Theory of the Lamb shift in muonic tritium and the muonic He3 ion

Abstract

Due to recent experimental efforts on light muonic atoms, we consider the quantum electrodynamics (QED) theory of two-body muonic atoms, namely, of those with $A=3$. Here we present the results for the Lamb shift and fine structure up to the order ${\ensuremath{\alpha}}^{5}m$ for the $n=2$ levels, which in particular include (1) pure QED contributions, (2) the coefficient to the ${r}_{N}^{2}$ term with QED corrections (where ${r}_{N}$ is the rms nuclear charge radius), and (3) the general expressions for the nuclear-structure contributions consistent with the presented QED theory. We revisit theory for the muonic helium-3 ion by rechecking all the relevant theoretical contributions and develop a theory of muonic tritium. We also reestimate the uncertainty of the nuclear-structure contribution.