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.

arXiv comment9 pages

References in corpus (7)

• Theory of Light Hydrogenlike Atoms
• Lamb Shift in Muonic Hydrogen
• Light-by-light scattering in the Lamb shift and the bound electron g factor
• Delbruck scattering and the g-factor of a bound electron
• Non-relativistic contributions in order ${\alpha }^5{m}_{\mu }{c}^2$ to the Lamb shift in muonic hydrogen, deuterium and helium ion
• Contribution of Light-by-Light Scattering to Energy Levels of Light Muonic Atoms
• The ${\alpha }^2(Z\alpha {)}^{4}m$ contributions to the Lamb shift and the fine structure in light muonic atoms

Cited by in corpus (4)

• The Lamb shift of the $1s$ state in hydrogen: two-loop and three-loop contributions
• Virtual Delbrück scattering and the Lamb shift in light hydrogen-like atoms
• Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory
• Energy interval 3S-1S in muonic hydrogen