Hyperfine Structure Constants Research Articles

Nuclear parity- and time-reversal-symmetry violation in the HgH201 molecule

Investigation of the nuclear magnetic quadrupole moment (MQM) is an excellent way to reveal the new physics in the hadron sector of matter. Therefore, we investigate the violation of parity ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) invariance induced by the MQM of the $^{201}\mathrm{Hg}$ nucleus in the HgH molecule, which has been proposed as a very promising candidate for the experimental search of the electric dipole moment of electron [M. G. Kozlov and A. Derevianko, Phys. Rev. Lett. 97, 063001 (2006)]. We report the precise value of the molecular parameter, ${W}_{\text{M}}$, associated with the $\mathcal{P},\mathcal{T}$-odd nuclear MQM-electron interaction in $^{201}\mathrm{HgH}$ using the four-component relativistic coupled-cluster method. This parameter is required to interpret the experimental $\mathcal{P},\mathcal{T}$-odd frequency shift in terms of the MQM of nuclei. Furthermore, the magnetic hyperfine structure (HFS) constants of the molecule are computed at the same level of theory. We also study the role of core-correlating functions and the virtual energy functions in the calculations of the HFS constant and ${W}_{\text{M}}$. The most reliable value of ${W}_{\text{M}}$ in HgH is obtained as $3.22\ifmmode\times\else\texttimes\fi{}{10}^{33}$ Hz/$e$ ${\mathrm{cm}}^{2}$ with an uncertainty of around 6%.

Relativistic coupled-cluster investigation of parity (P) and time-reversal (T ) symmetry violations in HgF.

We employ the Z-vector method in the four-component relativistic coupled-cluster framework to calculate the parity (P) and time-reversal (T ) symmetry violating scalar-pseudoscalar nucleus-electron interaction constant (Ws), the effective electric field (Eeff) experienced by the unpaired electron, and the nuclear magnetic quadrupole moment-electron interaction constant (WM) in the open-shell ground electronic state of HgF. The molecular frame dipole moment and the magnetic hyperfine structure (HFS) constant of the molecule are also calculated at the same level of theory. The outcome of our study is that HgF has a high value of Eeff (115.9 GV/cm), Ws (266.4 kHz), and WM (3.59 × 1033 Hz/e cm2), which shows that it can be a possible candidate for the search of new physics beyond the standard model. Our results are in good agreement with the available literature values. Furthermore, we investigate the effect of the basis set and the virtual energy functions on the computed properties. The role of the high-energy virtual spinors is found to be significant in the calculation of the HFS constant and the P,T-odd interaction coefficients.

Investigating ground-state fine-structure properties to explore suitability of boronlike S11+−K14+ and galliumlike Nb10+−Ru13+ ions as possible atomic clocks

We study various properties of the $2p\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2}\ensuremath{-}2p\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2}$ fine-structure splittings in the boronlike ${\mathrm{S}}^{11+}, {\mathrm{Cl}}^{12+}, {\mathrm{Ar}}^{13+}$, and ${\mathrm{K}}^{14+}$ ions and the $4p\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2}\ensuremath{-}4p\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2}$ fine-structure splittings in the galliumlike ${\mathrm{Nb}}^{10+}, {\mathrm{Mo}}^{11+}, {\mathrm{Tc}}^{12+}$, and ${\mathrm{Ru}}^{13+}$ ions to find out the feasibility of using these highly charged ions as suitable optical atomic clocks. The roles of the electron correlations due to the Dirac-Coulomb-Breit Hamiltonian and accounting for lower-order quantum electrodynamics effects are shown explicitly in the calculations of electron affinities, excitation energies, transition-matrix elements, lifetimes, hyperfine-structure constants, and electric quadrupole moments of the states involved with clock transitions using a relativistic couple-cluster method. We also estimate the most commonly appearing systematic effects in the atomic clock experiments due to the electric quadrupole, the second-order Zeeman, both the dc and ac Stark, and the black-body radiation shifts in the aforementioned fine-structure splittings to demonstrate typical orders of magnitude of fractional frequency shifts.

Spectroscopy of the S01−D21 clock transition in Lu+176

High precision spectroscopy of the $^1S_0$-to-${^1}D_2$ clock transition of $^{176}$Lu is reported. Measurements are performed with Hertz level precision with the accuracy of the hyperfine-averaged frequency limited by the calibration of an active hydrogen maser to the SI definition of the second via a GPS link. The measurements also provide accurate determination of the $^1D_2$ hyperfine structure. Hyperfine structure constants associated with the magnetic octupole and electric hexadecapole moments of the nucleus are considered, which includes a derivation of correction terms from third-order perturbation theory.

