BaF Molecule Research Articles

Optical control of BaF molecules trapped in neon ice

We have trapped BaF molecules in neon ice and used laser-induced fluorescence spectroscopy to map out their optical transitions. Our measurements show that the neon lattice does not significantly perturb certain optical transitions in trapped BaF molecules. We used one such transition to optically pump and detect spin resonances in the molecules. This demonstration of optical control of trapped heavy polar molecules offers opportunities to advance physical chemistry and ultra-high-energy physics.

Accurate calculation of the interaction of a barium monofluoride molecule with an argon atom: A step towards using matrix isolation of BaF for determining the electron electric dipole moment

Calculations of the BaF–Ar triatomic system are performed with a relativistic Hamiltonian and coupled cluster theory at the CCSD(T) level for 1386 positions of the Ar atom relative to the BaF molecule. Calculations are repeated with increasing basis sets (double-, triple-, quadruple- and quintuple-zeta), and these are extrapolated to estimate the complete-basis-set limit. The resulting energies provide a potential energy for the interaction of an Ar atom with a BaF molecule. A fit is presented that parametrizes this potential. This work is needed for an understanding of the position, modes of motion and energy shifts of BaF isolated in an Ar matrix. This understanding will guide the EDM3 collaboration in its pursuit of a precision measurement of the electron electric dipole moment using BaF isolated in a cryogenic Ar matrix.

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 homologof Ra.

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 Ws.

A supersonic laser ablation beam source with narrow velocity spreads.

A supersonic beam source for SrF and BaF molecules is constructed by combining the expansion of carrier gas (a mixture of 2% SF6 and 98% argon) from an Even-Lavie valve with laser ablation of a barium/strontium metal target at a repetition rate of 10 Hz. Molecular beams with a narrow translational velocity spread are produced at relative values of Δv/v = 0.053(11) and 0.054(9) for SrF and BaF, respectively. The relative velocity spread of the beams produced in our source is lower in comparison with the results from other metal fluoride beams produced in supersonic laser ablation sources. The rotational temperature of BaF is measured to be 3.5 K. The source produces 6 × 108 and 107 molecules per steradian per pulse in the X2Σ+ (ν = 0, N = 1) state of BaF and SrF molecules, respectively, a state amenable to Stark deceleration and laser cooling.

Relativistic coupled-cluster study of BaF in search of violation

BaF is one of the potential candidates for the experimental search of the electric dipole moment of the electron (eEDM). The NL-eEDM collaboration is building a new experimental set up to measure the eEDM using the BaF molecule (The NL-eEDM collaboration, 2018 Eur. Phys. J. D 72: 197). To analyze the results of such an experiment, one would require the accurate value of the molecular -odd interaction parameters that cannot be measured from any experiment. In this work, we report the precise value of the -odd interaction parameters of the BaF molecule obtained from the four-component relativistic coupled-cluster calculations. We also calculate the hyperfine structure (HFS) constants of the same molecule to assess the reliability of the reported molecular parameters. The calculated HFS constants show good agreement with the available experimental values. Further, the systematic effects of electron-correlation along with the roles of inner-core electrons and the virtual energy functions in the calculation of the studied properties of BaF are investigated.

Significance of Non-Linear Terms in the Relativistic Coupled-Cluster Theory in the Determination of Molecular Properties

The relativistic coupled-cluster (RCC) theory has been applied recently to a number of heavy molecules to determine their properties very accurately. Since it demands large computational resources, the method is often approximated to single and double excitations (RCCSD method). The effective electric fields ( E e f f ) and molecular permanent electric dipole moments (PDMs) of SrF, BaF, and mercury monohalides (HgX with X = F, Cl, Br, and I) molecules are of immense interest for probing fundamental physics. In our earlier calculations of E e f f and PDMs for the above molecules, we neglected the non-linear terms in the property evaluation expression of the RCCSD method. In this work, we demonstrate the roles of these terms in determining the above quantities and their computational time scalability with the number of processors of a computer. We also compare our results with previous calculations that employed variants of RCC theory, as well as other many-body methods and available experimental values.

Laser cooling and trapping of polar molecules

Different from atoms, molecules have unique properties, and play an important role in the research of atomic, molecular and optical physics. Cold molecules have important applications in science and have been studied for more than 20 years. But traditional methods, such as the Stark decelerator, have hit a bottleneck: it is hard to increase the phase space density of molecules. Extending the direct laser-cooling technique to new molecular species has recently been a hot topic and also a big challenge. In this review paper, on one hand, we make a brief review to recent progresses on the direct laser cooling of polar molecules. On the other hand, a demonstration on the feasibility of laser cooling BaF molecule has been experimentally illustrated, including the analysis on the molecular energy levels, measurements of the high-resolution spectroscopy, efficient pre-cooling and state preparation via buffer-gas cooling and detailed investigations on the molcule-light interactions. All these results not only pave the way for future laser-cooling and -trapping experiments, but also serve as a reference for the laser-cooling explorations on new molecular species.

