Proton form-factor dependence of the finite-size correction to the Lamb shift in muonic hydrogen

The measurement of the 2P^{F=2}_{3/2} to 2S^{F=1}_{1/2} transition in muonic hydrogen by Pohl et al. and subsequent analysis has led to the conclusion that the rms radius of the proton differs from the accepted (CODATA) value by approximately 4%, corresponding to a 4.9 sigma discrepancy. We investigate the finite-size effects - in particular the dependence on the shape of the proton electric form-factor - relevant to this transition using bound-state QED with nonperturbative, relativistic Dirac wave-functions for a wide range of idealised charge-distributions and a parameterization of experimental data in order to comment on the extent to which the perturbation-theory analysis which leads to the above conclusion can be confirmed. We find no statistically significant dependence of this correction on the shape of the proton form-factor.