Ab initio studies of electron correlation effects in magnetic dipolar hyperfine interaction of Cs

The hyperfine-structure constant A of the S, P, and D states in Cs atom with the principal quantum number are calculated using the Dirac–Fock approximation, the low-order many-body perturbation theory, and relativistic coupled-cluster method in single and double approximations with and without the inclusion of nonlinear terms. The importance of electron correlation effects, especially the nonlinear corrections of the cluster operators, is demonstrated by comparing the results of various approximations with available experimental values. Moreover, the correlation trends for individual electron correlation effects involving direct, core-polarization, and pair-correlation ones in members of Rydberg series are also investigated in the framework of the coupled-cluster theory. Some interesting features are observed.

Theoretical studies of the EPR parameters and local structure for the trigonal Yb3+ center in YAl3(BO3)4 crystal

Yttrium aluminium borate crystals have excellent physical and chemical properties. In this paper, the electron paramagnetic resonance (EPR) g factors g//, g^ of Yb3+ and hyperfine structure constants A//, A^ of 171Yb3+ and 173Yb3+ isotopes in YAl3(BO3)4 crystal are calculated from the perturbation formulas. The crystal field parameters are obtained from the superposition model and the crystal structure data. The EPR parameters for trigonal Yb3+ centers in YAl3(BO3)4 are reasonably explained by considering the defect structures of doped Yb3+ centers. In the calculation, we also find that Yb3+ ion does not exactly reside in Y3+ site, but suffers an angle distortion Dq (≈ 3.98 Å) with C3 axis. The results are discussed.

Theoretical studies of the defect structures and spin Hamiltonian parameters for manganese(II) and nickel(II) doped Zn(en)3(NO3)2 single crystals

ABSTRACTThe spin Hamiltonian parameters (g factors, hyperfine structure constants and zero-field splittings D and E) and local structures for Mn2+ and Ni2+ in [Zn(en)3](NO3)2 single crystal are theoretically investigated from the perturbation calculations for trigonally distorted 3d5 and trigonally (or orthorhombically) distorted 3d8 cluster. The trigonal Mn2+ and Ni2+ centres are found to undergo the moderate angular variations Δβ of 4.5° and 5.2°, respectively, related to host Zn2+ site due to size mismatch. The orthorhombic Ni2+ centre shows the relative axial elongation ratio ρ (≈ 2.5%) and the relative perpendicular bond length variation ratio τ (≈0.2%). For Mn2+ centre, the contributions to g-shifts ΔgCT (or hyperfine structure constants ACT and zero-field splitting DCT) from charge-transfer (CT) mechanism are opposite in sign and five times (or 5% and 8%) in magnitude compared with those from crystal-field (CF) mechanism. For the trigonal Ni2+ centre, ΔgCT (or DCT) are the same (or opposite) in sign and 17% (or 2%) in magnitude related to those from CF mechanism. For the orthorhombic Ni2+ centre, ΔgCT and ECT (or DCT) are same (or opposite) in sign and 16% and 48% (or 442%) in magnitude with respect to those from the CF mechanism. The signs and magnitudes of the trigonal distortion angles δβ (≈ −0.3 and 0.4°) related to an ideal octahedron and the local angular variations Δβ related to the host bond angle are suitably illustrated by those of the axial distortion degree (ADD) and the angular variation degree (AVD) of the systems, respectively.

Revised energy levels and hyperfine structure constants of Ta I

A wave number calibrated Fourier transform spectrum, extending from the UV-region (211 nm) to the infrared region (4.6 µm), was used to determine with high accuracy the center of gravity wave numbers of hyperfine structure - resolved Ta I spectral lines. The majority of the hyperfine constants, necessary for this step, were known from literature. For some energy levels, the constants were determined in this work. From the obtained wave numbers of altogether 3249 spectral lines, we calculated in a global fit procedure the energies of 216 levels with even parity and 290 levels with odd parity. A comparison between our results and (partially unpublished) energy values from the literature is given, as well as a compilation of available hyperfine structure constants.

