Hydrogen-Deuterium $1\mathit{S}-2\mathit{S}$ Isotope Shift and the Structure of the Deuteron

We have determined the hydrogen-deuterium isotope shift of the $1S-2S$ two-photon resonance with a 150-fold increase in accuracy compared to previous measurements. Our experimental result of $670994334.64\left(15\right)$ kHz has been obtained with an optical frequency comb generator and a ${\mathrm{CH}}_4$-stabilized He-Ne reference laser which provides the frequency stability of our spectrometer while switching between the isotopes. From this measurement we derive values for the difference of the mean square charge radii of the proton and deuteron $r_d^2{-r}_p^2=3.8212\mathrm{}\left(15\right){\mathrm{fm}}^2$, and for the deuteron structure radius $r_{\mathrm{str}}=1.975\mathrm{}35\left(85\right)$ fm.