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 Delta n = 0 and Delta l not equal 0. Here we consider the Lamb shift in the leading nonrelativistic approximation, i.e., within an approach based on a certain Schrodinger equation. That is valid for low and medium Z as long as (Z alpha)(2) << 1. The result is a function of a few parameters, including kappa=Z alpha m(mu)/m(e), n and l. We present various asymptotics and in particular we study a region of validity of asymptotics with large and small kappa. Special attention is paid to circular states, which are considered in a limit of n >> 1.