Thorium Monoxide Research Articles

Structural and electronic phase transitions of thorium monoxide from first-principles calculations

Because of the innovative concepts for creating the thorium fuel cycle as an alternative nuclear energy source, thorium and its compounds have attracted a lot of attention. It is essential to study the physical properties that are necessary for the basic understanding and practical application of these materials. Thorium monoxide has already drawn researchers' attention as a metal oxide. Under different pressure conditions, the crystal structures, electronic band structures, phonon dispersions, mechanical properties, and thermodynamic properties of ThO have been determined using a particle swarm optimization structure prediction method in conjunction with first-principles calculations. Previous experiments agree with our results for the lattice constants of the phase of Fm3‾m. Moreover, a novel structure of R-3m is predicted to be thermally stable at a pressure of roughly 22 GPa. The phase is then also mechanically and dynamically stable, according to the findings of our computed elastic constants and phonon dispersion. The phase change from Fm3‾m to R-3m has not, however, been associated with any electronic transitions, and as both phases are mental, they may have excellent thermal conductivity. We further calculated the results of the Helmholtz free energy, entropy, specific heat, internal energy, bulk modulus, shear modulus, Young's modulus, Poisson's ratio, and Debye temperature based on the stable dynamics and mechanical properties, which reveal that they all could be good fuel. The results provide key insights into understanding the structural and electronic behaviors of ThO under the condition of external pressure.

Theoretical molecular spectroscopy of actinide compounds: the ThO molecule

The tiny-core generalised (Gatchina) relativistic pseudopotential (GRPP) model provides an accurate approximation for many-electron Hamiltonians of molecules containing heavy atoms, ensuring a proper description of the effects of non-Coulombian electron-electron interactions, electronic self-energy and vacuum polarisation. Combining this model with electron correlation treatment in the frames of the intermediate Hamiltonian Fock space coupled cluster theory employing incomplete main model spaces, one obtains a reliable and economical tool for excited state modelling. The performance of this method is assessed in applications to ab initio modelling of excited electronic states of the thorium monoxide molecule with term energies below 20,000 cm. Radiative lifetimes of excited states are estimated using truncated expansions of effective and metric operators in powers of cluster amplitudes.

Thorium and Rare Earth Monoxides and Related Phases

Thorium was a part of energy infrastructure in the 19th century due to the refractory and electronic properties of its dioxide. It will be a part of future energy infrastructure as the most abundant energy reserve based on nuclear fission. This paper discusses the solid-state chemistry of the monoxides and related rocksalt phases of thorium and the rare earths, both at atmospheric and at high pressure. The existence of solid thorium monoxide was first suggested more than 100 years ago; however, it was never obtained in bulk and has been studied mostly theoretically. Monoxides of lanthanides from Eu to Ho are ferromagnetic semiconductors sought for spintronics and were studied in thin films. La to Sm metallic monoxides were synthesized in bulk at pressures below 5 GPa. Recently, ThO formation in thin films has been reported and the stability of bulk ThO at high pressure was theoretically predicted based on first principles computations at 0 K. New ab initio computations were performed accounting for temperature effects up to 1000 K using lattice dynamics in the quasi-harmonic approximation. New computational results confirm the stabilization of pure ThO above 30 GPa and suggest the possibility of high-pressure synthesis of (Th,Nd)O at 1000 K and 5 GPa.

Measurement of the H3Δ1 radiative lifetime in ThO

The best limit on the electron electric dipole moment (eEDM) comes from the ACME II experiment [Nature \textbf{562} (2018), 355-360] which probes physics beyond the Standard Model at energy scales well above 1 TeV. ACME II measured the eEDM by monitoring electron spin precession in a cold beam of the metastable H$^3\Delta_1$ state of thorium monoxide (ThO) molecules, with an observation time $\tau \approx 1$ ms for each molecule. We report here a new measurement of the lifetime of the ThO (H$^3\Delta_1$) state, $\tau_H = 4.2\pm 0.5$ ms. Using an apparatus within which $\tau \approx \tau_H$ will enable a substantial reduction in uncertainty of an eEDM measurement.

