Nuclear Electric Quadrupole Moment Research Articles

Nuclear moments: recent developments

The author has for many years kept a watching brief on the experimental study of nuclear electro-magnetic moments. Accurate values of nuclear magnetic dipole and electric quadrupole moments are a major product and the life blood of hyperfine interaction studies and their manifold applications. This paper outlines recent changes in the type of moment measurements being undertaken and the effect of modern complex electronic configuration computation on the extracted moment values.

Reexamination of nuclear magnetic dipole and electric quadrupole moments of polonium isotopes

Reexamination of nuclear magnetic dipole and electric quadrupole moments of polonium isotopes

Measurements of binding energies and electromagnetic moments of silver isotopes – A complementary benchmark of density functional theory

We report on a set of high-precision measurements of nuclear binding and excitation energies, as well as nuclear spins, magnetic dipole and electric quadrupole moments of neutron-rich silver isotopes, 113−123Ag. The measurements were performed using the JYFLTRAP mass spectrometer and the collinear laser spectroscopy beamline at the Ion Guide Isotope Separator On-Line (IGISOL) facility. For the first time, we can firmly establish the ordering of the long-lived Iπ=1/2−,7/2+ states in these isotopes, and pin down the inversion of these two levels at either A=121(N=74) or A=123(N=76). We compare these findings to calculations performed with density functional theory (DFT), from which we establish the crucial role that the spin-orbit strength and time-odd mean fields play in the simultaneous description of electromagnetic moments and nuclear binding.

Variation of the Quadrupole Hyperfine Structure and Nuclear Radius due to an Interaction with Scalar and Axion Dark Matter.

Atomic spectroscopy is used to search for the space-time variation of fundamental constants which may be due to an interaction with scalar and pseudoscalar (axion) dark matter. In this Letter, we study the effects that are produced by the variation of the nuclear radius and electric quadrupole moment. The sensitivity of the electric quadrupole hyperfine structure to both the variation of the quark mass and the effects of dark matter exceeds that of the magnetic hyperfine structure by 1-2 orders of magnitude. Therefore, the measurement of the variation of the ratio of the electric quadrupole and magnetic dipole hyperfine constants is proposed. The sensitivity of the optical clock transitions in the Yb^{+} ion to the variation of the nuclear radius allows us to extract, from experimental data, limits on the variation of the hadron and quark masses, the QCD parameter θ and the interaction with axion dark matter.

Theoretical hyperfine splittings of Be2+7,9 ions for future studies of nuclear properties

The authors demonstrate that higher-order quantum-electrodynamic calculations improve the accuracy of theoretical hyperfine splittings for heliumlike beryllium by two orders of magnitude. The consequent sensitivity to the nuclear Zemach radius and electric quadrupole moment opens the way to measurements of these nuclear properties to an accuracy of 5% or better; thus providing a critical test of nuclear structure models, especially for the isotope ${}^{7}$Be.

Electric Quadrupole Moment of 7Li nucleus using Complex Generator Co-ordinate Technique

The electric quadrupole moment (EQM) of a nucleus is an important parameter used to determine the departure of the nucleus from its spherical shape. Besides the study of the nucleus, determination of the EQM value finds applications in solid state physics and in other areas such as chemical, medical and biological sciences. This paper focuses on a method developed for the calculation of nuclear structural properties of light nuclear systems which is used here to calculate the nuclear electric quadrupole moment for the ground state of 7lithium nucleus. In this approach the required anti-symmetrized nuclear wave function is constructed by using combination of shell model, cluster model, resonating group method, generator coordinate method, and the complex generator coordinate technique. The ground state of 7li nucleus is considered as a nuclear system consisting of one alpha cluster, one deuteron cluster and a neutron cluster. The wave function is written by taking internal spatial function, spin, and isospin functions where arguments of the internal function of clusters include the parameter coordinates and generator coordinates. The consideration of the parameters viz., total angular momentum, spin, and definite parity of the nucleus makes the approach inclusive. While the relative motion wave functions are taken into account between the alpha cluster and deuteron cluster and secondly between the alpha cluster and neutron cluster. The potential chosen in this approach is the Wood-Saxon potential which is somewhat between harmonic oscillator potential well and square well potential. By incorporating all the aforesaid inputs, a matrix of 7×7 order is constructed which leads to the calculation of EQM of 7lithium. The results compared with the available experimental and other theoretical data. The present value of EQM is found in good agreement with experimental data.

