The reduced-mass dependence of relativistic and radiative effects in simple muonic bound systems is investigated. The spin-dependent nuclear recoil correction of order (Zα)4μ3/m2N is evaluated for muonic hydrogen and deuterium and muonic helium ions (μ is the reduced mass and mN is the nuclear mass). Relativistic corrections to vacuum polarization of order α(Zα)4μ are calculated, with a full account of the reduced-mass dependence. The results shift theoretical predictions. The radiative-recoil correction to vacuum polarization of order α(Zα)5-ln2(Zα) μ2/mN is obtained in leading logarithmic approximation. The results emphasize the need for a unified treatment of relativistic corrections to vacuum polarization in muonic hydrogen, muonic deuterium, and muonic helium ions, where the mass ratio of the orbiting particle to the nuclear mass is larger than the fine-structure constant.



Keywords and Phrases

Fine Structure Constants; Helium Ion; Logarithmic Approximation; Mass Ratio; Muonic Deuterium; Muonic Hydrogen; Nuclear Mass; Nuclear Recoil; Radiative Effects; Radiative-recoil Corrections; Relativistic Correction; Theoretical Prediction; Vacuum Polarization; Deuterium; Electrodynamics; Electromagnetism; Helium; Hydrogen; Polarization; Vacuum

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

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© 2011 American Physical Society (APS), All rights reserved.

Publication Date

01 Jul 2011

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Physics Commons