Electrostatic focusing of cold and heavy molecules for the ACME electron EDM search

The current best upper limit for electron electric dipole moment (EDM), |d e| < 1.1 × 10−29 e cm (90% confidence), was set by the ACME Collaboration in 2018. The ACME experiment uses a spin-precession measurement in a cold beam of thorium monoxide (ThO) molecules to detect d e. An improvement in statistical uncertainty would be possible with more efficient use of molecules from the cryogenic buffer gas beam source. Here, we demonstrate electrostatic focusing of the ThO beam with a hexapole lens. This results in a factor of 16 enhancement in the molecular flux detectable downstream, in a beamline similar to that built for the next generation of ACME. We also demonstrate an upgraded rotational cooling scheme that increases the ground state population by 3.5 times compared to no cooling, consistent with expectations and a factor of 1.4 larger than previously in ACME. When combined with other demonstrated improvements, we project over an order of magnitude improvement in statistical sensitivity for the next generation ACME electron EDM search.

SPECTROSCOPIC AND THERMOCHEMICAL PROPERTIES OF ACTINIDE-CONTAINING SPECIES FROM FIRST PRINCIPLES: THORIUM AND AMERICIUM MONOXIDE MOLECULES

A relativistic version of a composite ab initio treatment of molecular spectroscopy and thermochemistry is developed, focusing on high-accuracy description of the properties of actinide (An) containing species. It is based on combining the calculation results at levels of theory with sufficiently full account of electron correlation, e.g., at the CCSDT(Q) level, but tackling only scalar relativity, with those obtained from more rigorous four-component relativistic calculations with the Dirac–Coulomb Hamiltonian. High accuracy achievable via this approach is revealed taking the examples of thorium and americium monoxide molecules. The errors in ab initio values for the bond length re, vibrational frequency ωe, and atomization energy D0 of the ThO molecule did not exceed 0.001 Å, 2.5 cm–1, and 0.5 kcal/mol, respectively. The composite numerical values for the first ionization potentials of the AmO molecule and the Am atom deviate from the experimental data just by 0.03 eV and 1 cm–1, respectively. For the first time, the proposed approach enabled high-accuracy evaluation of the molecular constants re, ωe and D0 for AmO and AmO+, as well as the second and third ionization potentials of the Am atom. The calculation results are indicative of a minor actinide contraction of the An–O bonds on going through the molecular series ThO → UO → AmO: the bond length in AmO is by 0.0073 Å shorter than that in ThO. The re(An–O) value is shown to be linearly dependent on the actinide atomic number in the periodic table. The results obtained may be used as benchmarks for parametrizing and calibrating the DFT functionals designed for treating An-containing molecules.

Attaining the shot-noise-limit in the ACME measurement of the electron electric dipole moment

Experimental searches for the electron electric dipole moment, de, probe new physics beyond the Standard Model. Recently, the ACME Collaboration set a new limit of (ACME Collaboration 2018 Nature 562 355–60), constraining time reversal symmetry (T) violating physics in the 3–100 TeV energy scale. ACME extracts de from the measurement of electron spin precession due to the thorium monoxide (ThO) molecule’s internal electric field. This recent ACME II measurement achieved an order of magnitude increased sensitivity over ACME I by reducing both statistical and systematic uncertainties in the measurement of the electric dipole precession frequency. The ACME II statistical uncertainty was a factor of 1.7 above the ideal shot-noise limit. We have since traced this excess noise to timing imperfections. When the experimental imperfections are eliminated, we show that shot noise limit is attained by acquiring noise-free data in the same configuration as ACME II.

The electronic structure of thorium monoxide: Ligand field assignment of states in the range 0-5 eV.

