Non-perturbative Analysis of the Influence of the Proton Magnetization   and Charge Densities on the Hyperfine Splitting of Muonic Hydrogen
  We investigate the influence of the spatial extent of the proton magnetization and charge densities on the 2S hyperfine splitting in muonic hydrogen. The use of a non-perturbative relativistic Dirac approach leads to corrections of 15% to values obtained from the perturbative treatment encapsulated by the Zemach radius, which surpass the next-leading order contribution in the perturbation series by an order of magnitude. 
J. D. Carroll, A. W. Thomas, G. A. Miller, and J. Rafelski
physics.atom-ph hep-ph nucl-th