Approaching meV level for transition energies in the radium monofluoride molecule RaF and radium cation Ra$^+$ by including quantum-electrodynamics effects

TL;DR

This paper reports highly precise theoretical calculations of transition energies in radium monofluoride and radium cation, incorporating quantum electrodynamics effects to achieve accuracy within a few meV, surpassing traditional chemical accuracy.

Contribution

The study introduces non-perturbative inclusion of QED effects in molecular calculations, significantly improving the accuracy of transition energy predictions for RaF and Ra$^+$.

Findings

QED effects are crucial for resolving discrepancies with experimental data.

Achieved accuracy within a few meV, surpassing chemical accuracy.

Enhanced theoretical methods for predicting molecular transition energies.

Abstract

Highly accurate theoretical predictions of transition energies in the radium monofluoride molecule, $^{226}$RaF and radium cation, $^{226}$Ra$^+$, are reported. The considered transition $X~^2\Sigma_{1/2} \to A~^2\Pi_{1/2}$ in RaF is one of the main features of this molecule and can be used to laser cool RaF for subsequent measurement of the electron electric dipole moment. For molecular and atomic predictions we go beyond the Dirac-Coulomb Hamiltonian and treat high-order electron correlation effects within the coupled cluster theory with the inclusion of quadruple and ever higher amplitudes. Effects of quantum electrodynamics (QED) are included non-perturbatively using the model QED operator that is implemented now for molecules. It is shown that the inclusion of QED effects in molecular and atomic calculations is a key ingredient in resolving the discrepancy between the theoretical values obtained within the Dirac-Coulomb-Breit Hamiltonian and the experiment. The remaining deviation from the experimental values is within a few meV. This is more than an order of magnitude better than the "chemical accuracy", 1 kcal/mol=43 meV, that is usually considered as a guiding thread in theoretical molecular physics.