Configuration interaction ligand field theory (CI LFT) calculations of the electronic energy levels of ThO were performed by treating the molecular electronic states as Th 2+ free-ion levels perturbed by the ligand field of O2- . Twenty nine experimentally characterized ThO v = 0 energy levels, together with the energy difference between the v = 0 levels of the Y and W states were fitted using a CI LFT model that included Th 2+ 7s 2 , 6d7s, 6d2 , 7s7p, 6d7p, 5f7s, and 7p2 configurations. Predictions from these calculations were used to provide tentative assignments for 171 out of 250 ThO band heads listed by Gatterer et al. ["Molecular Spectra of Metallic Oxides", Specola Vaticana (1957)]. Term energies for 30 electronic states have been determined based on these assignments. Subsequently, the CI LFT model was refined by fitting to a set of 59 electronic term energies. The inclusion of CI effects together with integer valence, atomic-in-molecule, ionic bonding ideas reveals atomic energy level patterns that are multiply replicated in the molecular energy level patterns of six Th 2+ O2- atomic ion configurations (6d7s, 6d2 , 7s7p, 6d7p, 5f7s, and 7p2 ) revealing the underlying atomic ion structure that gives rise to the complex and seemingly erratic unassigned bands reported in the Vatican Atlas. © 2018 Wiley Periodicals, Inc.

Methods, analysis, and the treatment of systematic errors for the electron electric dipole moment search in thorium monoxide

We recently set a new limit on the electric dipole moment of the electron (eEDM) (J Baron et al and ACME collaboration 2014 Science 343 269–272), which represented an order-of-magnitude improvement on the previous limit and placed more stringent constraints on many charge-parity-violating extensions to the standard model. In this paper we discuss the measurement in detail. The experimental method and associated apparatus are described, together with the techniques used to isolate the eEDM signal. In particular, we detail the way experimental switches were used to suppress effects that can mimic the signal of interest. The methods used to search for systematic errors, and models explaining observed systematic errors, are also described. We briefly discuss possible improvements to the experiment.

Probing Chemical Bonding and Electronic Structures in ThO- by Anion Photoelectron Imaging and Theoretical Calculations.

Because of renewed research on thorium-based molten salt reactors, there is growing demand and interest in enhancing the knowledge of thorium chemistry both experimentally and theoretically. Compared with uranium, thorium has few chemical studies reported up to the present. Here we report the vibrationally resolved photoelectron imaging of the thorium monoxide anion. The electron affinity of ThO is first reported to be 0.707 ± 0.020 eV. Vibrational frequencies of the ThO molecule and its anion are determined from Franck-Condon simulation. Spectroscopic evidence is obtained for the two-electron transition in ThO-, indicating the strong electron correlation among the (7sσ)2(6dδ)1 electrons in ThO- and the (7sσ)2 electrons in ThO. These findings are explained by using quantum-chemical calculations including spin-orbit coupling, and the chemical bonding of gaseous ThO molecules is analyzed. The present work will enrich our understanding of bonding capacities with the 6d valence shell.

Formation of solid thorium monoxide at near-ambient conditions as observed by neutron reflectometry and interpreted by screened hybrid functional calculations

Oxidation of a ∼1000 Å sputter-deposited thorium thin film at 150 °C in 100 ppm of flowing oxygen in argon produces the long-sought solid form of thorium monoxide. Changes in the scattering length density (SLD) distribution in the film over the 700-min experiment measured by in-situ, dynamic neutron reflectometry (NR) shows the densities, compositions and thickness of the various thorium oxides layers formed. Screened, hybrid density-functional theory calculations of potential thorium oxides aid interpretation, providing atomic-level picture and energetics for understanding oxygen migration. NR provided evidence of the formation of substoichiometric thorium oxide, ThOy (y < 1) at the interface between the unreacted thorium metal and its dioxide overcoat which grows inward, consuming the thorium at a rate of 2.1 Å/min while y increases until reaching 1:1 oxygen-to-thorium. Its presence indicates that kinetically-favored solid-phase ThO can be preferentially generated as a majority phase under the thermodynamically-favored ThO2 top layer at conditions close to ambient.

In search of discrete symmetry violations beyond the standard model: Thorium monoxide reloaded.

We present an updated electron electric dipole moment (EDM) effective electric field of Eeff= 75.2 GV/cm and 229Th magnetic hyperfine interaction constant A|| = -1266 MHz, the nucleon-electron scalar-pseudoscalar interaction constant WS = 106.0 kHz, and the molecule-frame static electric dipole moment D = -4.41 D for the Δ13 science state of ThO. The criticisms of the results from Fleig and Nayak [J. Mol. Spectrosc. 300, 16 (2014)] made in Skripnikov and Titov [J. Chem. Phys. 142, 024301 (2015)] are addressed and largely found to be unsubstantiated within the framework of the present approach. The present findings confirm the slightly relaxed constraints on relevant beyond-standard-model parameters, in particular the electron EDM, de, and the nucleon-electron scalar-pseudoscalar coupling constant, CS.