Studies on EPR Parameters and Local Structures for the Rhombic Cu2+ Center in the ZnGeO4 · 6H2O Crystal

The electron paramagnetic resonance (EPR) parameters (g factors and hyperfine structure constants) and local structures for the impurity Cu2+ center in ZnGeO4 · 6H2O crystal are theoretically studied using the perturbation formulas of these parameters for a 3d9 ion in rhombically elongated octahedra. These formulas are based on a two-spin-orbit-parameter model in which the contributions to the EPR parameters due to both the spin-orbit parameter of the central 3dn ion and that of ligand ion are included. Based on the calculation, the relative axial elongation ratio ρ (≈7.3%) along z-axis and the relative planar bond length variation τ (≈4.3%) along x- and y-axes are found for [Cu(H2O)6]2+ cluster in ZnGeO4 · 6H2O crystal. The above local rhombic distortions of the Jahn–Teller nature around Cu2+ can suitably account for the axial and perpendicular anisotropies of the observed EPR parameters.

Nobelium energy levels and hyperfine-structure constants

Advances in laser spectroscopy of superheavy ($Z>100$) elements enabled determination of the nuclear moments of the heaviest nuclei, which requires high-precision atomic calculations of the relevant hyperfine structure (HFS) constants. Here, we calculated the HFS constants and energy levels for a number of nobelium (Z=102) states using the hybrid approach, combining linearized coupled-cluster and configuration interaction methods. We also carried out an extensive study of the No energies using 16-electron configuration interaction method to determine the position of the (5f^{13}7s^2 6d) and (5f^{13}7s^2 7p) levels with a hole in the 5f shell to evaluate their potential effect on the hyperfine structure calculations of the low-lying (5f^{14}7s6d) and (5f^{14}7s7p) levels. We find that unlike the case of Yb, the mixing of the low-lying levels with filled and unfilled f shell is small and does not significantly influence their properties. The resulting HFS constants for the 5f^{14}7s7p 1P1 level, combined with laser-spectroscopy measurement, were used to extract nobelium nuclear properties [S. Raeder et al., Phys. Rev. Lett. 120, 232503 (2018)]

Investigations of the electron paramagnetic resonance parameters and defect structures for Cu2+ ions in BeO crystal with trigonally distorted tetrahedral symmetry

Abstract The electron paramagnetic resonance(EPR) parameters (g factors gi and hyperfine structure constants Ai, where i = x, z) for Cu2+ ions embedded in beryllium oxide (BeO) crystal at Be2+ sites with C3v local symmetry have been calculated by the complete diagonalization method (CDM) and high-order perturbation theory method (PTM). The calculated results from the two methods are in reasonable agreement with the observed data available. The defect structural data of the trigonal Cu2+ center in beryllium oxide are determined from the calculations and analyses. The calculated results show that the Be2+ ions are replaced by Cu2+ ions in BeO crystal and the ligands undergo outward movement.

Spin-Hamiltonian parameters and tetragonal distortion for the (WO6)7− octahedral centers in the WO3-doped Zn(PO4)2 ZnO nanopowders

The spin-Hamiltonian parameters (g factors g//, g⊥ and hyperfine structure constants A//, A⊥) of the tetragonal (WO6)7− octahedral center in the WO3-doped Zn(PO4)2ZnO nanopowders are investigated from the high-order perturbation formulas resting on the two-mechanism (crystal-field and charge-transfer mechanisms) model with a suitable assignment of the absorption band at about 14,370 cm−1. The calculated results are in keeping with the experimental values. The tetragonal distortion of the (WO6)7− octahedral center is also achieved on the basis of the calculation. The outcomes are discussed.

Hyperfine Anomalies in Gd and Nd

The hyperfine anomalies in Gd and Nd have been extracted from experimental hyperfine structure constants. In addition to the values of the hyperfine anomaly, new improved values of the nuclear magnetic dipole moment ratios are derived.

Theoretical studies of the Spin Hamiltonian parameters and local structures for Cu2+ centers in MNB ternary glasses

ABSTRACTThe spin Hamiltonian parameters (g factors g|| and g⊥ and the hyperfine structure constants A|| and A⊥) for the doped Cu2+ ion (in the form of CuO) in ternary glasses (i.e. xMgO·(30-x)Na2O·69B2O3·CuO, with 5 < x < 17 mol%) are theoretically investigated based on the high-order perturbation formulas for a tetragonally elongated octahedral 3d9 complex. In these formulas, the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the spin Hamiltonian parameters with the tetragonal distortion (characterized by relative tetragonal elongation δ along the C4 axis due to the Jahn–Teller effect) of [CuO6]10− cluster. The concentration dependences of the spin Hamiltonian parameters are illustrated by the approximately linear increases of the cubic field parameter Dq and the covalency factor N as well as the relative elongation δ with increasing the MgO concentration x. Based on the calculation, the [CuO6]10− clusters in the MNB glasses are found to suffer the relative elongations of about δ (≈ 0.125 Å) along the tetragonal axis due to the Jahn–Teller effect. The theoretical results show good agreement with the experimental data. And the improvement is also achieved in present work with respect to the previous theoretical analysis based on the conventional crystal-field model formulas by including the ligand orbital and spin–orbit coupling contributions.

