Molecules containing heavy and octupole deformed radioactive nuclei are predicted to provide enhanced sensitivity to investigate the violation of fundamental symmetries and to search for physics beyond the Standard Model of particle physics. However, experimental measurements of such radioactive systems are scarce. Octupole deformed nuclei are very rare in nature or do not occur naturally. Thus, their study requires to overcome major experimental challenges. This contribution will discuss the recent achievements in laser spectroscopy of radioactive molecules at CRIS, ISOLDE-CERN. This talk will discuss recent spectroscopy measurements of short-lived radium fluoride molecules (RaF) alongside future perspectives in the study of other radioactive molecules. The impact of these developments in fundamental physics research will be discussed.

Heavy diatomic molecules are currently considered to be among the most sensitive systems used in the search for the eEDM and in probing of the Standard Model of particle physics. In certain molecules effects resulting from both parity violation and time-reversal violation (P,T- odd effects) are considerably enhanced with respect to atomic systems. The strength of these interactions grows with atomic number, nuclear spin and nuclear deformation. RaF is of particular interest because it is predicted to have an electronic structure appropriate for laser cooling and also being sensitive to the new phenomenaL.V. Skripnikov. J. Chem. Phys. 153, 114114, 2020 The suitability of RaF for laser-cooling depends critically on its energy levels structure, lifetimes of its excited states, vibrational branching ratios and electronic transition probabilities. Although experimental knowledge of radioactive molecules is scarce, a recent workR.F. Garcia Ruiz et al. Nature, 581, 396-400, 2020resented an approach for performing laser spectroscopy of short-lived radioactive molecules, using the highly sensitive collinear resonance ionization method. As an example of the novel technique RaF was used. This work aims to determine properties at the highest possible level of computational accuracy, following the procedure from our earlier workY. Hao et al. J. Chem . Phys. 151, 034302, 2019 to conclude on the suitability of RaF for laser-cooling and compare with existing experimental data. We present high-accuracy relativistic Fock-Space coupled cluster calculations of the potential energy curves and the spectroscopic constants of the ground state and the lower excited states of RaF. The ionization potential of RaF was calculated and the Franck-Cordon factors were obtained, based on calculated potential energy curves. We have also calculated the TDMs of different transitions using multireference configuration interaction approach. Based on defined TDMs and experimental transitions, lifetimes of the excited states in RaF were determined. The new results are compared with existing theoretical and experimental data.

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L.V. Skripnikov. J. Chem. Phys. 153, 114114, 2020. R.F. Garcia Ruiz et al. Nature, 581, 396-400, 2020p Y. Hao et al. J. Chem . Phys. 151, 034302, 2019,

To find a new physics beyond the Standard Model (SM), it is necessary to investigate effects that violate the invariance with respect to spatial reflections and time reversal, such as the electric dipole moment of an electron (eEDM) and the scalar-pseudoscalar electron-nuclear interaction. Triatomic molecules that we study in this paper combine the advantages of the opposite parity closely spaced levels (l-doublets) and the possibility of laser cooling that makes them promising species for high-precision experiments. The average value of the operators responsible for the violation of spatial and temporal parity can be affected by the vibrational modes of molecules, which were not previously taken into account in theoretical calculations. We computed the parameters of P, T-odd interactions of E_eff and E_s for nonlinear configurations of the RaOH A. Zakharova, A. Petrov, P,T-odd effects for RaOH molecule in the excited vibrational state, arXiv:2012.08427 [physics.atom-ph]nd YbOH molecules with subsequent averaging over the vibrational wave function. We also obtained the value of l-doubling, that determines the value of the external field necessary for the maximum sensitivity of the molecule to P, T-odd effects. We obtained molecular orbitals by the Dirac-Hartree-Fock method implemented in Dirac 19 software package. Potential surfaces were calculated by the coupled cluster method taking into account triple excitations (CCSD(T)). To describe the electronic structure of heavy atoms, we used a generalized effective core potential with the restoration of the correct behavior of four-component spinors in the core region. This method was extended by us to complex molecular spinors. The vibrational wave functions were obtained in the Born-Oppenheimer approximation by the coupled channel method.

