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On the basis of quasipotential method in quantum electrodynamics we calculatenuclear finite size radiative corrections of order $\alpha(Z \alpha)^5$ to theLamb shift in muonic hydrogen and helium. To construct the interactionpotential of particles, which gives the necessary contributions to the energyspectrum, we use the method of projection operators to states with a definitespin. Separate analytic expressions for the contributions of the muonself-energy, the muon vertex operator and the amplitude with spanning photonare obtained. We present also numerical results for these contributions usingmodern experimental data on the electromagnetic form factors of light nuclei.

Radiative nonrecoil nuclear finite size corrections of order $\alpha(Z \alpha)^5$ to the Lamb shift in light muonic atoms