Which oxidation state of uranium and thorium as point defects in xenotime is favorable?

Relativistic study of xenotime, YPO$_4$, containing atoms thorium and uranium as point defects is performed in the framework of cluster model with using the compound-tunable embedding potential (CTEP) method proposed by us recently. The Y-(PO$_4$)$_6$-Y'$_{22}$-O'$_{104}$ cluster for xenotime is considered, in which central part, [Y-(PO$_4$)$_6$]$^{-15}$, is the main cluster, whereas outermost 22 atoms of yttrium and 104 atoms of oxygen are treated as its environment and compose electron-free CTEP with the total charge of $+15$. The P and O atoms of the orthophosphate groups nearest to the central Y atom are treated at all-electron level. The central Y, its substitutes, Th and U, together with environmental Y atoms are described within different versions of the generalized relativistic pseudopotential method. Correctness of our cluster and CTEP models, constructed in the paper, is justified by comparing the Y-O and P-O bond lengths with corresponding periodic structure values of the \ypo4 crystal, both experimental and theoretical. Using this cluster model, chemical properties of solitary point defects, X = U, Th, in xenotime are analyzed. It has been shown that the oxidation state ${+3}$ is energetically more profitable than ${+4}$ not only for thorium but for uranium as well ($\Delta E \approx 5$ eV) despite the notably higher ionic radius of U$^{+3}$ compared to Y$^{+3}$, whereas ionic radii of U$^{+4}$ and Y$^{+3}$ are close. This leads to notable local deformation of crystal geometry around the U$^{+3}$ impurity in xenotime and contradicts to widespread opinion about favorite oxidation state of uranium in such kind of minerals.Comment: 8 pages, 4 figures, 3 table

Compound-tunable embedding potential method to model local electronic excitations on ff-element ions in solids: Pilot relativistic coupled cluster study of Ce and Th impurities in yttrium orthophosphate, YPO4_4

A method to simulate local properties and processes in crystals with impurities via constructing cluster models within the frame of the compound-tunable embedding potential (CTEP) and highly-accurate {\it ab initio} relativistic molecular-type electronic structure calculations is developed and applied to the Ce and Th-doped yttrium orthophosphate crystals, YPO$_4$, having xenotime structure. Two embedded cluster models are considered, the "minimal" one, YO$_8$@CTEP$_{\rm min}$, consisting of the central Y$^{3+}$ cation and its first coordination sphere of eight O$^{2-}$ anions (i.~e.\ with broken P--O bonds), and its extended counterpart, Y(PO$_4$)$_6$@CTEP$_{\rm ext}$, implying the full treatment of all atoms of the PO$_4^{3-}$ anions nearest to the central Y$^{3+}$ cation. CTEP$_{\rm min,ext}$ denote here the corresponding cluster environment described within the CTEP method. The relativistic Fock-space coupled cluster (FS RCC) theory is applied to the minimal cluster model to study electronic excitations localized on Ce$^{3+}$ and Th$^{3+}$ impurity ions. Calculated transition energies for the cerium-doped xenotime are in a good agreement with the available experimental data (mean absolute deviation of ca.0.3 eV for $4f{\to}5d$ type transitions). For the thorium-doped crystal the picture of electronic states is predicted to be quite complicated, the ground state is expected to be of the $6d$ character. The uncertainty for the excitation energies of thorium-doped xenotime is estimated to be within 0.35 eV. Radiative lifetimes of excited states are calculated at the FS RCC level for both doped crystals. The calculated lifetime of the lowest $5d$ state of Ce$^{3+}$ differs from the experimentally measured one by no more than twice

Broadband velocity modulation spectroscopy of HfF^+: towards a measurement of the electron electric dipole moment

Precision spectroscopy of trapped HfF^+ will be used in a search for the permanent electric dipole moment of the electron (eEDM). While this dipole moment has yet to be observed, various extensions to the standard model of particle physics (such as supersymmetry) predict values that are close to the current limit. We present extensive survey spectroscopy of 19 bands covering nearly 5000 cm^(-1) using both frequency-comb and single-frequency laser velocity-modulation spectroscopy. We obtain high-precision rovibrational constants for eight electronic states including those that will be necessary for state preparation and readout in an actual eEDM experiment.Comment: 13 pages, 7 figures, 3 table