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Footnotes:

A. Zakharova, A. Petrov, P,T-odd effects for RaOH molecule in the excited vibrational state, arXiv:2012.08427 [physics.atom-ph]a

To reproduce accurately experimental values of hyperfine spliting of heavy atoms one have to take into account the corrections for the distribution of charge (the Breit-Rosenthal effectM. Crawford, Phys. Rev. 76, 1310 (1949). and magnetization (the Bohr-Weisskopf effectA. Bohr and V. Weisskopf, Physical Review 77, 94 (1950). over the nucleus. In the presented study, a program was written to calculate the Bohr-Weisskopf correction in the one-particle model of the nucleus, in which the distribution of the valence nucleon is found from the solution of the Schrödinger equation with the Woods-Saxon potential. It was used to calculate the hyperfine structure of a neutral Tl atom, as well as a hyperfine magnetic anomaly - a special combination of hyperfine interaction constants and g factors of two different isotopes, which is quite sensitive to differences in the magnetization distribution. By comparing the results obtained with the model of a uniformly magnetized ballProsnyak, S. D., Maison, D. E., Skripnikov, L. V., The Journal of Chemical Physics, 152(4), 044301. (2020). it was shown that, with a sufficient accuracy, the ratio of anomalies for two electronic states is stable with respect to the choice of the nuclear model and its parametersS. Schmidt, J. Billowes, M. Bissell, K. Blaum, R. G. Ruiz, H. Heylen, S. Malbrunot-Ettenauer, G. Neyens, W. Nörtershäuser, G. Plunien, et al., Phys. Lett. B 779, 324 (2018). This fact is important because it is used to predict the magnetic moments of short-lived nuclei. In addition, the differential hyperfine anomaly was calculated in the above mentioned nuclear models and the results obtained were compared with experimental data. Calculations of the electronic structure were carried out with the support of the grant of the Russian Science Foundation (project 19-72-10019). The calculation of the correction for the Breit interaction in the Gaunt approximation was carried out with the support of the RFBR grant (project 20-32-70177).

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Footnotes:

M. Crawford, Phys. Rev. 76, 1310 (1949).) A. Bohr and V. Weisskopf, Physical Review 77, 94 (1950).) Prosnyak, S. D., Maison, D. E., Skripnikov, L. V., The Journal of Chemical Physics, 152(4), 044301. (2020)., S. Schmidt, J. Billowes, M. Bissell, K. Blaum, R. G. Ruiz, H. Heylen, S. Malbrunot-Ettenauer, G. Neyens, W. Nörtershäuser, G. Plunien, et al., Phys. Lett. B 779, 324 (2018)..

Considering the great potential for investigations of T,P-violating effects on HfF⁺ ions [1], it was proposed in Ref. [2] to use ¹⁷⁷Hf¹⁹F⁺ and ¹⁷⁹Hf¹⁹F⁺ ions to measure nuclear magnetic quadrupole moment (MQM) of ¹⁷⁷Hf and ¹⁷⁹Hf nuclei which have spins I = 7/2 and I=9/2 respectively. The important characteristic of the experiments on HfF⁺ is that rotating magnetic and electric fields are used to trap ions [1]. In this case, the magnetic field, in contrast to experiments in static fields, is not an auxiliary tool, but should ensure a nonzero energy shift due to possible T,P-odd effects [3]. To completely polarize the molecule and to access the maximum T,P-odd effect both rotating electric and magnetic fields should be large enough. The saturating value of the magnetic field is strongly depends on the considered Zeeman sublevel of the ion. These values are required to plan the experiment and their calclation is the main aim of the work. To populate the required levels in experiments one needs to know energy levels structure. This problem is especially important for ^177,179\textHfF⁺ since it has dense spectrum due to high nuclear spins of ^177,179\textHf. Further, the knowledge of g-factors helps to control and suppress systematic effects due to stray magnetic field therefore calculations of these properties in external fields are also made in our work [4]. [1] W. B. Cairncross, D. N. Gresh, M. Grau, K. C. Cossel, T. S. Roussy, Y. Ni, Y. Zhou, J. Ye, and E. A. Cornell, Phys. Rev. Lett.119, 153001 (2017) [2] V. V. Flambaum, D. DeMille, and M. G. Kozlov, Phys. Rev. Lett. 113, 103003 (2014) [3] A. N. Petrov, Phys. Rev. A 97, 052504 (2018). [4] I. P. Kurchavov and A. N. Petrov, Phys. Rev. A, 102, 032805 (2020)

