Paper detail

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