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 Δn = 0 and Δl ≠ 0. Here we consider the Lamb shift in the leading non-relativistic approximation, i.e., within an approach based on a certain Schroedinger equation. That is valid for low and medium Z as long as (Zα)2 << 1. The results 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. (authors)