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 $(v=0, L=0)\to (v^{\prime }=1, L^{\prime }=0)$ in the ${\mathrm{H}}_2^{+}$ and ${\mathrm{HD}}^{+}$ molecular ions are presented and compared with calculations performed in the adiabatic approximation. The residual uncertainty from this contribution in the transition frequencies is shown to be a few tens of Hz.

• Received 10 February 2017

DOI:https://doi.org/10.1103/PhysRevA.95.042514