Light-by-light-scattering contributions to the Lamb shift in light muonic atoms

Abstract

We consider one-loop light-by-light-scattering contributions to the Lamb shift of the $1s,2s,2p$ states in light muonic hydrogen like atoms at $Z\le 10$. The contributions are of the order ${\alpha }^5{m}_{\mu }$ (with diverse dependence on the nuclear charge $Z$). Those include the contributions of the so-called Wichmann-Kroll potential ($\alpha (Z\alpha {)}^4{m}_{\mu }$), the virtual Delbrück scattering (${\alpha }^2(Z\alpha {)}^3{m}_{\mu }$), etc. The results are obtained in a nonrelativistic approximation. For the calculation of the virtual-Delbrück-scattering contribution, we have constructed an effective potential in the coordinate space which may be applied to other calculations in muonic atoms.

Comments: 9 pages