Global rovibrational fits for AlCl, BiCl, and BiF: Benchmarks for novel physics

Global fits combining existing rotational spectroscopy data for both chlorine isotopologues of AlCl and BiCl provide 2x/8x improved precision in hyperfine parameters like the nuclear electric quadrupole moment coupling terms (eQq) for use in novel physics applications, and include Born–Oppenheimer Breakdown (BOB) terms. The BiF fit combines existing data for a range of rotational transitions, providing an almost 3x more precise eQq benchmark for theoretical work on related molecules used in searches for the electric dipole moment of the electron (eEDM). Our AlCl nuclear electric quadrupole moment ratio Q(35Cl):Q(37Cl) of 1.26858(37) confirms many previous values, while enabling a more precise BiCl eQq value and informing reference work choices for nuclear physics Q-values for both Cl isotopes.

Ab initio calculations of the hyperfine structure of 109Cd, 109Cd+ and reevaluation of the nuclear quadrupole moment Q(109Cd)

Large scale ab initio calculations of the electric contribution (i.e. the electric field gradient (EFG)) to the electric quadrupole hyperfine interaction constants B for the state of 109Cd+ ion and the states of neutral 109Cd atom were performed. To probe the sensitivity of B to different electron correlation effects, six sets of variational multi-configuration Dirac–Hartree–Fock and relativistic configuration interaction calculations employing different strategies were carried out. The calculated EFGs, together with experimental values of B, allow us to extract a new value of the nuclear electric quadrupole moment Q(109Cd) = 0.634(22) b which is about 5% larger than the recommended value (Stone 2016 At. Data Nucl. Data Tables 111–112 1; Pyykkö 2018 Mol. Phys. 116 1328). Efforts were made to provide a realistic theoretical uncertainty for the final Q value based on statistical principles and correlation with the magnetic dipole hyperfine interaction constant A.

Nuclear DFT analysis of electromagnetic moments in odd near doubly magic nuclei

We use the nuclear density functional theory to determine nuclear electric quadrupole and magnetic dipole moments in all one-particle and one-hole neighbours of eight doubly magic nuclei. We align angular momenta along the intrinsic axial-symmetry axis with broken time-reversal symmetry, which allows us to explore fully the self-consistent charge, spin, and current polarisation. Spectroscopic moments are determined for symmetry-restored wave functions and compared with available experimental data. We find that the obtained polarisations do not call for using quadrupole- or dipole-moment operators with effective charges or effective g-factors.

A Nuclear Electric Quadrupole Moment Of 6Li Nucleus Using Hyperfine Structure In Atomic Spectra

The nuclear electric quadrupole moment (QM) is one of the most important bulk properties of the nucleus with which nuclear deformations can be investigated. In this paper the electric quadrupole moment for 6Li nucleus in the ground state is calculated from the hyperfine structure of atomic spectra. Initially a cluster model wavefunction is constructed in shell model using Resonating Group Method (RGM), Generate coordinate method (GCM) and Complex Generator Coordinate Technique (CGCT). CGCT transforms the cluster model wavefunction into antisymmetrized product of single particle wavefunction. The wavefunction is written with the total angular momentum, relative motion between alpha and deuteron clusters, definite parity and spin. The calculations have been made by taking Wood- Saxon potential. The results obtained are compared and found reasonably well in agreement with the experimental results.

A Review of Novel Instrumentation for Matrix Independent Ultratrace Analysis of Radionuclides using Collinear Resonance Ionisation Spectroscopy (CRIS)

The CRIS setup at CERN-ISOLDE is a high resolution laser spectroscopy experiment that is used to characterise exotic radionuclei with very low production rates. Acquisition of hyperfine spectra enable nuclear spins and precise values of nuclear magnetic dipole and electric quadrupole moments to be determined. The high sensitivity of the CRIS technique combined with the high selectivity make it an ideal candidate for quantitation of analytes in complex matrices. This review article reports on novel instrumentation under development at the University of Manchester, utilising the CRIS technique for targeted matrix independent ultra-trace analysis.

Precision Calculation of Hyperfine Constants for Extracting Nuclear Moments of ^{229}Th.

Determination of nuclear moments for many nuclei relies on the computation of hyperfine constants, with theoretical uncertainties directly affecting the resulting uncertainties of the nuclear moments. In this work, we improve the precision of such a method by including for the first time an iterative solution of equations for the core triple cluster amplitudes into the relativistic coupled-cluster method, with large-scale complete basis sets. We carried out calculations of the energies and magnetic dipole and electric quadrupole hyperfine structure constants for the low-lying states of ^{229}Th^{3+} in the framework of such a relativistic coupled-cluster single double triple method. We present a detailed study of various corrections to all calculated properties. Using the theory results and experimental data, we found the nuclear magnetic dipole and electric quadrupole moments to be μ=0.366(6)μ_{N} and Q=3.11(2) eb, respectively, and reduce the uncertainty of the quadrupole moment by a factor of 3. The Bohr-Weisskopf effect of the finite nuclear magnetization is investigated, with bounds placed on the deviation of the magnetization distribution from the uniform one.

