Hydrogen-deuterium isotope shift: From the1S−2S-transition frequency to the proton-deuteron charge-radius difference

We analyze and review the theory of the hydrogen-deuterium isotope shift for the $1S$-$2S$ transition, which is one of the most accurately measured isotope shifts in any atomic system, in view of a recently improved experiment. A tabulation of all physical effects that contribute to the isotope shift is given. These include the Dirac binding energy, quantum electrodynamic effects, including recoil corrections, and the nuclear-size effect, including the pertaining relativistic and radiative corrections. From a comparison of the theoretical result $\Delta f_{\mathrm{th}}=670\hspace{0.5em}999\hspace{0.5em}566.90(66)(60)\hspace{0.5em}\text{kHz}$ (exclusive of the nonrelativistic nuclear-finite-size correction) and the experimental result $\Delta f_{\mathrm{expt}}=670\hspace{0.5em}994\hspace{0.5em}334\hspace{0.5em}605(15)\hspace{0.5em}\mathrm{Hz}$, we infer the deuteron-proton charge-radius difference $\langle r^2\rangle {}_d-\langle r^2\rangle {}_p=3.820\hspace{0.5em}07(65)\hspace{0.5em}{\mathrm{fm}}^2$ and the deuteron structure radius $r_{\mathrm{str}}=1.975\hspace{0.5em}07(78)\hspace{0.5em}\mathrm{fm}$.