Electric dipole moments and the search for new physics

Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires complementary searches in atomic-molecular-and-optical, nuclear and particle physics. In this report, we discuss the current status and prospects in the near future for a compelling suite of such experiments, along with developments needed in the encompassing theoretical framework.Comment: Contribution to Snowmass 2021; updated with community edits and endorsement

Review of solar energetic particle models

Solar Energetic Particle (SEP) events are interesting from a scientific perspective as they are the product of a broad set of physical processes from the corona out through the extent of the heliosphere, and provide insight into processes of particle acceleration and transport that are widely applicable in astrophysics. From the operations perspective, SEP events pose a radiation hazard for aviation, electronics in space, and human space exploration, in particular for missions outside of the Earth’s protective magnetosphere including to the Moon and Mars. Thus, it is critical to improve the scientific understanding of SEP events and use this understanding to develop and improve SEP forecasting capabilities to support operations. Many SEP models exist or are in development using a wide variety of approaches and with differing goals. These include computationally intensive physics-based models, fast and light empirical models, machine learning-based models, and mixed-model approaches. The aim of this paper is to summarize all of the SEP models currently developed in the scientific community, including a description of model approach, inputs and outputs, free parameters, and any published validations or comparisons with data.</p

Revisited T\mathcal{T}, P\mathcal{P}-odd spin-rotational Hamiltonian of HfF+^+ for precise eeEDM measurements

The current constraint on the electron electric dipole moment ($e$EDM), $|d_e|<4.1\times 10^{-30}$ ${e {\cdotp} {\rm cm}}$ (90\% confidence), was recently established using the trapped $^{180}$Hf$^{19}$F$^+$ molecular ions in the $J=1$ rotational level of its $^3\Delta_1$ electronic state [T. S. Roussy, L. Caldwell, T. Wright, et al., arxiv:2212.11841]. The extensive experimental study of the HfF$^+$ cation provides detailed spectroscopy of the $\Omega-$doublet levels in the external rotating electric and magnetic fields. We showed that previously developed theoretical approaches can fully reproduce the latest experimental data. Their justification from the first principles is very important for the examination of both modern molecular theory and possible systematic uncertainties in the interpretation of the experimental data obtained with high accuracy

THE MOLECULAR FRAME ELECTRIC DIPOLE MOMENT AND HYPERFINE INTERACTIONS IN HAFNIUM FLUORIDE, HfF

Author Institution: Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287; Petersburg Nuclear Physics Institute, Gatchina, 188300, Russia and Quantum Mechanics Division, St. Petersburg State University, St. Petersburg 198904, RussiaThe identification of HfF$^{+}$ as a possible candidate for a \textit{d}_{e}} measurement has stimulated new interest in the spectroscopy of both HfF$^{+}$ , \textbf{134}, 201102 (2011).}$^{,}$ , \textbf{546}, 1 (2012).}$^{,}$ , \textbf{272}, 32 (2012).} and neutral HfF $^{a,}$ ,\textbf{276-277}, 49 (2012).}. Studies of the neutral are relevant because photoionization schemes can be used to produce the cations. More importantly, computational methodologies used to predict the electronic wavefunction of HfF$^{+}$ can be effectively assessed by making a comparison of predicted and experimental properties of the neutral, which are more readily determinable. The (1,0)[17.9]2.5 -$\textit{X}^{2}\Delta_{3/2}$ band of hafnium monofluoride (HfF) has been recorded using high-resolution laser-induced fluorescence spectroscopy both field-free and in the presence of a static electric field. The field-free spectra of $^{177}$HfF, $^{179}$HfF, and $^{180}$HfF were model to generate a set of fine and hyperfine parameters for the $\textit{X}^{2}\Delta_{3/2}$ (v=0) and [17.9]2.5 (v=1) states. The observed optical Stark shifts for the $^{180}$HfF isotopologue were analyzed to produce the molecular frame electric dipole moments of 1.66(1)D and 0.419(7)D for the $\textit{X}^{2}\Delta_{3/2}$ and [17.9]2.5 states, respectively. A two-step $\textit{ab initio}$ calculation consisting of a two-component generalized relativistic effective core potential calculation (GRECP) followed by a restoration of the proper four-component wavefunction was performed to predict the properties of ground state HfF