One-loop vacuum polarization at m$\alpha$7 and higher orders for three-body molecular systems

Abstract

We present calculations of the one-loop vacuum polarization correction (Uehling potential) for the three-body problem in the NRQED formalism. The case of one-electron molecular systems is considered. Numerical results of the vacuum polarization contribution at m$\alpha$7 and higher orders for the fundamental transitions (v = 0, L = 0) $\to$ (v ' = 1, L ' = 0) in the H2+ and HD+ molecular ions are presented and compared with calculations performed in the adiabatic approximation. The residual uncertainty from this contribution on the transition frequencies is shown to be of a few tens of Hz.

References in corpus (4)

• Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD+
• Relativistic corrections of mα^6 order to the ro-vibrational spectrum of H_2^+ and HD^+ molecular ions
• Hydrogen molecular ions for improved determination of fundamental constants
• Test of the theoretical hyperfine structure of the molecular hydrogen ion at the 1-ppm level

Cited by in corpus (5)

• Fundamental transitions and ionization energies of the hydrogen molecular ions at the few ppt level
• Self-consistent extraction of spectroscopic bounds on light new physics
• Proton-electron mass ratio from HD${}^{+}$ revisited
• Prospects for the determination of fundamental constants with beyond-state-of-the-art uncertainty using molecular hydrogen ion spectroscopy
• Ro-vibrational spin-averaged transitions in the hydrogen molecular ions