Recoil corrections to the energy levels of hydrogenic atoms

Abstract

We have completed the calculation of pure-recoil corrections of order $(Z\alpha {)}^6$ to Coulombic bound states of two spin-1/2 fermions without approximation in the particle masses. Our result applies to systems of arbitrary mass ratio such as muonium and positronium, and also hydrogen and muonic hydrogen (with the neglect of proton structure effects). We have shown how the two-loop master integrals that occur in the relativistic region can be computed in analytic form, and suggest that the same method can be applied to the three-loop integrals that would be present in a calculation of order $(Z\alpha {)}^7$ corrections.

6 pages, 2 figures

References in corpus (6)

• Lectures on differential equations for Feynman integrals
• The NRQED lagrangian at order 1/M^4
• NRQED approach to the fine and hyperfine structure corrections of order $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ -- Application to the hydrogen atom
• Nuclear recoil corrections to the Lamb shift of hydrogen and light hydrogen-like ions
• Quantum electrodynamics of two-body systems with arbitrary masses
• Relativistic Ritz approach to hydrogen-like atoms I: theoretical considerations

Cited by in corpus (2)

• Update of Muonium 1S-2S transition frequency
• Measurement of the ${\text{1}}^{\text{3}}{\text{S}}_{\text{1}}\to {\text{2}}^{\text{3}}{\text{S}}_{\text{1}}$ interval in positronium using field-ionization of Rydberg states