The molecular ion TaO⁺ is a promising candidate to explore new physics beyond the Standard Model in both the leptonic and hadronic sectors via precision measurements of the electron's Electric Dipole Moment (eEDM) and Nucleus Magnetic Magnetic Quadrupole Moment (NMQM) [citation]. Similar to ThF⁺ that is under active investigation[citation], the eEDM sensitive state of TaO⁺, ³∆₁, is predicted to be the ground state that facilitates a long coherent measurement[citation]. Although TaO⁺ has a smaller effective electric field (20.2 GV/cm) than ThF⁺ (35.2 GV/cm), it has a non-zero nuclear spin (I = 7/2) for which the latter is 0, allowing for studies of symmetry break in the nucleus, such as the NMQM, in a single experimental system. To perform the above mentioned precision measurements, the first step is to create TaO⁺ in the rovibraonic ground state (³∆₁, v⁺=0, and J⁺=1). We plan to implement Resonant Enhanced Multiphoton Ionization (REMPI) method to create TaO⁺ from its neutral precursor TaO in a supersonic cooled molecular beam. To locate an appropriate intermediate electronic state for the REMPI scheme, we perform laser induced fluorescence spectroscopy of TaO in the regime of 30,000-45,000 cm⁻¹ that is unexplored. Preliminary results of the survey spectroscopy and experimental design of the precision measurements will be discussed in this presentation.

Studying the effects of spatial parity (P) nonconservation of fundamental interactions in atoms and molecules, it is possible to refine the parameters of the standard model in laboratory conditions, as well as to set constraints on the parameters of its extensions. Such experiments [1] were most successfully carried out for the Cs atom. Using the expression for the P-odd electron-nuclear weak interaction and expanding it in a series in terms of the multipole moments of the nuclear density, one can obtain the quadrupole term [2,3]. Since the weak charge of the neutron considerably exceeds the weak charge of the proton, the main contribution to the considered interaction is due to the neutron subsystem of the nucleus. Therefore, by studying the interaction of this type, it is possible (for the first time) to study the quadrupole distribution of neutrons in a nucleus. Using a two-step method for calculating the properties of atoms in compounds of heavy elements [4], we study the P-odd tensor interaction of the electron subsystem with the neutron quadrupole moment of the nucleus in the TaO⁺ cation. We also study a possible contribution of the P-odd interaction of electrons with the Tl anapole moment. Finally, the energy levels of the TaO⁺ molecule are predicted. The study was supported by a grant from the Russian Science Foundation (project No. 19-72-10019). 1. C. S. Wood, S. C. Bennett, D. Cho, B. P. Masterson, J. L. Roberts, C. E. Tanner, and C. E. Wieman, Science 275, 1759 (1997). 2. V.V. Flambaum, V.A. Dzuba, C. Harabati, Phys. Rev. A 96, 012516 (2017). 3. L.V. Skripnikov, A. N. Petrov, A. V. Titov, V. V. Flambaum, Phys. Rev. A 99, 012517 (2019). 4. A. V. Titov, N. S. Mosyagin, A. N. Petrov, T. A. Isaev, D. P. DeMille, Progr. Theor. Chem. Phys. 15, 253 (2006).

