Second-order corrections to the wave function at origin in muonic hydrogen and pionium

Abstract

Non-relativisitic second-order corrections to the wave function at origin in muonic and exotic atoms are considered. The corrections are due to the electronic vacuum polarization. Such corrections are of interest due to various effective approaches, which take into account QED and hadronic effects. The wave function at origin plays a key role in the calculation of the pionium lifetime, various finite nuclear size effects and the hyperfine splitting. The results are obtained for the $1s$ and $2s$ states in pionic and muonic hydrogen and deuterium and in pionium, a bound system of ${\pi }^{+}$ and ${\pi }^{-}$. Applications to the hyperfine structure and the Lamb shift in muonic hydrogen are also considered.

4 pages, 5 figures

References in corpus (2)

• First measurement of the ${\pi }^{+}{\pi }^{-}$ atom lifetime
• Hadronic atoms in QCD + QED

Cited by in corpus (17)

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• High-energy electrons from the muon decay in orbit: radiative corrections
• Contribution of Light-by-Light Scattering to Energy Levels of Light Muonic Atoms
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• Muonic hydrogen and the proton size
• Energy interval 3S-1S in muonic hydrogen
• Irreducible Three-Loop Vacuum-Polarization Correction in Muonic Bound Systems
• The Uehling correction in muonic atoms exactly in Zα
• Relativistic and Recoil Corrections to Light-Fermion Vacuum Polarization for Bound Systems of Spin-0, Spin-1/2, and Spin-1 Particles
• Recoil corrections to $\mu$H hyperfine splitting