these measurements with laser excitation schemes.

Further reading