Measuring the electric dipole moment of the electron in BaF

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

Structure, branching ratios, and a laser-cooling scheme for theBaF138molecule

For laser cooling considerations, we have theoretically investigated the electronic, rovibrational and hypefine structures of BaF molecule. The highly diagonal Franck-Condon factors and the branching ratios for all possible transitions within the lowest-lying four electronic states have also been calculated. Meanwhile, the mixing between metastable A'2{\Delta} and A2{\Pi} states and further the lifetime of the {\Delta} state have been estimated since the loss procedure via {\Delta} state would like fatally destroy the main quasi-cycling {\Sigma}-{\Pi} transition for cooling and trapping. The resultant hyperfine splittings of each rovibrational states in X2{\Sigma}+ state provide benchmarksfor sideband modulations of cooling and repumping lasers and remixing microwaves to address all necessary levels. The calculated Zeeman shift and g-factors for both X and A states serve as benchmarks for selections of the trapping laser polarizations. Our study paves the way for future laser cooling and magneto-optical trapping of the BaF molecule.

Cumulants and waitingtime distribution of the photon emission from driven BaF molecule

In this paper, we consider a single BaF molecule driven by an external field. When the symmetry is broken, the states of the BaF molecule demonstrate the permanent dipole moments. An external laser field to excite BaF molecule transition from its ground state to its excited state, and a radio frequency field couple with the permanent dipole moment of the BaF. The first order and second order cumulants of the emission photons and the waiting time distribution are studied via the recently developed generating function approach, which is very convenient to study the counting statistics and the corresponding probability distributions. The results demonstrate that the radio frequency field could help the BaF molecule to absorb photons from the driving field. The second and third order waiting time distributions oscillate with the evolution time, which reflects the states oscillating with the external radio frequency field.

Determination of molecular hyperfine-structure constant using the second-order relativistic many-body perturbation theory

The spin-rotational Hamiltonian parameters ${A}_{\ensuremath{\parallel}}$ and ${A}_{\ensuremath{\perp}}$ for the BaF molecule are calculated using four-component relativistic spinors at the second-order many-body perturbation theory (MBPT) level via the Z-vector technique. The second-order MBPT is applied to assess the accuracy of the computed hyperfine-structure constants before studying the problem with the state-of-the-artcoupled cluster with single and double excitations (CCSD) method which is highly accurate but computationally more expensive than MBPT. The hyperfine-structure constants $A$ and ${A}_{d}$ resulted from these calculations agree favorably well with experimental findings and with other correlated calculations. The convergence behavior of $A$ and ${A}_{d}$ with respect to the number of active orbitals used in the perturbative calculations suggests that our estimated $A$ and ${A}_{d}$ values should be accurate.

Perturbative calculations of P, T-odd effects in heavy polar diatomic molecules

A fully-relativistic second order many-body perturbation theory (MBPT(2)) is employed to compute the P, T-odd interaction constant Wd of the ground (2Σ1/2) states of YbF and BaF molecules. Since MBPT(2) incorporates the correlation and relaxation effects in a balanced manner, we expect that the present estimates of Wd will be important to provide a reliable limit on the electron's electric dipole moment (EDM) de

Core-Penetrating Rydberg Series of BaF: Single-State and Two-State Fits of New Electronic States in the 4.4 ≤ n* ≤ 14.3 Region

We report results of optical–optical double-resonance studies of the Rydberg states of the BaF molecule in the energy region of E = 33100–38200 cm−1 (4.4 ≤ n* ≤ 14.3). Barium monofluoride molecules have been produced in a resistively heated high-temperature oven from BaF2 powder mixed with a small amount of boron powder. We have observed more than 50 new electronic states. Forty-nine of them have been rotationally analyzed and assigned to eight Rydberg series (four 2Σ+, one 2Π, two 2Δ, and one 2Φ). Single-state and two-state fits have been carried out. Multiple local perturbations have been analyzed. Formation of supercomplexes in the Rydberg spectrum of BaF has been discussed.

Lifetime measurements of the A 2Π 1/2 state of BaF using laser spectroscopy

A time-resolved experiment on the lowest-lying radiative state of barium fluoride has been performed by applying laser resonance methods in the near infra-red wavelength region. The A 2Π 1/2 state has been examined using a single-mode Ti:sapphire laser. The radiative lifetime obtained for the A 2Π 1/2 state of the BaF molecule was 56.0±0.9 ns (1 σ error-limits).