Correlation trends in the magnetic hyperfine structure of atoms: A relativistic coupled-cluster case study

The role of electron correlation in the hyperfine structure of alkali metals and alkaline earth metal monopositive ions in their ground electronic configuration is investigated using the Z-vector method in a relativistic coupled-cluster regime within the singles and doubles approximation. The systematic effects of core-correlating functions, polarization of core electrons, and high-lying virtual functions on core electrons correlation are studied. The study reveals that the core-correlating function plays a significant role in core polarization and thus is very important for precise calculation of the wave function near the nuclear region. The inner-core electrons (1s-2p) require very high virtual energy functions for proper correlation. Therefore, the all-electron correlation treatment and the inclusion of higher-energy virtual functions are the key factors for precise calculation of the hyperfine structure constant of atoms. Our calculated values are in excellent agreement with the available experimental values, which also implies that the wave function produced by the Z-vector method is accurate enough for further calculation of the parity- and time-reversal symmetry-violating properties in atoms and molecules.

Identification of new electronic levels in the holmium atom and investigation of their hyperfine structure

In this work the hyperfine structure of some tens of unclassified spectral lines in the holmium atom was investigated with the method of laser induced fluorescence in a hollow cathode discharge lamp. As a result, 21 new electronic odd-parity levels, with previously unknown energies within the range 33000–42000 cm−1, were identified and their hyperfine structure constants A and B were determined. The experimental data obtained will facilitate the semi-empirical fit of the fine and hyperfine structure of the odd-parity level system for the atomic holmium, currently in progress in our group.

Hyperfine structure measurements of neutral vanadium by inter-modulated laser-induced fluorescence spectroscopy in the wavelength range from 800 nm to 830 nm

The hyperfine structure of eight spectral lines of neutral vanadium is investigated by Doppler-reduced inter-modulated laser-induced fluorescence spectroscopy using a Ti-Sa laser in the wavelength range from 800 nm to 830 nm. The spectra are compared with previous measurements with Doppler-limited laser-induced fluorescence spectroscopy. Improved and revised magnetic dipole hyperfine structure constants A are presented for five levels as well as new electric quadrupole hyperfine structure constants B for two levels.

Calculation of Francium Hyperfine Anomaly

The Dirac–Hartree–Fock plus many-body perturbation theory (DHF + MBPT) method has been used to calculate hyperfine structure constants for Fr. Calculated hyperfine structure anomaly for hydrogen-like ion is in good agreement with analytical expressions. It has been shown that the ratio of the anomalies for s and p1/2 states is weakly dependent on the principal quantum number. Finally, we estimate Bohr–Weisskopf corrections for several Fr isotopes. Our results may be used to improve experimental accuracy for the nuclear g factors of short-lived isotopes.

Hyperfine structure investigations in atomic iodine

Experimental results of the hyperfine structure (hfs) constants of levels of the iodine atom are reported. The absorption spectra of 50 transitions in the near infrared spectral region were observed using concentration modulation technique with a tunable single-mode cw Ti:Sapphire laser. Magnetic dipole hfs constants A and electric quadrupole hfs constants B for 54 levels were determined, out of which for 10 levels were examined for the first time, the constants were confirmed for 44 levels.

Ab initio calculations of the hyperfine structure of zinc and evaluation of the nuclear quadrupole moment Q(Zn67)

The relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) and the non-relativistic multiconfiguration Hartree-Fock (MCHF) methods have been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants of zinc. The calculated electric field gradients for the $ 4s 4p \,\, ^3 \! P^o_{1} $ and $ 4s 4p \,\, ^3 \! P^o_{2} $ states, together with experimental values of the electric quadrupole hyperfine structure constants, made it possible to extract a nuclear electric quadrupole moment $ Q(^{67}{\rm Zn}) = 0.122(10) $ b. The error bar has been evaluated in a quasi-statistical approach - the calculations had been carried out with eleven different methods, and then the error bar has been estimated from the differences between the results obtained with those methods.