Non-Perturbative Relativistic Calculation of the Muonic Hydrogen Spectrum

Abstract

We investigate the muonic hydrogen 2P^{F=2}_{3/2} to 2S^{F=1}_{1/2} transition through a precise, non-perturbative numerical solution of the Dirac equation including the finite-size Coulomb force and finite size vacuum polarization. The results are compared with earlier perturbative calculations of (primarily) Borie, Martynenko, and Pachucki; and experimental results recently presented by Pohl et al., in which this very comparison is interpreted as requiring a modification of the proton charge radius from that obtained in electron scattering and electronic hydrogen analyses. We find no significant discrepancy between the perturbative and non-perturbative calculations, and present our results as confirmation of the perturbative methods.