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.
U. D. Jentschura, "Relativistic Reduced-Mass and Recoil Corrections to Vacuum Polarization in Muonic Hydrogen, Muonic Deuterium, and Muonic Helium Ions," Physical Review A - Atomic, Molecular, and Optical Physics, vol. 84, no. 1, pp. 012505-1-012505-6, American Physical Society (APS), Jul 2011.
The definitive version is available at https://doi.org/10.1103/PhysRevA.84.012505
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)
Article - Journal
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