Hyperfine and nuclear quadrupole splitting of the NV− ground state in 4H -SiC

Optically addressable spin-triplet defects in silicon carbide, such as divacancies and negatively charged nitrogen vacancy $({\mathrm{NV}}^{\ensuremath{-}})$ allow to develop modern quantum technologies operating in the near-infrared range based on the well-developed semiconductor material. Here, by means of both high-frequency (94 GHz) pulsed electron paramagnetic resonance (EPR) and electron-nuclear double Rresonance (ENDOR) techniques the ground state properties of the negatively charged ${\mathrm{NV}}^{\ensuremath{-}}$ defect in $4H$-SiC were studied. We experimentally determined the ordering of the ground state spin sublevels and established the sign of the zero-field splitting to be positive as predicted by theory. Analysis of nuclear magnetic resonance transitions in ENDOR spectra allowed to determine the sign, symmetry, and absolute values of the hyperfine interaction of the ${\mathrm{NV}}^{\ensuremath{-}}$ defect electron spin with $^{14}\mathrm{N}$ nuclear spin as ${\mathit{A}}_{\ensuremath{\parallel}}=\ensuremath{-}1.142\phantom{\rule{4pt}{0ex}}\mathrm{MHz}$ and ${\mathit{A}}_{\ensuremath{\perp}}=\ensuremath{-}1.184\phantom{\rule{4pt}{0ex}}\mathrm{MHz}$. The absolute value of the nuclear quadrupole interaction constant reflecting an interaction between the $^{14}\mathrm{N}$ nuclear electric quadrupole moment with the electric field gradient was determined to be $|{\mathit{C}}_{q}|=2.44\phantom{\rule{4pt}{0ex}}\mathrm{MHz}$. This large value is compatible with a threefold coordinated $^{14}\mathrm{N}$ nucleus with uniaxial symmetry and proves conclusively the existence of a nearestneighbor ${\mathrm{N}}_{\mathrm{C}}{\mathrm{V}}_{\mathrm{Si}}$ pair in the material. For this ${\mathrm{NV}}^{\ensuremath{-}}$ defect, an ensemble (Hahn-echo) coherence time of ${\mathit{T}}_{\text{2}}=49\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$ was measured, a value which is in the range previously reported for silicon vacancy spin ensembles and slightly longer than ${\mathit{T}}_{\text{2}}=40\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$ measured here on the divacancy spin ensemble.

Solid-state nuclear magnetic resonance of spin-9/2 nuclei 115 In and 209 Bi in functional inorganic complex oxides.

Indium and bismuth are technologically important elements, in particular as oxides for optoelectronic applications. 115 In and 209 Bi are both I = 9/2 nuclei with high natural abundances and moderately high frequencies but large nuclear electric quadrupole moments. Leveraging the quadrupolar interaction as a measure of local symmetry and polyhedral distortions for these nuclei could provide powerful insights on a range of applied materials. However, the absence of reported nuclear magnetic resonance (NMR) parameters on these nuclei, particularly in oxides, hinders their use by the broader materials community. In this contribution, solid-state 115 In and 209 Bi NMR of three recently discovered quaternary bismuth or indium oxides are reported, supported by density functional theory calculations, numerical simulations, diffraction and additional multinuclear (27 Al, 69,71 Ga, and 121 Sb) solid-state NMR measurements. The compounds LiIn2 SbO6 , BiAlTeO6 , and BiGaTeO6 are measured without special equipment at 9.4 T, demonstrating that wideline techniques such as the QCPMG pulse sequence and frequency-stepped acquisition can enable straightforward extraction of quadrupolar tensor information in I = 9/2 115 In and 209 Bi even in sites with large quadrupolar coupling constants. Relationships are described between the NMR observables and local site symmetry. These are amongst the first reports of the NMR parameters of 115 In, 121 Sb, and 209 Bi in oxides.

Microscopic study of shape evolution and some important ground state properties of 190–210Au isotopes

In this paper, we have examined the nuclear structural properties of 190–210Au isotopes within the framework of the Hartree–Fock–Bogoliubov Model. For the theoretical calculations, we have used the UNEDF2 and SKP interactions. The studies include the shape evolution, quadrupole deformation parameter [Formula: see text], nuclear electric quadrupole moment Q(b), single-particle energy levels, the binding energy per nucleon, nuclear charge radius, neutron rms radius, proton rms radius and neutron skin thickness. To analyze the accuracy of our theoretical results, we have presented the comparative analysis with experimental data and finite-range droplet model calculations. The adequate resemblance with experimental data is supporting our studies. We observe the oblate-prolate shape coexistence for 190Au, 193Au and 195Au using the UNEDF2 interaction.