It was recently shown that coupling of ultralight scalar dark matter to the standard model leads to oscillations of fundamental constants and, therefore, may be observed in clock-comparison experiments. Highly charged ions such as Ir¹⁷⁺ allow for the development of novel atomic clocks with high sensitivity to the variation of the fine-structure constant and, therefore, dark matter searches. The clock transitions are weak and very difficult to identity without accurate theoretical predictions. In the case of Ir¹⁷⁺, even stronger electric-dipole (E1) transitions eluded observations despite years of effort raising the possibility that theory predictions are grossly wrong. In this work, we have developed a broadly-applicable approach that drastically increases the ability to accurately predict properties of complex atoms and applied it to Ir¹⁷⁺ providing accurate predictions of transition wavelengths and E1 transition rates. Our results explain the lack of observation of the E1 transitions and provide a pathway towards detection of clock transitions. Computational advances demonstrated in this work are widely applicable to most elements in the periodic table and will allow to solve numerous problems in atomic physics, astrophysics, and plasma physics. We are currently developing an online portal with access to a database of high-precision atomic properties and a package of atomic codes that can be used to compute these properties.

Pure quantum states of charged molecules can now be prepared, coherently manipulated, and efficiently detected in high-resolution spectroscopy experiments by employing quantum-logic spectroscopy, an action spectroscopy at the single quantum level. The coupled harmonic motion of co-trapped ions can be utilized to transfer action information from a ßpectroscopy" molecular ion to an easily manipulated and detected atomic “logic” ion. With this technique and precise characterization of the systematic effects of the trap RF electric field on molecular levels, we demonstrate hertz-level resolution in terahertz-scale rotational spectroscopy of a single CaH⁺ molecule using a Ca⁺ logic ion. Precision measurements of molecular transitions can be used to determine molecular properties, and here we experimentally determine the CaH⁺ dipole moment for the first time. In addition to detecting departure from the initial state, we can also detect arrival into the final state, facilitating confirmation of transition assignment in cases where the spectrum is congested or a priori information is limited. Because all of our laser operations on the molecule are driving stimulated Raman transitions with the lasers far detuned from molecular transitions, the techniques should be generalizable to a wide variety of charged molecules.

-A.L. Collopy et al., in preparation -Chou, C-W. et al., Science 367, 6485 (2020) -Lin, Y. et al. Nature 581, 273–277(2020)

Although numerous doubly positively charged diatomic molecules (diatomic dications) are known from investigations using mass spectrometry and ab-initio quantum chemistry, only three of them, NO²⁺, N₂²⁺ and DCl²⁺, have been studied using rotationally resolved optical spectroscopyP. C. Cosby, R. Möller, and H. Helm, Phys. Rev. A 28, 766 (1983), D. Cossart, M. Bonneau, and J. M. Robbe, J. Mol. Spectrosc. 125, 413 (1987), S. G. Cox, A. D. J. Critchley, P. S. Kreynin, I. R. McNab, R. C. Shiell, and F. E. Smith, Phys. Chem. Chem. Phys. 5, 663 (2003)nd only about a dozen by vibrationally resolved double-ionization methods J. H. D. Eland and R. Feifel, Double Photoinisation Spectra of Molecules (Oxford University Press, 2018) So far, no thermodynamically stable diatomic dication has been characterized spectroscopically, primarily because of experimental difficulties associated with their synthesis in sufficient densities in the gas phase. Indeed, such molecules typically involve, as constituents, rare-gas, halogen, or chalcogen, and metal atoms. We report on a new approach to study molecular dications based on high-resolution PFI-ZEKE photoelectron spectroscopy of the singly charged parent molecular cation and present the first spectroscopic characterization of a thermodynamically stable diatomic dication, MgAr²⁺. We have observed the partially resolved rotational structure of several vibrational levels of the ground electronic state of MgAr²⁺ using a resonant (1+1'+1") three-photon excitation scheme. From the analysis of the photoelectron spectra of ²⁴MgAr⁺ and ²⁶MgAr⁺ we have determined the potential-energy function of the electronic ground state of MgAr²⁺, its dissociation (binding) energy (D₀=10690(3) cm⁻¹), and its harmonic (ω_e(²⁴MgAr²⁺)=327.02(11) cm⁻¹) and anharmonic (ω_ex_e(²⁴MgAr²⁺)=2.477(15) cm⁻¹) vibrational constants. The analysis enables us to explain quantitatively how the strong bond arises in this dication despite the fact that Ar and Mg²⁺ both have a full-shell rare-gas electronic configuration.

