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Molecular properties of the thallium monocyanide (Tl·CN) system in its ground electronic state are studied using high-precision ab initio relativistic two-component pseudopotential replacing 60 inner-core electrons of Tl. A relativistic coupled-cluster method with single, double and perturbative triple amplitudes is employed to account for electronic correlations. Extrapolation of results to the complete basis set limit is used for all studied properties. The global potential energy minimum of Tl·CN corresponds to the linear cyanide (TlCN) isomer, while the non-rigid isocyanide-like (TlNC) structure lies by approximately 11 kJ/mol higher in energy. The procedure of restoration of the wavefunction in the “core” region of Tl atom was applied to calculate the interaction of the Tl nuclear Schiff moment with electrons. The parameter X of the interaction of the Tl nuclear Schiff moment with electrons in the linear TlCN molecule equals 7150 a.u. The prospects of using the TlCN molecule for the experimental detection of the nuclear Schiff moment are discussed.

Molecular spectroscopy offers opportunities for the exploration of the fundamental laws of nature and the search for new particle physics beyond the standard model 1 – 4 . Radioactive molecules—in which one or more of the atoms possesses a radioactive nucleus—can contain heavy and deformed nuclei, offering high sensitivity for investigating parity- and time-reversal-violation effects 5 , 6 . Radium monofluoride, RaF, is of particular interest because it is predicted to have an electronic structure appropriate for laser cooling 6 , thus paving the way for its use in high-precision spectroscopic studies. Furthermore, the effects of symmetry-violating nuclear moments are strongly enhanced 5 , 7 – 9 in molecules containing octupole-deformed radium isotopes 10 , 11 . However, the study of RaF has been impeded by the lack of stable isotopes of radium. Here we present an experimental approach to studying short-lived radioactive molecules, which allows us to measure molecules with lifetimes of just tens of milliseconds. Energetically low-lying electronic states were measured for different isotopically pure RaF molecules using collinear resonance ionisation at the ISOLDE ion-beam facility at CERN. Our results provide evidence of the existence of a suitable laser-cooling scheme for these molecules and represent a key step towards high-precision studies in these systems. Our findings will enable further studies of short-lived radioactive molecules for fundamental physics research. Measurements of low-energy electronic states of radium monofluoride validate predictions of the use of this short-lived radioactive molecule in exploring fundamental physics and provide evidence of its suitability for laser cooling.

Radium compounds have attracted recently considerable attention due to both development of experimental techniques for high-precision laser spectroscopy of molecules with short-lived nuclei and amenability of certain radium compounds for direct cooling with lasers. Currently, radium monofluoride (RaF) is one of the most studied molecules among the radium compounds, both theoretically and recently also experimentally. Complementary studies of further diatomic radium derivatives are highly desired to assess the influence of chemical substitution on diverse molecular parameters, especially on those connected with laser cooling, such as vibronic transition probabilities, and those related to violations of fundamental symmetries. In this article high-precision \\emph{ab initio} studies of electronic and vibronic levels of diatomic radium monochloride (RaCl) are presented. Recently developed approaches for treating electronic correlation with Fock-space coupled cluster methods are applied for this purpose. Theoretical results are compared to an early experimental investigation by Lagerqvist and used to partially reassign the experimentally observed transitions and molecular electronic levels of RaCl. Effective constants of \\(\\mathcal{P}\\)-odd hyperfine interaction \\(W_{\\rm{a}}\\) and \\(\\mathcal{P,T}\\)-odd scalar-pseudoscalar nucleus-electron interaction \\(W_{\\rm{s}}\\) in the ground electronic state of RaCl are estimated within the framework of a quasirelativistic Zeroth-Order Regular Approximation approach and compared to parameters in RaF and RaOH.

Recently a number of diatomic and polyatomics molecules has been identified as a prospective systems for Doppler/Sisyphus cooling. Doppler/Sisyphus cooling allows to decrease the kinetic energy of molecules down to microkelvin temperatures with high efficiency and then capture them to molecular traps, including magneto-optical trap. Trapped molecules can be used for creation of molecular fountains and/or performing controlled chemical reactions, high-precision spectra measurements and a multitude of other applications. Polyatomic molecules with heavy nuclei present considerable interest for the search for \"new physics\" outside of Standard Model and other applications including cold chemistry, photochemistry, quantum informatics etc. Herein we would like to attract attention to radium monohydroxide molecule (RaOH) which is on the one hand an amenable object for laser cooling and on the other hand provides extensive possibilities for searching for P-odd and P,T-odd effects. At the moment RaOH is the heaviest polyatomic molecule proposed for direct cooling with lasers.

Isotope shifts of \\(^{223-226,228}\\)Ra\\(^{19}\\)F were measured for different vibrational levels in the electronic transition \\(A^{2}{}{\\Pi}_{1/2}\\leftarrow X^{2}{}{\\Sigma}^{+}\\). The observed isotope shifts demonstrate the particularly high sensitivity of radium monofluoride to nuclear size effects, offering a stringent test of models describing the electronic density within the radium nucleus. Ab initio quantum chemical calculations are in excellent agreement with experimental observations. These results highlight some of the unique opportunities that short-lived molecules could offer in nuclear structure and in fundamental symmetry studies.

