Precision calculation of the bound-electron $g$ factor in molecular hydrogen ions

Fuente: arXiv
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Main Authors: Kullie, Ossama, Nogueira, Hugo D., Karr, Jean-Philippe
Format: Preprint
Published: 2025
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author Kullie, Ossama
Nogueira, Hugo D.
Karr, Jean-Philippe
author_facet Kullie, Ossama
Nogueira, Hugo D.
Karr, Jean-Philippe
contents We calculate the bound-electron $g$ factor for a wide range of rovibrational states of the molecular hydrogen ions H$_2^+$ and HD$^+$. Relativistic and QED corrections of orders up to $α^5$ are taken into account. All contributions are calculated in a nonrelativistic QED framework, except for relativistic corrections of order $(Zα)^4$ and above, which are obtained by calculating the relativistic $g$ factor using a precise minmax finite element solution of the two-center Dirac equation. A relative accuracy of $4-5 \times 10^{-11}$ is achieved for the scalar $g$ factor component, which represents an improvement by more than three orders of magnitude over previous calculations. These results are useful for internal state identification and rovibraional spectroscopy of single molecular hydrogen ions in Penning traps, and open a new avenue towards precision tests of QED.
format Preprint
id arxiv_https___arxiv_org_abs_2508_04242
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Precision calculation of the bound-electron $g$ factor in molecular hydrogen ions
Kullie, Ossama
Nogueira, Hugo D.
Karr, Jean-Philippe
Atomic Physics
We calculate the bound-electron $g$ factor for a wide range of rovibrational states of the molecular hydrogen ions H$_2^+$ and HD$^+$. Relativistic and QED corrections of orders up to $α^5$ are taken into account. All contributions are calculated in a nonrelativistic QED framework, except for relativistic corrections of order $(Zα)^4$ and above, which are obtained by calculating the relativistic $g$ factor using a precise minmax finite element solution of the two-center Dirac equation. A relative accuracy of $4-5 \times 10^{-11}$ is achieved for the scalar $g$ factor component, which represents an improvement by more than three orders of magnitude over previous calculations. These results are useful for internal state identification and rovibraional spectroscopy of single molecular hydrogen ions in Penning traps, and open a new avenue towards precision tests of QED.
title Precision calculation of the bound-electron $g$ factor in molecular hydrogen ions
topic Atomic Physics
url https://arxiv.org/abs/2508.04242