Lamb Shift In Muonic Atoms Research Articles

Subtractions and the effective Salpeter term for the Lamb shift in muonic atoms with the nuclear spin I \u2260 1\u22152

While taking into account the nuclear-structure contributions to the Lamb shift, one has to make various subtractions for the two-photon exchange contributions. Such subtractions should be consistent with the structureless part of theory. We study here the subtractions for a two-body atomic systems which consist of a pointlike lepton (an electron or a muon) and a nucleus with spin 0, 1/2, and 1, and find the recoil contribution in order (Zα)5 due to the subtractions for I = 0, 1. (The related contribution to the energy levels for I = 1∕2 of order (Zα)5m is called the Salpeter term.)Graphical abstract

Muonic hydrogen and the third Zemach moment

We determine the third Zemach moment of hydrogen (<r^3>_(2)) using only the world data on elastic electron-proton scattering. This moment dominates the O (Z alpha)^5 hadronic correction to the Lamb shift in muonic atoms. The resulting moment, <r^3 >_(2) = 2.71(13) fm^3, is somewhat larger than previously inferred values based on models. The contribution of that moment to the muonic hydrogen 2S level is -0.0247(12) meV.

Non-Perturbative Mass and Charge Renormalization in Relativistic No-Photon Quantum Electrodynamics

Starting from a formal Hamiltonian as found in the physics literature – omitting photons – we define a renormalized Hamiltonian through charge and mass renormalization. We show that the restriction to the one-electron subspace is well-defined. Our construction is non-perturbative and does not use a cut-off. The Hamiltonian is relevant for the description of the Lamb shift in muonic atoms.