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In connection with recent and proposed experiments, and new theoretical results, my previous calculations of the Lamb shift in muonic hydrogen will be reviewed and compared with other work. In addition, numerical results for muonic deuterium and helium will be presented. Some previously neglected (but very small) effects are included.

The Lamb shift in muonic hydrogen continues to be a subject of experimental and theoretical investigation. Here my older work on the subject is updated to provide a complementary calculation of the energies of the 2p-2s transitions in muonic hydrogen. IntroductionThe 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]. In view of a proposed measurement of the Lamb shift im muonic hydrogen [2], an improved theoretical analysis seems to be desirable. Since the first theoretical analysis [3], the subject of the Lamb shift (the 2p-2s transition) in light muonic atoms has been investigated with increasing precision by a number of authors [4,5,6,7,8,9,10]. The present paper provides an independent recalculation of some of the most important effects, including hyperfine structure, and a new calculation of some terms that were omitted in the most recent literature, such as the virtual Delbrück effect [11]. An alternative calculation of the relativistic recoil correction is presented.In

Recent experimental investigations of atomic x rays in protonium have revived interest in the atomic cascade process. Following a calculation of Leon and Bethe, which includes chemical and Auger deexcitation, Stark mixing and 'annihilation, as wdl as radiative transitions, we investigate the dependence of the yields of K and L x rays on the target density, and on the hadronic shifts and widths of the 1s and 2p levels. Numerical results are also given for kaonic, pionic, and muonic hydrogen.

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