Wichmann-Kroll correction for the ground states of bi-muonic helium atoms

The effect of vacuum polarization in the ground 1S1(L=0)-states of bi-muonic helium atoms is considered. The main attention is given to the second order correction (so-called Wichmann-Kroll correction) to the vacuum polarization. The corresponding energy shifts for the ground states in the bi-muonic He3μ2 and He4μ2 atoms have been determined numerically. It is shown that the bi-muonic He3μ2 and He4μ2 helium atoms are very promising atomic systems to study the effect of vacuum polarization and measure the contribution of related radiative corrections to the free electromagnetic field Lagrangian.