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

Abstract

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 $\ensuremath{\Delta}{f}_{\mathrm{th}}=670 999 566.90(66)(60) \text{kHz}$ (exclusive of the nonrelativistic nuclear-finite-size correction) and the experimental result $\ensuremath{\Delta}{f}_{\mathrm{expt}}=670 994 334 605(15) \mathrm{Hz}$, we infer the deuteron-proton charge-radius difference $\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}{}_{d}\ensuremath{-}\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}{}_{p}=3.820 07(65) \phantom{\rule{0ex}{0ex}}{\mathrm{fm}}^{2}$ and the deuteron structure radius ${r}_{\mathrm{str}}=1.975 07(78) \mathrm{fm}$.