### Abstract

Quantum electrodynamic (QED) effects that shift the binding energies of hydrogenic energy levels have been expressed in terms of a semi-analytic expansion in powers of Zα and ln[(Zα)^{-2}], where Z is the nuclear charge number and α is the fine-structure constant. For many QED effects, numerical data are available in the domain of high Z where the Zα expansion fails. In this Letter, we demonstrate that it is possible, within certain limits of accuracy, to extrapolate the Zα-expansion from the low-Z to the high-Z domain. We also review two-loop self-energy effects and provide an estimate for the problematic nonlogarithmic coefficient B_{60}.

Original language | English |
---|---|

Pages (from-to) | 225-230 |

Number of pages | 6 |

Journal | Physics Letters B |

Volume | 564 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - Jul 10 2003 |

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### Keywords

- Asymptotic problems and properties
- General properties of perturbation theory
- QED radiative corrections

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Extrapolation of the Zα-expansion and two-loop bound-state energy shifts.** / Jentschura, U.

Research output: Contribution to journal › Article

*Physics Letters B*, vol. 564, no. 3-4, pp. 225-230. https://doi.org/10.1016/S0370-2693(03)00562-8

}

TY - JOUR

T1 - Extrapolation of the Zα-expansion and two-loop bound-state energy shifts

AU - Jentschura, U.

PY - 2003/7/10

Y1 - 2003/7/10

N2 - Quantum electrodynamic (QED) effects that shift the binding energies of hydrogenic energy levels have been expressed in terms of a semi-analytic expansion in powers of Zα and ln[(Zα)-2], where Z is the nuclear charge number and α is the fine-structure constant. For many QED effects, numerical data are available in the domain of high Z where the Zα expansion fails. In this Letter, we demonstrate that it is possible, within certain limits of accuracy, to extrapolate the Zα-expansion from the low-Z to the high-Z domain. We also review two-loop self-energy effects and provide an estimate for the problematic nonlogarithmic coefficient B60.

AB - Quantum electrodynamic (QED) effects that shift the binding energies of hydrogenic energy levels have been expressed in terms of a semi-analytic expansion in powers of Zα and ln[(Zα)-2], where Z is the nuclear charge number and α is the fine-structure constant. For many QED effects, numerical data are available in the domain of high Z where the Zα expansion fails. In this Letter, we demonstrate that it is possible, within certain limits of accuracy, to extrapolate the Zα-expansion from the low-Z to the high-Z domain. We also review two-loop self-energy effects and provide an estimate for the problematic nonlogarithmic coefficient B60.

KW - Asymptotic problems and properties

KW - General properties of perturbation theory

KW - QED radiative corrections

UR - http://www.scopus.com/inward/record.url?scp=0141751036&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141751036&partnerID=8YFLogxK

U2 - 10.1016/S0370-2693(03)00562-8

DO - 10.1016/S0370-2693(03)00562-8

M3 - Article

VL - 564

SP - 225

EP - 230

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 3-4

ER -