Stability of a new cubic monoxide of Thorium under pressure.

Density functional theory has been applied to elucidate the stability of thorium monoxide (ThO). It is found out that the pressure can stabilize the rocksalt phase of ThO, and the transition pressure is estimated between 14 and 22 GPa. The stability of ThO can be attributed due to the gradually filling 5f orbitals at the expense of 7s and 6d electrons in Th metal. For ThO, the pressure induces stronger Th-O bond reflected by the newly established 6d-2p hybridization which is the dominant cause of its stability. The phonon dispersion curves of the rocksalt phase show the positive frequencies which indicates its dynamical stability. Our successful prediction of the stabilization of the metallic ThO has proposed a route to synthesize novel actinide monoxides.

Theoretical study of thorium monoxide for the electron electric dipole moment search: Electronic properties of H3Δ1 in ThO

Recently, improved limits on the electron electric dipole moment, and dimensionless constant, kT,P, characterizing the strength of the T,P-odd pseudoscalar–scalar electron–nucleus neutral current interaction in the H3Δ1 state of ThO molecule were obtained by the ACME collaboration [J. Baron et al., Science 343, 269 (2014)]. The interpretation of the experiment in terms of these fundamental quantities is based on the results of theoretical study of appropriate ThO characteristics, the effective electric field acting on electron, Eeff, and a parameter of the T,P-odd pseudoscalar–scalar interaction, WT,P, given in Skripnikov et al. [J. Chem. Phys. 139, 221103 (2013)] by St. Petersburg group. To reduce the uncertainties of the given limits, we report improved calculations of the molecular state–specific quantities Eeff, 81.5 GV/cm, and WT,P, 112 kHz, with the uncertainty within 7% of the magnitudes. Thus, the values recommended to use for the upper limits of the quantities are 75.8 GV/cm and 104 kHz, correspondingly. The hyperfine structure constant, molecule-frame dipole moment of the H3Δ1 state, and the H3Δ1 → X1Σ+ transition energy which, in general, can serve as a measure of reliability of the obtained Eeff and WT,P values are also calculated. In addition, we report the first calculation of g-factor for the H3Δ1 state of ThO. The results are compared to the earlier experimental and theoretical studies, and a detailed analysis of uncertainties of the calculations is given.

Vibrational quenching of the electronic ground state in ThO in cold collisions withHe3

We measure the ratio $\ensuremath{\gamma}$ of the momentum transfer--to--vibrational quenching cross section for molecular thorium monoxide (ThO) [$X{(}^{1}{\ensuremath{\Sigma}}^{+})$, $v=1$, $J=0$] in collisions with atomic helium between 800 mK and 2.4 K. We find $\ensuremath{\gamma}\ensuremath{\sim}{10}^{4}$. We also observe indirect evidence for ThO-He van der Waals complex formation, which has been predicted by theory [Tscherbul, Sayfutyarova, Buchachenko, and Dalgarno, J. Chem. Phys. 134, 144301 (2011)], and in conjunction, we determine the three-body recombination rate constant at 2.4 K, ${\ensuremath{\Gamma}}_{3}=8\ifmmode\pm\else\textpm\fi{}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}33}$ ${\mathrm{cm}}^{6}$ ${\mathrm{s}}^{\ensuremath{-}1}$.

Zeeman interaction in ThOH3Δ1for the electron electric-dipole-moment search

The current limit on the electron's electric dipole moment, $|{d}_{e}|&lt;8.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}29}$ $e\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$ (90% confidence), was set using the molecule thorium monoxide (ThO) in the $J=1$ rotational level of its $H{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Delta}}_{1}$ electronic state [J. Baron et al., Science 343, 269 (2014)]. This state in ThO is very robust against systematic errors related to magnetic fields or geometric phases, due in part to its $\ensuremath{\Omega}$-doublet structure. These systematics can be further suppressed by operating the experiment under conditions where the $g$-factor difference between the $\ensuremath{\Omega}$ doublets is minimized. We consider the $g$ factors of the ThO $H{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Delta}}_{1}$ state both experimentally and theoretically, including dependence on $\ensuremath{\Omega}$ doublets, the rotational level, and the external electric field. The calculated and measured values are in good agreement. We find that the $g$-factor difference between $\ensuremath{\Omega}$ doublets is smaller in $J=2$ than in $J=1$ and reaches zero at an experimentally accessible electric field. This means that the $H,J=2$ state should be even more robust against a number of systematic errors compared to $H,J=1$.