Microscopic study of shape evolution and ground-state properties of Iodine isotopes

In this paper, we investigated the shape evolution and ground-state properties of 108−144I isotopes using Hartree–Fock-Bogoliubov Model while employing the axially deformed single-particle harmonic oscillator basis for the expansion of quasiparticle wave functions. We have used SKP and UNEDF2 models to perform the theoretical calculations. We have presented the shape evolution and final values of the quadrupole deformation parameter β 2 of iodine isotopes. We have used the final values of the β 2 for studying the ground-state properties of the iodine isotopic chain. The investigated ground-state properties are the nuclear electric quadrupole moment, single-particle energy levels, the binding energy per nucleon, pairing energy, one-neutron separation energy, two-neutron separation energy, nuclear charge radius, neutron rms radius, proton rms radius, and neutron skin thickness. After using the SKP parameterization on 109I, we have observed the shape coexistence of prolate and oblate shape. Similarly, after using the UNEDF2 parameterization on 110I, 112I, 114I, 115I, 116I, 117I, 118I, and 119I, we discover the shape coexistence of prolate and oblate shape.

Hyperfine structure study of Tc97,98,99 in a new laser ion source for high-resolution laser spectroscopy

Using a novel concept for efficient laser spectroscopy, we investigated the hyperfine splittings of three different atomic transitions in the long-lived isotopes $^{97\ensuremath{-}99}\mathrm{Tc}$. Despite the refractory character of the element technetium, sample sizes as low as ${10}^{11}$ atoms were sufficient to achieve excellent signal-to-noise ratios at a spectroscopic linewidth of less than 100 MHz. The obtained spectra were analyzed in detail, which results in a very good consistency for the extracted hyperfine parameters from the different transitions. The presented measurements provide the first hyperfine structure data for the isotopes $^{97,98}\mathrm{Tc}$ from which, in combination with the known nuclear moments of $^{99}\mathrm{Tc}$, their nuclear magnetic dipole and electric quadrupole moments were extracted. In addition, the experimental data confirm the predicted nuclear spin of $^{98}\mathrm{Tc}$ to $I=6$. In combination with atomic Multiconfiguration Dirac-Hartree-Fock calculations, the observed isotope shifts were investigated and the changes in mean-square charge radii were determined.

Theoretical analysis of the relativistic hyperfine interaction in 131Xe I

The relativistic hyperfine constants of the heavy inert gas element xenon-131 isotope have been calculated. The calculations, executed through the Multiconfiguration Dirac-Hartree-Fock method, yield the hyperfine constants of 128 levels belonging to the ns[K]J (n = 6, 7, 8, 9), nf [K]J (n = 4, 5, 6), nd[K]J (n = 5, 6, 7, 8), np[K]J (n = 6, 7, 8) and 5g[K]J intermediate Rydberg series. In order to draw further insights into the precision of our calculations and the accuracy of the obtained data, the resulting magnetic dipole and electric quadrupole hyperfine constants are analysed by comparing them with other experimental and theoretical results available in the atomic spectra database. Indeed, a satisfactory agreement is observed between our results and the other experimental and theoretical ones. Moreover, the absence of the hyperfine anomaly enables us to highlight the plausibility of our theoretical results through the calculation of the ratio A129A131 for a given state. The obtained values are found to be compatible with the ratio of nuclear moments of 129Xe and 131Xe isotopes. The consistency of these two different analyses confirms the accuracy of our data, on the one hand and classifies them as a reference in identifying the experimental spectrum in xenon, on the other hand. Based on this accuracy, the calculated values of the hyperfine constants for the levels under consideration, accompanied by the experimental values of the nuclear magnetic dipole and electric quadrupole moments, facilitated the calculation of the mean value of the magnetic as well as the electric field gradients produced by the electron at the tiny nucleus.

High-resolution laser resonance ionization spectroscopy of ^{143-147}Pm

We present the results of high-resolution laser spectroscopy of the long-lived radioactive isotopes ^{143-147}Pm. The hyperfine structures and isotope shifts in two different atomic ground-state transitions at 452 nm and 468 nm were probed by in-source laser spectroscopy at the RISIKO mass separator in Mainz, using the PI-LIST ion source. From the hyperfine coupling constants the nuclear magnetic dipole and electric quadrupole moments for ^{143-147}Pm were derived, and the measured isotope shifts allowed the extraction of changes in nuclear mean square charge radii.

Accurate nuclear quadrupole moment of ruthenium from the molecular method.

The nuclear electric quadrupole moment (NQM) of ruthenium was reevaluated by means of the molecular method. Therefore, four-component relativistic electronic structure calculations of the electric field gradient at the Ru nucleus in ruthenium monocarbide, which were done with the coupled cluster methodology and carefully augmented large basis sets, were combined with the respective nuclear quadrupole coupling constant from experiments. This provided a recommended NQM value of (425 ± 13) mbarn for 101Ru.