### Abstract

We study a specific correction to the Bethe logarithm induced by potentials which are proportional to a Dirac-δ function in coordinate space ('local potentials'). Corrections of this type occur naturally in the calculation of various self-energy corrections to the energy of bound states. Examples include logarithmic higher-order binding corrections to the two-loop self-energy, vacuum-polarization induced corrections to the self-energy and radiative corrections induced by the finite size of the nucleus. We obtain results for excited S and P states and find that the dependence of the corrections on the principal quantum number is remarkable. For the ground state, we find a small modification as compared to previously reported results. Our results are based on mathematical techniques for the treatment of quantum electrodynamic bound states introduced discussed previously by Jentschura and Pachucki (2002 J. Phys. A: Math. Gen. 35 1927).

Original language | English |
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Journal | Journal of Physics A: Mathematical and General |

Volume | 36 |

Issue number | 15 |

DOIs | |

Publication status | Published - Apr 18 2003 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Radiative energy shifts induced by local potentials.** / Jentschura, U.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Radiative energy shifts induced by local potentials

AU - Jentschura, U.

PY - 2003/4/18

Y1 - 2003/4/18

N2 - We study a specific correction to the Bethe logarithm induced by potentials which are proportional to a Dirac-δ function in coordinate space ('local potentials'). Corrections of this type occur naturally in the calculation of various self-energy corrections to the energy of bound states. Examples include logarithmic higher-order binding corrections to the two-loop self-energy, vacuum-polarization induced corrections to the self-energy and radiative corrections induced by the finite size of the nucleus. We obtain results for excited S and P states and find that the dependence of the corrections on the principal quantum number is remarkable. For the ground state, we find a small modification as compared to previously reported results. Our results are based on mathematical techniques for the treatment of quantum electrodynamic bound states introduced discussed previously by Jentschura and Pachucki (2002 J. Phys. A: Math. Gen. 35 1927).

AB - We study a specific correction to the Bethe logarithm induced by potentials which are proportional to a Dirac-δ function in coordinate space ('local potentials'). Corrections of this type occur naturally in the calculation of various self-energy corrections to the energy of bound states. Examples include logarithmic higher-order binding corrections to the two-loop self-energy, vacuum-polarization induced corrections to the self-energy and radiative corrections induced by the finite size of the nucleus. We obtain results for excited S and P states and find that the dependence of the corrections on the principal quantum number is remarkable. For the ground state, we find a small modification as compared to previously reported results. Our results are based on mathematical techniques for the treatment of quantum electrodynamic bound states introduced discussed previously by Jentschura and Pachucki (2002 J. Phys. A: Math. Gen. 35 1927).

UR - http://www.scopus.com/inward/record.url?scp=0037453740&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037453740&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/36/15/103

DO - 10.1088/0305-4470/36/15/103

M3 - Article

AN - SCOPUS:0037453740

VL - 36

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 15

ER -