Lamb Shift of Muonic Deuterium and Hydrogen

My previous calculations of the Lamb shift in muonic hydrogen are reviewed and compared with other work. In addition, numerical results for muonic deuterium are presented. Introduction The energy levels of muonic atoms are very sensitive to effects of quantum electrodynamics (QED), nuclear structure, and recoil, since the muon is about 206 times heavier than the electron [1]. A number of theoretical analyses of the Lamb shift (the 2p-2s transition) in light muonic atoms have been published [2, 3, 4, 5, 6, 15, 7, 9, 16], most recently in view of a proposed measurement of the Lamb shift im muonic hydrogen [8]. The present paper repeats the independent recalculation of some of the most important effects [3] and extends the numerical calculations to the case of muonic deuterium, including effects that were not considered previously [10]. Muonic deuterium is in many ways similar to muonic hydrogen, but there are some differences. In addition to the different mass the deuteron has spin 1 and both magnetic and quadrupole moments. In the numerical calculations the fundamental constants from CODATA 2002 ([11]): α Also, the following properties of the proton and deuteron were used: m p = 938.272 MeV/c 2 , R p = 0.875 ± 0.007 fm (other recent values are discussed below) and µ p = 2.79285 µ N. Also, m d = 1875.613 MeV/c 2 , R d = 2.139 ± 0.003 fm and µ d = 0.85744 µ N = 0.307012 µ p. ([11]) The deuteron has spin 1 and thus has both magnetic and quadrupole moments. The quadrupole moment of the deuteron is taken to be Q = 0.