Electronic vacuum polarisation effect on the muon dynamics in nuclear field

Muon dynamics in the nuclear field is investigated when taking into account the electronic vacuum polarization. We present the results of numerical solution of the generalized dynamical equation for the Lamb shifts of energy levels of muonic atoms with the different atomic numbers. It is shown that in describing the energy levels of muonic atoms the effect of the nonlocality of the interaction of the muon with the nucleus is not significant. It is also shown that this effect can be significant in the processes of the interaction of muon with the radiation field accompanied by the creation of the electron-positron pairs.