New logarithmic radiative corrections to the hyperfine splitting in hydrogenic atoms

Abstract

We report here on the calculation of new radiative corrections to the hyperfine splitting in hydrogenic atoms. The result for the correction ΔE to the 1S state is ΔE/EF= (αw/π)(-2/3 ln2 + lnw · · [8/3 ln2 — 37/72 — 4/15]), wherew=(αZ)2 andEfis the lowest-order splitting. The last term is due to vacuum polarization. A brief description is given of the method of calculation, which employs the free-propagator expansion of the bound-electron Green’s function. In the important case of hydrogen, the new corrections tend to slightly worsen the already unsatisfactory agreement of theory with experiment. The relevance of this result to the proton structure problem is briefly discussed. Integral expressions are given for the « mean electromagnetic radius » of the proton in terms of the proton charge and magnetic moment form factors in momentum space.