Nuclear Charge Radii of Silicon Isotopes.

The nuclear charge radius of ^{32}Si was determined using collinear laser spectroscopy. The experimental result was confronted with ab initio nuclear lattice effective field theory, valence-space in-medium similarity renormalization group, and mean field calculations, highlighting important achievements and challenges of modern many-body methods. The charge radius of ^{32}Si completes the radii of the mirror pair ^{32}Ar-^{32}Si, whose difference was correlated to the slope L of the symmetry energy in the nuclear equation of state. Our result suggests L≤60 MeV, which agrees with complementary observables.

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.

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 2P3/2 → 7s 2S1/2 (535 nm), 6p 2P1/2 → 6d 2D3/2 (277 nm), and 6p 2P1/2 → 7s 2S1/2 (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 2P3/2 → 7s 2S1/2 and 6p 2P1/2 → 6d 2D3/2 transitions. It was shown that the value of the specific mass shift factor for the 6p 2P3/2 → 7s 2S1/2 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.

Compound-tunable embedding potential method: analysis of pseudopotentials for Yb in YbF2, YbF3, YbCl2 and YbCl3 crystals.

The compound-tunable embedding potential (CTEP) method developed in [Lomachuk et al., Phys. Chem. Chem. Phys., 2020, 22, 17922; Maltsev et al., Phys. Rev. B, 2021, 103, 205105] to describe the electronic structure of fragments and point defects in materials is applied to crystals containing periodically arranged lanthanide atoms, which can have an open 4f-shell. We consider YbF2, YbF3, YbCl2, and YbCl3 crystals for the pilot CTEP studies such that 4f-electrons are not treated explicitly at the CTEP generation stages. Instead, the pseudopotentials with 60 and 59 electrons in the core for Yb(II) and Yb(III), correspondingly, are applied and the latter treats the "4f-hole-in-core". At the final stage, the two-component embedded cluster study of fragments of YbHaln crystals (Hal = F, Cl; n = 2, 3) is performed using the CTEP method and a relativistic pseudopotential with 28 electrons in the core for the central Yb atom. Remarkable agreement of the electronic densities within the YbHal2 fragments with those of the original periodic crystal calculation is demonstrated. The calculated interatomic distances between the central Yb and nearest halide atoms are in pretty good agreement with the experimental data, the deviations are within 0.015 Å for all the studied crystals. Thus, the overall accuracy for the crystal characteristics evaluated using CTEP in the combined periodic-structure and embedded cluster study is comparable with that of Yb-containing molecular calculations.

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 2Π1/2 and 2Π3/2 states, but lead consistently and unambiguously to deviations from experimental-based adiabatic transition energy estimates for the 2Σ1/2 excited electronic state, and show that more measurements are needed to clarify spectroscopic assignment of the 2Δ state.

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.

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

Highly accurate theoretical predictions of transition energies in the radium monofluoride molecule, 226RaF, and radium cation, 226Ra+, are reported. The considered transition X2Σ1/2 → A2Π1/2 in RaF is one of the main features of this molecule and can be used to laser-cool RaF for a subsequent measurement of the electron electric dipole moment. For molecular and atomic predictions, we go beyond the Dirac-Coulomb Hamiltonian and treat high-order electron correlation effects within the coupled cluster theory with the inclusion of quadruple and ever higher amplitudes. The effects of quantum electrodynamics (QED) are included non-perturbatively using the model QED operator that is now implemented for molecules. It is shown that the inclusion of the QED effects in molecular and atomic calculations is a key ingredient in resolving the discrepancy between the theoretical values obtained within the Dirac-Coulomb-Breit Hamiltonian and the experiment. The remaining deviation from the experimental values is within a few meV. This is more than an order of magnitude better than the "chemical accuracy," 1 kcal/mol = 43 meV, that is usually considered as a guiding thread in theoretical molecular physics.

Nuclear magnetization distribution effect in molecules: Ra+ and RaF hyperfine structure.

