High accuracy theoretical investigations of CaF, SrF, and BaF and implications for laser-cooling

The NL-eEDM collaboration is building an experimental setup to search for the permanent electric dipole moment of the electron in a slow beam of cold barium fluoride molecules [Eur. Phys. J. D, 72, 197 (2018)]. Knowledge of molecular properties of BaF is thus needed to plan the measurements and in particular to determine an optimal laser-cooling scheme. Accurate and reliable theoretical predictions of these properties require incorporation of both high-order correlation and relativistic effects in the calculations. In this work theoretical investigations of the ground and the lowest excited states of BaF and its lighter homologues, CaF and SrF, are carried out in the framework of the relativistic Fock-space coupled cluster (FSCC) and multireference configuration interaction (MRCI) methods. Using the calculated molecular properties, we determine the Franck-Condon factors (FCFs) for the $A^2\Pi_{1/2} \rightarrow X^2\Sigma^{+}_{1/2}$ transition, which was successfully used for cooling CaF and SrF and is now considered for BaF. For all three species, the FCFs are found to be highly diagonal. Calculations are also performed for the $B^2\Sigma^{+}_{1/2} \rightarrow X^2\Sigma^{+}_{1/2}$ transition recently exploited for laser-cooling of CaF; it is shown that this transition is not suitable for laser-cooling of BaF, due to the non-diagonal nature of the FCFs in this system. Special attention is given to the properties of the $A'^2\Delta$ state, which in the case of BaF causes a leak channel, in contrast to CaF and SrF species where this state is energetically above the excited states used in laser-cooling. We also present the dipole moments of the ground and the excited states of the three molecules and the transition dipole moments (TDMs) between the different states.Comment: Minor changes; The following article has been submitted to the Journal of Chemical Physics. After it is published, it will be found at https://publishing.aip.org/resources/librarians/products/journals

Systematic study and uncertainty evaluation of P, T-odd molecular enhancement factors in BaF

A measurement of the magnitude of the electric dipole moment of the electron (eEDM) larger than that predicted by the Standard Model (SM) of particle physics is expected to have a huge impact on the search for physics beyond the SM. Polar diatomic molecules containing heavy elements experience enhanced sensitivity to parity (P) and time-reversal (T)-violating phenomena, such as the eEDM and the scalar-pseudoscalar (S-PS) interaction between the nucleons and the electrons, and are thus promising candidates for measurements. The NL-eEDM collaboration is preparing an experiment to measure the eEDM and S-PS interaction in a slow beam of cold BaF molecules [P. Aggarwal et al., Eur. Phys. J. D 72, 197 (2018)]. Accurate knowledge of the electronic structure parameters, Wd and Ws, connecting the eEDM and the S-PS interaction to the measurable energy shifts is crucial for the interpretation of these measurements. In this work, we use the finite field relativistic coupled cluster approach to calculate the Wd and Ws parameters in the ground state of the BaF molecule. Special attention was paid to providing a reliable theoretical uncertainty estimate based on investigations of the basis set, electron correlation, relativistic effects, and geometry. Our recommended values of the two parameters, including conservative uncertainty estimates, are 3.13 ±0.12×1024Hzecm for Wd and 8.29 ± 0.12 kHz for W

Measuring the electric dipole moment of the electron in BaF

Abstract: We investigate the merits of a measurement of the permanent electric dipole moment of the electron (eEDM) with barium monofluoride molecules, thereby searching for phenomena of CP violation beyond those incorporated in the standard model (SM) of particle physics. Although the BaF molecule has a smaller enhancement factor in terms of the effective electric field than other molecules used in current studies (YbF, ThO and ThF+), we show that a competitive measurement is possible by combining Stark-deceleration, laser-cooling and an intense primary cold source of BaF molecules. With the long coherent interaction times obtainable in a cold beam of BaF, a sensitivity of 5 × 10−30 e⋅cm for an eEDM is feasible. We describe the rationale, the challenges and the experimental methods envisioned to achieve this target. Graphical abstract: [Figure not available: see fulltext.]

Benchmarking of the Fock-space coupled-cluster method and uncertainty estimation: Magnetic hyperfine interaction in the excited state of BaF

We present an investigation of the performance of the relativistic multireference Fock-space coupled-cluster (FSCC) method for predicting molecular hyperfine structure (HFS) constants, including a thorough computational study to estimate the associated uncertainties. In particular, we considered the F19 HFS constant in the ground and excited states of BaF. The ab initio values were compared to the recent experimental results, and good overall agreement within the theoretical uncertainties was found. This work demonstrates the predictive power of the FSCC method and the reliability of the established uncertainty estimates, which can be crucial in cases where the calculated property cannot be directly compared to experiment

High accuracy theoretical investigations of CaF, SrF, and BaF and implications for laser-cooling

The NL-eEDM collaboration is building an experimental setup to search for the permanent electric dipole moment of the electron in a slow beam of cold barium fluoride molecules [NL-eEDM Collaboration, Eur. Phys. J. D 72, 197 (2018)]. Knowledge of the molecular properties of BaF is thus needed to plan the measurements and, in particular, to determine the optimal laser-cooling scheme. Accurate and reliable theoretical predictions of these properties require the incorporation of both high-order correlation and relativistic effects in the calculations. In this work, theoretical investigations of the ground and lowest excited states of BaF and its lighter homologs, CaF and SrF, are carried out in the framework of the relativistic Fock-space coupled cluster and multireference configuration interaction methods. Using the calculated molecular properties, we determine the Franck-Condon factors (FCFs) for the A2Π1/2→X2ς1/2+ transition, which was successfully used for cooling CaF and SrF and is now considered for BaF. For all three species, the FCFs are found to be highly diagonal. Calculations are also performed for the B2ς1/2+→X2ς1/2+ transition recently exploited for laser-cooling of CaF; it is shown that this transition is not suitable for laser-cooling of BaF, due to the nondiagonal nature of the FCFs in this system. Special attention is given to the properties of the A′2Δstate, which in the case of BaF causes a leak channel, in contrast to CaF and SrF species where this state is energetically above the excited states used in laser-cooling. We also present the dipole moments of the ground and excited states of the three molecules and the transition dipole moments (TDMs) between the different states. Finally, using the calculated FCFs and TDMs, we determine that the A2Π1/2→X2ς1/2+ transition is suitable for transverse cooling in BaF