Nonperturbative relativistic calculation of the muonic hydrogen spectrum

J. D. Carroll, A. W. Thomas, J. Rafelski, and G. A. Miller

Phys. Rev. A 84, 012506 – Published 15 July 2011

Abstract

We investigate the muonic hydrogen $2 P_{3 / 2}^{F = 2}$ to $2 S_{1 / 2}^{F = 1}$ transition through a precise, nonperturbative 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) [E. Borie, Phys. Rev. A 71, 032508 (2005); E. Borie and G. A. Rinker, Rev. Mod. Phys. 54, 67 (1982); E. Borie, Z. Phys. A 275, 347 (1975) and A. P. Martynenko, Phys. Rev. A 71, 022506 (2005); A. Martynenko, Phys. At. Nucl. 71, 125 (2008), and K. Pachucki, Phys. Rev. A 53, 2092 (1996)] and experimental results recently presented by Pohl et al. [Nature (London) 466, 213 (2010)], 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 nonperturbative calculations, and we present our results as confirmation of the perturbative methods.