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

## TL;DR

This paper calculates high-order vacuum polarization corrections for one-electron molecular ions in NRQED, providing precise transition frequency contributions with residual uncertainties of a few tens of Hz.

## Contribution

It introduces detailed numerical calculations of vacuum polarization effects at mα7 and higher orders for three-body molecular systems within the NRQED framework, improving precision in transition frequency predictions.

## Key findings

- Vacuum polarization correction at mα7 and higher orders quantified.
- Residual uncertainty on transition frequencies is a few tens of Hz.
- Comparison with adiabatic approximation shows good agreement.

## 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) $\rightarrow$ (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.