Mass Measurements and the Bound--Electron g Factor
  The accurate determination of atomic masses and the high-precision measurement of the bound-electron g factor are prerequisites for the determination of the electron mass, which is one of the fundamental constants of nature. In the 2002 CODATA adjustment [P. J. Mohr and B. N. Taylor, Rev. Mod. Phys. 77, 1 (2005)], the values of the electron mass and the electron-proton mass ratio are mainly based on g factor measurements in combination with atomic mass measurements. In this paper, we briefly discuss the prospects for obtaining other fundamental information from bound-electron g factor measurements, we present some details of a recent investigation of two-loop binding corrections to the g factor, and we also investigate the radiative corrections in the limit of highly excited Rydberg S states with a long lifetime, where the g factor might be explored using a double resonance experiment. 
U. D. Jentschura, A. Czarnecki, K. Pachucki and V. A. Yerokhin