Confronting Higgcision with electric dipole moments

Current data on the signal strengths and angular spectrum of the 125.5 GeV Higgs boson still allow a CP-mixed state, namely, the pseudoscalar coupling to the top quark can be as sizable as the scalar coupling: $C_u^S \approx C_u^P =1/2$. CP violation can then arise and manifest in sizable electric dipole moments (EDMs). In the framework of two-Higgs-doublet models, we not only update the Higgs precision (Higgcision) study on the couplings with the most updated Higgs signal strength data, but also compute all the Higgs-mediated contributions from the 125.5 GeV Higgs boson to the EDMs, and confront the allowed parameter space against the existing constraints from the EDM measurements of Thallium, neutron, Mercury, and Thorium monoxide. We found that the combined EDM constraints restrict the pseudoscalar coupling to be less than about $10^{-2}$, unless there are contributions from other Higgs bosons, supersymmetric particles, or other exotic particles that delicately cancel the current Higgs-mediated contributions.

Shot-noise-limited spin measurements in a pulsed molecular beam

Heavy diatomic molecules have been identified as good candidates for use in electron electric dipole moment (eEDM) searches. Suitable molecular species can be produced in pulsed beams, but with a total flux and/or temporal evolution that varies significantly from pulse to pulse. These variations can degrade the experimental sensitivity to changes in spin precession phase of an electri- cally polarized state, which is the observable of interest for an eEDM measurement. We present two methods for measurement of the phase that provide immunity to beam temporal variations, and make it possible to reach shot-noise-limited sensitivity. Each method employs rapid projection of the spin state onto both components of an orthonormal basis. We demonstrate both methods using the eEDM-sensitive H state of thorium monoxide (ThO), and use one of them to measure the magnetic moment of this state with increased accuracy relative to previous determinations.

Advanced cold molecule electron EDM

Measurement of a non-zero electric dipole moment (EDM) of the electron within a few orders of magnitude of the current best limit of |d_e| < 1.05 e -27 e cm would be an indication of physics beyond the Standard Model. The ACME Collaboration is searching for an electron EDM by performing a precision measurement of electron spin precession in the metastable H state of thorium monoxide (ThO) using a slow, cryogenic beam. We discuss the current status of the experiment. Based on a data set acquired from 14 hours of running time over a period of 2 days, we have achieved a 1-sigma statistical uncertainty of 1 e -28 e cm/T^(1/2), where T is the running time in days.

Magnetic and electric dipole moments of theH3Δ1state in ThO

The metastable $H\phantom{\rule{4pt}{0ex}}{}^{3}{\ensuremath{\Delta}}_{1}$ state in the thorium monoxide (ThO) molecule is highly sensitive to the presence of a $CP$-violating permanent electric dipole moment of the electron (eEDM) [E. R. Meyer and J. L. Bohn, Phys. Rev. A 78, 010502 (2008)]. The magnetic dipole moment ${\ensuremath{\mu}}_{H}$ and the molecule-fixed electric dipole moment ${D}_{H}$ of this state are measured in preparation for a search for the eEDM. The small magnetic moment ${\ensuremath{\mu}}_{H}=8.5(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{4pt}{0ex}}{\ensuremath{\mu}}_{B}$ displays the predicted cancellation of spin and orbital contributions in a ${}^{3}{\ensuremath{\Delta}}_{1}$ paramagnetic molecular state, providing a significant advantage for the suppression of magnetic field noise and related systematic effects in the eEDM search. In addition, the induced electric dipole moment is shown to be fully saturated in very modest electric fields (10 V/cm). This feature is favorable for the suppression of many other potential systematic errors in the ThO eEDM search experiment.