### Abstract

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/mN2 is evaluated for muonic hydrogen and deuterium and muonic helium ions (μ is the reduced mass and m_{N} 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/m_{N} 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.

Original language | English |
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Article number | 012505 |

Journal | Physical Review A |

Volume | 84 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 11 2011 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

**Relativistic reduced-mass and recoil corrections to vacuum polarization in muonic hydrogen, muonic deuterium, and muonic helium ions.** / Jentschura, U.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Relativistic reduced-mass and recoil corrections to vacuum polarization in muonic hydrogen, muonic deuterium, and muonic helium ions

AU - Jentschura, U.

PY - 2011/7/11

Y1 - 2011/7/11

N2 - 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/mN2 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.

AB - 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/mN2 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.

UR - http://www.scopus.com/inward/record.url?scp=79961080190&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79961080190&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.84.012505

DO - 10.1103/PhysRevA.84.012505

M3 - Article

AN - SCOPUS:79961080190

VL - 84

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 1

M1 - 012505

ER -