The scaling of nuclear spin-dependent parity violating effects with increasing nuclear charge \\(Z\\) is discussed in two series of isovalent open-shell diatomic molecules. The parameter \\(W_\\mathrm{a}\\) characterising the strength of parity violation in diatomic molecules is calculated in the framework of the zeroth-order regular approximation (ZORA) and found to be in good agreement with the \\(R(Z) Z^k\\) scaling law derived for atoms in which \\(R(Z)\\) represents a relativistic enhancement factor. The influence of electron correlation is studied on the molecular level, with spin-polarisation effects being conveniently accounted for by a previously established approximate relation between the hyperfine coupling tensor and \\(W_\\mathrm{a}\\). For high accuracy predictions of parity violating effects in radium fluoride the necessity for systematically improvable correlation calculations is emphasised.

Photoelectron circular dichroism refers to the forward/backward asymmetry in the photoelectron angular distribution with respect to the propagation axis of circularly polarized light. It has recently been demonstrated in femtosecond multi-photon photoionization experiments with randomly oriented camphor and fenchone molecules [C. Lux et al., Angew. Chem. Int. Ed. 51, 5001 (2012);C. S. Lehmann et al., J. Chem. Phys. 139, 234307 (2013)]. A theoretical framework describing this process as (2+1) resonantly enhanced multi-photon ionization is constructed, which consists of two-photon photoselection from randomly oriented molecules and successive one-photon ionisation of the photoselected molecules. It combines perturbation theory for the light-matter interaction with ab initio calculations for the two-photon absorption and a single-center expansion of the photoelectron wavefunction in terms of hydrogenic continuum functions. It is verified that the model correctly reproduces the basic symmetry behavior expected under exchange of handedness and light helicity. When applied it to fenchone and camphor, semi-quantitative agreement with the experimental data is found, for which a sufficient d wave character of the electronically excited intermediate state is crucial.

The study of molecular systems provides exceptional opportunities for the exploration of the fundamental laws of nature and for the search for physics beyond the Standard Model of particle physics. Measurements of molecules composed of naturally occurring nuclei have provided the most stringent upper bounds to the electron electric dipole moment to date, and offer a route to investigate the violation of fundamental symmetries with unprecedented sensitivity. Radioactive molecules - where one or more of their atoms possesses a radioactive nucleus - can contain heavy and deformed nuclei, offering superior sensitivity for EDM measurements as well as for other symmetry-violating effects. Radium monofluoride, RaF, is of particular interest as it is predicted to have an appropriate electronic structure for direct laser cooling. Furthermore, some Ra isotopes are known to be octupole deformed, thereby resulting in a large enhancement of their symmetry-violating nuclear moments. Until now,however, no experimental measurements of RaF have been performed, and their study is impeded by major experimental challenges, as no stable isotopes of radium exist. Here, we present a novel experimental approach to study short-lived radioactive molecules using the highly sensitive collinear resonance ionisation method. With this technique we have measured, for the first time, the energetically low-lying electronic states for each of the isotopically pure RaF molecules at the ISOLDE-CERN. Our results provide strong evidence of the existence of a suitable laser-cooling scheme for these molecules and constitute a pivotal step towards high-precision studies in these systems. Our findings open up new opportunities in the synthesis, manipulation and study of short-lived radioactive molecules, which will have a direct impact in many-body physics, astrophysics, nuclear structure, and fundamental physics research.

The parameter \\(W_\\mathrm{a}\\), which characterizes nuclear spin-dependent parity violation effects within the effective molecular spin-rotational Hamiltonian, was computed for the electronic ground state of radium fluoride (RaF) and found to be one of the largest absolute values predicted so far. These calculations were performed with the complex generalised Hartree-Fock method within a two-component (quasi-relativistic) zeroth-order regular approximation framework. Peculiarities of the molecular electronic structure of RaF lead to highly diagonal Franck-Condon matrices between vibrational states of the electronic ground and first excited states, which renders the molecule in principle suitable for direct laser cooling. As a trapped gas of cold molecules offers a superior coherence time, RaF can be considered a promising candidate for high-precision spectroscopic experiments aimed at the search of molecular parity-violation effects.

Relativistic ab initio calculations have been performed to assess the suitability of RaF for experimental search of P- and T,P-violating interactions. The parameters of P- and T,P-odd terms of the spin-rotational Hamiltonian have been calculated for the \\({^2}\\Sigma\\) electronic ground state of RaF molecule. They include the parameter \\(W_a\\), which is critical in experimental search for nuclear anapole moment and the parameters \\(W_d\\) and \\(W_{\\rm SP}\\) required to obtain restrictions on the electric dipole moment of the electron and T,P-odd scalar-pseudoscalar interactions, respectively. The parameter \\(X\\) corresponding to the \"volume effect\" in the T,P\\(-\\)odd interaction of the \\(^{223}\\)Ra nuclear Schiff moment with electronic shells of RaF has also been computed. Spectroscopic and hyperfine structure constants for \\(^{223}\\)RaF and \\(^{223}\\)Ra\\(^+\\) have been computed as well, demonstrating the accuracy of the methods employed.