Frequency Metrology of Helium around 1083 nm and Determination of the Nuclear Charge Radius

We measure the absolute frequency of seven out of the nine allowed transitions between the 2(3)S and 2(3)P hyperfine manifolds in a metastable He-3 beam by using an optical frequency comb synthesizer-assisted spectrometer. The relative uncertainty of our measurements ranges from 1 x 10(-11) to 5 x 10(-12), which is, to our knowledge, the most precise result for any optical He-3 transition to date. The resulting 2(3)P-2(3)S centroid frequency is 276 702 827 204.8(2.4) kHz. Comparing this value with the known result for the He-4 centroid and performing ab initio QED calculations of the He-4-He-3 isotope shift, we extract the difference of the squared nuclear charge radii delta r(2) of He-3 and He-4. Our result for delta r(2) = 1.074(3) fm(2) disagrees by about 4 sigma with the recent determination [R. van Rooij et al., Science 333, 196 (2011)].