Vacuum polarization in muonic atoms: the Lamb shift at low and medium Z

In muonic atoms the Uehling potential (an effect of a free electronic vacuum polarization loop) is responsible for the leading contribution to the Lamb shift causing the splitting of states with ∆n = 0 and ∆l 6= 0. Here we consider the Lamb shift in the leading nonrelativistic approximation, i.e., within an approach based on a certain Schrödinger equation. That is valid for low and medium Z as long as (Zα) ≪ 1. The result is a function of a few parameters, including κ = Zαmμ/me, n and l. We present various asymptotics and in particular we study a region of validity of asymptotics with large and small κ. Special attention is paid to circular states, which are considered in a limit of n ≫ 1. PACS. 36.10.Gv Mesonic atoms and molecules, hyperonic atoms and molecules – 31.30.Jv Relativistic and quantum electrodynamic effects in atoms and molecules