Recently, the first laser spectroscopy measurement of the radioactive RaF molecule has been reported by Ruiz et al. [Nature 581, 396 (2020)]. This and similar molecules are considered to search for the new physics effects. The radium nucleus is of interest as it is octupole-deformed and has close levels of opposite parity. The preparation of such experiments can be simplified if there are reliable theoretical predictions. It is shown that the accurate prediction of the hyperfine structure of the RaF molecule requires to take into account the finite magnetization distribution inside the radium nucleus. For atoms, this effect is known as the Bohr-Weisskopf (BW) effect. Its magnitude depends on the model of the nuclear magnetization distribution which is usually not well known. We show that it is possible to express the nuclear magnetization distribution contribution to the hyperfine structure constant in terms of one magnetization distribution dependent parameter: BW matrix element for 1s-state of the corresponding hydrogen-like ion. This parameter can be extracted from the accurate experimental and theoretical electronic structure data for an ion, atom, or molecule without the explicit treatment of any nuclear magnetization distribution model. This approach can be applied to predict the hyperfine structure of atoms and molecules and allows one to separate the nuclear and electronic correlation problems. It is employed to calculate the finite nuclear magnetization distribution contribution to the hyperfine structure of the 225Ra+ cation and 225RaF molecule. For the ground state of the 225RaF molecule, this contribution achieves 4%.

Actinide and lanthanide molecules to search for strong CP-violation.

The existence of the fundamental CP-violating interactions inside the nucleus leads to the existence of a nuclear Schiff moment. The Schiff moment potential corresponds to the electric field localized inside the nucleus and directed along its spin. This field can interact with electrons of an atom and induce the permanent electric dipole moment (EDM) of the whole system. The Schiff moment and the corresponding electric field are enhanced in the nuclei with octupole deformation leading to an enhanced atomic EDM. There is also a few-order enhancement of the T,P-violating effects in molecules due to the existence of energetically close levels of opposite parity. We study the Schiff moment enhancement in the class of diatomic molecules with octupole-deformed lanthanide and actinide nuclei: 227AcF, 227AcN, 227AcO+, 229ThO, 153EuO+ and 153EuN. Projecting the existing experimental achievements to measure the EDM in diamagnetic molecules with a spherical nucleus (205TlF) to the considered systems one can expect very high sensitivity to the quantum chromodynamics parameter [small theta, Greek, macron] and other hadronic CP-violation parameters surpassing the current best limits by several orders of magnitude. It can have a dramatic impact on the modern understanding of the nature of CP-violating fundamental interactions.

Compound-tunable embedding potential: which oxidation state of uranium and thorium as point defects in xenotime is favorable?

Modern strategies for the safe handling of high level waste (HLW) and its long-term disposal in deep geological formations include the immobilization of radionuclides in the form of mineral-like matrices. The most promising matrices for the immobilization of actinides are ceramic forms of waste based on phosphate minerals such as monazite, xenotime, and cheralite. However, the mechanism of substitution of lanthanides and Y by actinides in phosphate minerals is not entirely clear. We formulated a theoretical model, compound-tunable embedding potential (CTEP), that allows one to predict properties of such crystals with point defects. The reliability of the model is validated by a good agreement of calculated geometry parameters with available experimental data. The substitution of Y in the xenotime crystal by Th and U is studied by relativistic DFT in the framework of the CTEP method, based on constructing the embedding potential as the linear combination of short-range "electron-free" spherical "tunable" pseudopotentials. It is shown on the basis of the proposed model that oxidation state +3 is energetically more profitable than +4 not only for thorium but also for uranium as solitary point defects. This atypical oxidation state of U in the mineral is discussed.

New Nuclear Magnetic Moment of

A recent measurement of the hyperfine splitting in the ground state of Li-like ^{208}Bi^{80+} has established a "hyperfine puzzle"-the experimental result exhibits a 7σ deviation from the theoretical prediction [J. Ullmann et al., Nat. Commun. 8, 15484 (2017)NCAOBW2041-172310.1038/ncomms15484; J. P. Karr, Nat. Phys. 13, 533 (2017)NPAHAX1745-247310.1038/nphys4159]. We provide evidence that the discrepancy is caused by an inaccurate value of the tabulated nuclear magnetic moment (µ_{I}) of ^{209}Bi. We perform relativistic density functional theory and relativistic coupled cluster calculations of the shielding constant that should be used to extract the value of µ_{I}(^{209}Bi) and combine it with nuclear magnetic resonance measurements of Bi(NO_{3})_{3} in nitric acid solutions and of the hexafluoridobismuthate(V) BiF_{6}^{-} ion in acetonitrile. The result clearly reveals that µ_{I}(^{209}Bi) is much smaller than the tabulated value used previously. Applying the new magnetic moment shifts the theoretical prediction into agreement with experiment and resolves the hyperfine puzzle.