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

Opportunities for fundamental physics research with radioactive molecules

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

Ab initio study of electronic states and radiative properties of the AcF molecule

Relativistic coupled-cluster calculations of the ionization potential, dissociation energy, and excited electronic states under 35 000 cm-1 are presented for the actinium monofluoride (AcF) molecule. The ionization potential is calculated to be IPe = 48 866 cm-1, and the ground state is confirmed to be a closed-shell singlet and thus strongly sensitive to the T,P-violating nuclear Schiff moment of the Ac nucleus. Radiative properties and transition dipole moments from the ground state are identified for several excited states, achieving a mean uncertainty estimate of ∼450 cm-1 for the excitation energies. For higher-lying states that are not directly accessible from the ground state, possible two-step excitation pathways are proposed. The calculated branching ratios and Franck-Condon factors are used to investigate the suitability of AcF for direct laser cooling. The lifetime of the metastable (1)3Δ1 state, which can be used in experimental searches of the electric dipole moment of the electron, is estimated to be of order 1 ms.

Effective quantum electrodynamics: One-dimensional model of the relativistic hydrogen-like atom

We consider a one-dimensional effective quantum electrodynamics (QED) model of the relativistic hydrogen-like atom using delta-potential interactions. We discuss the general exact theory and the Hartree-Fock approximation. The present one-dimensional effective QED model shares the essential physical feature of the three-dimensional theory: the nuclear charge polarizes the vacuum state (creation of electron-positron pairs), which results in a QED Lamb-type shift of the bound-state energy. Yet, this 1D effective QED model eliminates some of the most serious technical difficulties of the three-dimensional theory coming from renormalization. We show how to calculate the vacuum-polarization density at zeroth order in the two-particle interaction and the QED Lamb-type shift of the bound-state energy at first order in the two-particle interaction. The present work may be considered a step toward the development of a quantum-chemistry effective QED theory of atoms and molecules.

Refined theoretical values of field and mass isotope shifts in thallium to extract charge radii of Tl isotopes

Electronic factors for the field and mass isotope shifts in the 6p ²P_3/2 → 7s ²S_1/2 (535 nm), 6p ²P_1/2 → 6d ²D_3/2 (277 nm), and 6p ²P_1/2 → 7s ²S_1/2 (378 nm) transitions in neutral thallium were calculated within the high-order relativistic coupled cluster approach. These factors were used to reinterpret previous experimental isotope shift measurements in terms of charge radii of a wide range of Tl isotopes. Good agreement between theoretical and experimental King-plot parameters was found for the 6p ²P_3/2 → 7s ²S_1/2 and 6p ²P_1/2 → 6d ²D_3/2 transitions. It was shown that the value of the specific mass shift factor for the 6p ²P_3/2 → 7s ²S_1/2 transition is not negligible compared with the value of normal mass shift in contrast to what had been suggested previously. Theoretical uncertainties in the mean square charge radii were estimated. They were substantially reduced compared with the previously ascribed ones and amounted to less than 2.6%. The achieved accuracy paves the way for a more reliable comparison of the charge radii trends in the lead region.

Accurate ab initio calculations of RaF electronic structure appeal to more laser-spectroscopical measurements

Recently, a breakthrough has been achieved in laser-spectroscopic studies of short-lived radioactive compounds with the first measurements of the radium monofluoride molecule (RaF) UV/vis spectra. We report results from high-accuracy ab initio calculations of the RaF electronic structure for ground and low-lying excited electronic states. Two different methods agree excellently with experimental excitation energies from the electronic ground state to the ²Π_1/2 and ²Π_3/2 states, but lead consistently and unambiguously to deviations from experimental-based adiabatic transition energy estimates for the ²Σ_1/2 excited electronic state, and show that more measurements are needed to clarify spectroscopic assignment of the ²Δ state.

Fock-space relativistic coupled cluster study on the RaF molecule promising for the laser cooling

The potential energy curves of the ground and five low-lying excited terms of the RaF molecule are calculated using the Fock-space relativistic coupled theory. The electronic term energies, equilibrium internuclear distances, transition and permanent dipole moments, sequences of vibrational energies, harmonic vibrational frequencies, Franck-Condon factors, and radiative lifetimes are predicted. The calculated spectroscopic constants are in good agreement with the available theoretical and experimental data. The scheme for the direct laser cooling involving the first excited A²П_1/2 state is proposed. The data obtained in this study suggests the A²П_1/2 → X²Σ⁺ channel in the RaF molecule is the almost ideal case for direct laser cooling. It is quite possible that the effective cooling scheme for the RaF molecule can be realized using only one pump laser.

The role of QED effects in transition energies of heavy-atom alkaline earth monofluoride molecules: A theoretical study of Ba+, BaF, RaF, and E120F

Heavy-atom alkaline earth monofluoride molecules are considered as prospective systems to study spatial parity or spatial parity and time-reversal symmetry violating effects such as the nuclear anapole moment or the electron electric dipole moment. A comprehensive and highly accurate theoretical study of the electronic structure properties and transition energies in such systems can simplify the preparation and interpretation of the experiments. However, almost no attempts to calculate quantum electrodynamics (QED) effects' contribution into characteristics of these neutral heavy-atom molecules have been performed. Recently, we have formulated and implemented such an approach to calculate QED contributions to transition energies of molecules [L. V. Skripnikov, J. Chem. Phys. 154, 201101 (2021)]. In this paper, we perform a benchmark theoretical study of the transition energies in the Ba⁺ cation and BaF molecule. The deviation of the calculated values from the experimental ones is of the order 10 cm^-1 and is more than an order of magnitude better than the "chemical accuracy," 350 cm^-1. The achievement of such an agreement has been provided, in particular, by the inclusion of the QED effects. The latter appeared to be not less important than the high-order correlation effects beyond the coupled cluster with single, double, and perturbative triple cluster amplitude level. We compare the role of QED effects for transition energies with heavier molecules-RaF and E120F, where E120 is the superheavy Z = 120 homolog of Ra.