Decay studies of the neutron-deficient isotopes 114–118Ba

The very neutron-deficient isotopes 114–118Ba were produced in 58Ni induced reactions on 58Ni, 60Ni or 63Cu targets. By on-line mass separation of BaF molecules formed in the separator ion source, exceptionally pure sources of these isotopes were available for spectroscopic studies. The β-decays of 114Ba ( T 1 2 = 0.43 −0.15 +0.30 s ), 115Ba ( T 1 2 = 0.45 ± 0.05 s ), 116Ba ( T 1 2 = 1.3 ± 0.2 s ) and 118Ba ( T 1 2 = 5.2 ± 0.2 s ) were investigated for the first time. 114Ba, 115Ba and 116Ba were identified as β-delayed proton emitters and absolute branching ratios for this decay mode were determined to be 20 ± 10%, >15%, and 3 ± 1%, respectively. In the decay study of 118Ba several γ transitions were identified. New information was also obtained on the β-delayed γ radiation of 117Ba. The spectroscopic data were used to determine the production cross-sections for all these isotopes. Results of our half-life measurements and β-delayed proton studies are confronted with theoretical predictions.

Enhancement of the electric dipole moment of the electron in the BaF molecule

We report results of ab initio calculation of the spin-rotational Hamiltonian parameters including $P$- and $P,T$-odd terms for the BaF molecule. The ground-state wave function of BaF molecule is found with the help of the relativistic effective core potential method followed by the restoration of molecular four-component spinors in the core region of barium in the framework of a nonvariational procedure. Core polarization effects are included with the help of the atomic many-body perturbation theory for the Barium atom. For the hyperfine constants the accuracy of this method is about 5--10 %.

The Rydberg spectrum of CaF and BaF: Calculation by R-matrix and generalized quantum defect theory

R-matrix theory combined with generalized quantum defect theory is used to calculate the electronic spectrum of the CaF and BaF molecules from the ground state up near the ionization limit. The approach, an effective one-electron method similar in spirit to the ligand-field model of Rice, Martin, and Field [S. F. Rice, H. Martin, and R. W. Field, J. Chem. Phys. 82, 5023 (1985)] and to the electrostatic polarization model of Törring, Ernst, and Kändler [T. Törring, W. E. Ernst, J. Kändler, J. Chem. Phys. 90, 4927 (1989)] removes many of the limitations inherent in the previous work. The resulting level energies (effective principal quantum numbers) are in good agreement with the available experimental data and constitute the first quantitative theoretical calculation of the full electronic spectrum of CaF and BaF. Limitations and possible extensions of the theory are discussed, and quantum defects of high orbital angular momentum states are predicted.

Dynamics of desorption of reaction products from reactions on large clusters

The reaction of barium trimers with molecules of SF6 has been investigated on large argon clusters (around 4000 atoms). The reaction is strongly exoergic (by approximately 5 eV) and leads to several reaction products; among which, the desorption of ground state BaF molecules is observed. The energetics of these molecules has been analysed by laser-induced fluorescence with subDoppler resolution. The rotational, vibrational and translational energy distributions are found to be thermal, with temperatures in the range 1600–2400 K. These temperatures are lower than those found in a preceding analysis of chemiluminescent desorbed products but remain much higher than the temperature of the cluster. This is interpreted by different time scales of interaction of the products with the cluster substrate: short times leading to highly internally excited products, long times to solvated products, with the ground state desorbed products appearing as intermediates in between.

Core-Penetrating Rydberg Series of BaF: New Electronic States in then* ≈ 4 Region

We report results of our studies of the electronic spectrum of the BaF molecule in the energy region ofT0= 31460–32400 cm−1(3.88 <n* < 4.16). We have observed four new electronic states (all constants in cm−1):K2Π1/2(T0= 31996), 4.082Σ+(T0= 32166.293(2),B0= 0.2333892(17)), 3.942Δ (T1= 32252.426(2),B1= 0.2294684(16),A1= 0.879(13)), andJ2Π (T0= 32297.918(2),B0= 0.22952165(51),A0= 57.196(1)). In addition, the previously observedG2Σ+(T0= 30969.715(2),B0= 0.2297411(13)) andH2Σ+(T0= 31606.238(2),B0= 0.23031573(85)) states were rotationally analyzed for the first time. We verified by isotope analysis that theG2Σ+state, previously reported by J. Singh and H. Mohan [Indian J. Pure Appl. Phys.11,918–922 (1973)], had been incorrectly assigned vibrationally. TheI2Σ+state, which Singh and Mohan observed at low resolution, was absent from our spectra and we suspect that this state belongs to a species other than BaF. Electronic term values for the remaining seven not yet observed BaF core-penetrating Rydberg states belown* = 6 were predicted by interpolation of well-characterized Rydberg series. We suggest that theE″ state, assigned by Effantinet al.as a2Π1/2state [C. Effantin, A. Bernard, J. D'Incan, E. Andrianavalona, and R. F. Barrow,J. Mol. Spectrosc.145,456–457 (1991)] must be reassigned as a2Δ state.