Lamb shift of electronic states in neutral muonic helium, an electron-muon-nucleus system

Neutral muonic helium is an exotic atomic system consisting of an electron, a muon, and a nucleus. Being a three-body system, it possesses a clear hierarchy. This allows us to consider it as a hydrogenlike atom with a compound nucleus, which is, in turn, another hydrogenlike system. There are a number of corrections to the Bohr energy levels, all of which can be treated as contributions of generic hydrogenlike theory. While the form of those contributions is the same for all hydrogenlike atoms, their relative numerical importance differs from atom to atom. Here, the leading contribution to the (electronic) Lamb shift in neutral muonic helium is found in a closed analytic form together with the most important corrections. We believe that the Lamb shift in neutral muonic hydrogen is measurable, at least through a measurement of the (electronic) $1s\text{−}2s$ transition. We present a theoretical prediction for the $1s\text{−}2s$ transitions with an uncertainty of 3 ppm ($9\mathrm{GHz}$), as well as for the $2s\text{−}2p$ Lamb shift with an uncertainty of $1.3\mathrm{GHz}$.

Figure 1

The fine structure and the Lamb shift of the energy levels at $n=2$ in hydrogen and neutral muonic helium (approximately to scale). The hyperfine and reduced-mass effects are neglected.