dorsal/arxiv
View SchemaTwo-Loop Bethe Logarithms for non-S Levels
| Authors | U. D. Jentschura |
|---|---|
| Categories | |
| ArXiv ID | physics/0612251 |
| URL | https://arxiv.org/abs/physics/0612251 |
| DOI | 10.1103/PhysRevA.74.062517 |
| Journal | Phys.Rev.A 74 (2006) 062517 |
Abstract
Two-loop Bethe logarithms are calculated for excited P and D states in hydrogenlike systems, and estimates are presented for all states with higher angular momenta. These results complete our knowledge of the P and D energy levels in hydrogen at the order of alpha^8 m_e c^2, where m_e is the electron mass and c is the speed of light, and scale as Z^6, where Z is the nuclear charge number. Our analytic and numerical calculations are consistent with the complete absence of logarithmic terms of order (alpha/pi)^2 (Z alpha)^6 ln[(Z alpha)^(-2)] m_e c^2 for D states and all states with higher angular momenta. For higher excited P and D states, a number of poles from lower-lying levels have to subtracted in the numerical evaluation. We find that, surprisingly, the corrections of the "squared decay-rate type" are the numerically dominant contributions in the order (alpha/pi)^2 (Z alpha)^6 m_e c^2 for states with large angular momenta, and provide an estimate of the entire B_60-coefficient for Rydberg states with high angular momentum quantum numbers. Our results reach the predictive limits of the quantum electrodynamic theory of the Lamb shift.
{
"annotation_id": "bda180cd-7dc0-4011-88ba-5cb8c4fce077",
"date_created": "2026-03-02T18:01:14.464000Z",
"date_modified": "2026-03-02T18:01:14.464000Z",
"file_hash": "e6f2f695b47fc6d598039da8ccf08be78c0241411bc0cab7e4dbbcf591285899",
"private": false,
"record": {
"abstract": "Two-loop Bethe logarithms are calculated for excited P and D states in\nhydrogenlike systems, and estimates are presented for all states with higher\nangular momenta. These results complete our knowledge of the P and D energy\nlevels in hydrogen at the order of alpha^8 m_e c^2, where m_e is the electron\nmass and c is the speed of light, and scale as Z^6, where Z is the nuclear\ncharge number. Our analytic and numerical calculations are consistent with the\ncomplete absence of logarithmic terms of order (alpha/pi)^2 (Z alpha)^6 ln[(Z\nalpha)^(-2)] m_e c^2 for D states and all states with higher angular momenta.\nFor higher excited P and D states, a number of poles from lower-lying levels\nhave to subtracted in the numerical evaluation. We find that, surprisingly, the\ncorrections of the \"squared decay-rate type\" are the numerically dominant\ncontributions in the order (alpha/pi)^2 (Z alpha)^6 m_e c^2 for states with\nlarge angular momenta, and provide an estimate of the entire B_60-coefficient\nfor Rydberg states with high angular momentum quantum numbers. Our results\nreach the predictive limits of the quantum electrodynamic theory of the Lamb\nshift.",
"arxiv_id": "physics/0612251",
"authors": [
"U. D. Jentschura"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1103/PhysRevA.74.062517",
"journal_ref": "Phys.Rev.A 74 (2006) 062517",
"title": "Two-Loop Bethe Logarithms for non-S Levels",
"url": "https://arxiv.org/abs/physics/0612251"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "9390e358-8c15-4481-ad9d-de89b12bb13b",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}