Hydrogen-deuterium isotope shift: From the 1S-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(th) = 670 999 566.90(66)(60) kHz (exclusive of the nonrelativistic nuclear-finite-size correction) and the experimental result Delta f(expt) = 670 994 334 605(15) Hz, we infer the deuteron-proton charge-radius difference < r(2)>(d) - < r(2)>(p) = 3.820 07(65) fm(2) and the deuteron structure radius r(str) = 1.975 07(78) fm.