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Footnotes:

P. C. Cosby, R. Möller, and H. Helm, Phys. Rev. A 28, 766 (1983), D. Cossart, M. Bonneau, and J. M. Robbe, J. Mol. Spectrosc. 125, 413 (1987), S. G. Cox, A. D. J. Critchley, P. S. Kreynin, I. R. McNab, R. C. Shiell, and F. E. Smith, Phys. Chem. Chem. Phys. 5, 663 (2003)a J. H. D. Eland and R. Feifel, Double Photoinisation Spectra of Molecules (Oxford University Press, 2018).

Accurate line lists are important for the description of the spectroscopic nature of small molecules. Given the significant role played by the CN radical in the chemical and astrophysical sciences, we present the process of creation for a new line list, from the collation of experimental data to the production of a hybrid line list. 8083 empirical rovibronic energy levels with uncertainties are determined for 8 doublet states of CN using the MARVEL (Measured Active Rotational-Vibrational Energy Levels) algorithm from 40,333 transitions. These empirical energy levels are utilised in a fitting process to create a spectroscopic model of the three lowest electronic states, using the nuclear motion program; DUO. A final Hybrid line list (up to 60, 000 cm⁻¹) has been created with the addition of results from a pre-existing model Hamiltonian line list (MoLList). Applications of the Spectroscopic Model are explored for the calculation of sensitivities to a variation of the proton-to-electron mass ratio.

We introduce a comb-referenced optical spectrometer operating in the long-wavelength (LW) part of the mid-infrared (MIR) region. It is based on an innovative laser source based on difference frequency generation between two MIR lasers, namely a cw DFB-QCL and a CO₂ laser, which produces widely tunable light from 12.1 to 14.8 μm with optical power up to 110 μW and MHz-level linewidth. We exploit it to give the first evidence of bending modes metrology in this region, with the assessment of several CO₂-based frequency benchmarks with uncertainties down to 30 kHz, and the accurate study of the ν₁₁ band of benzene, which is a significant testbed for the resolution of the spectrometer. These results foster optical metrology in a region not explored so far and pave the way for accurate rotationally-resolved studies of the energy structure of large molecules, such as aromatic hydrocarbons.

We introduce Multispectrum Rotational states Distribution Thermometry (MRDT) as a new optical method for primary thermometry that relies on the global fitting of multiple molecular absorption lines of the same band at different pressures. This allows leveraging the temperature-dependence of the Doppler width and also of the distribution of line intensities across the ro-vibrational band, provided a sufficiently accurate line-strength model is available. We give a preliminary demonstration of the method with a comb-locked frequency-swept cavity-ring-down spectrometer operated on the 3ν₁+ν₃ band of CO₂ located around 1577 nm, which stands out among other spectroscopic samples for the availability of several line intensity models of both experimental and theoretical origin. The spectra signal-to-noise ratio represents the main limitation to a combined uncertainty to 530 ppm, but the comparative analysis between different line-strength models shows promise to reduce the error budget to 33 ppm. As compared to Doppler-broadening-thermometry, an advantage of the approach is the reduced impact of a wrong modelling of the absorption line-shapes. In a reversed approach, MRDT can be applied on a gas of known temperature to set an upper limit to the accuracy of a given line intensity model.