Nuclear Magnetic Dipole Moments Research Articles

Measurements of Nuclear Magnetic Shielding in Molecules.

The origin of nuclear magnetic shielding in diamagnetic molecules is discussed, pointing out various contributions to the shielding from electrons and the effects of intra- and intermolecular interactions. In NMR practice, chemical shifts are determined first as the measure of shielding in observed samples. The descriptions of shielding and chemical shifts are not fully consistent. Gas phase studies permit the withdrawal of intermolecular contributions from shielding and obtaining the magnetic shielding data in isolated molecules. The shielding determination in molecules is possible using at least three methods delivering the reference shielding standards for selected nuclei. The known shielding of one magnetic nucleus can be transferred to other nuclei if the appropriate nuclear magnetic moments are available with satisfactory accuracy. It is possible to determine the nuclear magnetic dipole moments using the most advanced ab initio shielding calculations jointly with the NMR frequencies measurements for small-sized isolated molecules. Helium-3 gas is postulated as all the molecules' primary and universal reference standard of shielding. It can be easily applied using common deuterium lock solvents as the secondary reference standards. The measurements of absolute shielding are available for everyone with the use of standard NMR spectrometers.

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

Calculation of the Differential Breit-Rosenthal Effect in Pb

Recent advancements in studying long chains of unstable nuclei have revitalised interest in investigating the hyperfine anomaly. Hyperfine anomaly is particularly relevant for determining nuclear magnetic dipole moments using hyperfine structures where it limits the accuracy. This research paper focuses on the calculation of the differential Breit-Rosenthal effect for the 6p23P1,2, 1D2 and 6p7s3P1 states in Pb, utilising the multi-configurational Dirac-Hartree-Fock code, GRASP2018. The findings show that the differential Breit-Rosenthal effect is typically less than 0.1/fm2, which is often much smaller than the Bohr-Weisskopf effect. The differential Breit-Rosenthal effect for the 6p23P2 state is one order of magnitude smaller than the rest, which is why this state seems to be insensible to the hyperfine anomaly.

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.

Accurate determination of 6,7Li nuclear magnetic moments

We report an accurate determination of the nuclear magnetic dipole moments of 6,7Li from the measured ratio of the nuclear and the electron g-factors in atomic Li. The obtained results significantly improve upon the literature values and stress the importance of reliable theoretical calculations of the nuclear shielding corrections.

Hyperfine-induced effects on the linear polarization of the magnetic-quadrupole lines of spin-1/2 Be-like ions excited by electron impact

The linear polarization of magnetic-quadrupole emission lines 1s22s2p3/23P2→1s22s21S0 and 1s2s22p3/23P2→1s22s21S0 following electron-impact excitation of Be-like ions with nuclear spin I=1/2 is studied by employing the density-matrix theory and the relativistic distorted-wave theory. To explore the effects of the hyperfine interaction, detailed calculations are performed for the polarization of the magnetic-quadrupole lines emitted from AXe50+ (A = 125, 127, and 129) and ATl77+ (A = 187, 205, and 207) ions with different nuclear magnetic dipole moments μI at a series of impact electron energies. It is shown that the hyperfine interaction strongly lowers the polarization of the 1s22s2p3/23P2→1S0 line at all considered impact energies, while its effects behave less and less prominent with increasing impact energy for the 1s2s22p3/23P2→1S0 line. In addition, we also find that the polarization of the 1s22s2p3/23P2→1S0 line is much more sensitive to μI than that of the 1s2s22p3/23P2→1S0 line. In particular, for the 1s22s2p3/23P2→1S0 line of spin-1/2 Xe50+ ions, the differences in the polarization among the isotopes are significant. These findings indicate that precise polarization measurements of magnetic-quadrupole lines of Be-like ions are expected to be used for exploring the hyperfine interaction and even the nuclear magnetic dipole moment of nonzero-spin isotopes.

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 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.

Hyperfine-induced effects on the Kα1 angular distribution following electron-impact excitation of heliumlike spin- 1/2 Tl79+ ions

Angular distribution of the $K{\ensuremath{\alpha}}_{1}$ $(1s2p\phantom{\rule{0.16em}{0ex}}^{1,3}P_{1,2}\ensuremath{\rightarrow}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0})$ emission line following electron-impact excitation of heliumlike spin-1/2 ${\mathrm{Tl}}^{79+}$ ions is studied within the framework of the density-matrix theory and the relativistic distorted-wave theory. In particular, we aim to explore how a (nonzero) nuclear magnetic dipole moment ${\ensuremath{\mu}}_{I}$ affects the $K{\ensuremath{\alpha}}_{1}$ angular distribution due to the hyperfine interactions. To this end, detailed calculations are performed for selected spin-1/2 $_{81}^{A}\mathrm{Tl}^{79+}$ ($A=187$, 205, and 207) ions with large ${\ensuremath{\mu}}_{I}$. It is found that the hyperfine-induced effects on the $K{\ensuremath{\alpha}}_{1}$ angular distribution depend strongly on the impact electron energy. When compared with the case of zero-spin ${\mathrm{Tl}}^{79+}$ ions, the $K{\ensuremath{\alpha}}_{1}$ angular distribution becomes much more anisotropic for low impact energies, whereas this anisotropy decreases quickly at intermediate and high impact energies. Such a behavior is in sharp contrast to the results for the fine-structure-resolved $1s2p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}\ensuremath{\rightarrow}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ component [Phys. Rev. A 102, 042813 (2020)]. Therefore, accurate $K{\ensuremath{\alpha}}_{1}$ angular measurements at low impact electron energies could be employed as a sensitive tool to probe the hyperfine interaction in highly charged few-electron ions.

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.

$$^1$$H, $$^2$$H and $$^3$$H nuclear magnetic dipole moment effects on the electron energy states

$$^1$$H, $$^2$$H and $$^3$$H nuclear magnetic dipole moment effects on the electron energy states

Proton-neutron pairing correlations in the self-conjugate nucleus 42Sc

Collinear laser spectroscopy of the N=Z=21 self-conjugate nucleus 42Sc has been performed at the JYFL IGISOL IV facility in order to determine the change in nuclear mean-square charge radius between the Iπ=0+ ground state and the Iπ=7+ isomer via the measurement of the 42g,42mSc isomer shift. New multi-configurational Dirac-Fock calculations for the atomic mass shift and field shift factors have enabled a recalibration of the charge radii of the 42−46Sc isotopes which were measured previously. While consistent with the treatment of proton-neutron, proton-proton and neutron-neutron pairing on an equal footing, the reduction in size for the isomer is observed to be of a significantly larger magnitude than that expected from both shell-model and ab-initio calculations. The measured nuclear magnetic dipole moment and electric quadruple moment, on the other hand, are in good agreement with simple empirical estimates and shell-model calculations.

Calculation of the Differential Breit–Rosenthal Effect in the 6s6p 3P1,2 States of Hg

Studies of the hyperfine anomaly has found a renewed interest with the recent development of techniques to study the properties of long chains of unstable nuclei. By using the hyperfine structure for determining the nuclear magnetic dipole moments, the hyperfine anomaly puts a limit to the accuracy. In this paper, the differential Breit–Rosenthal effect is calculated for the 6s6p3P1,2 states in 199Hg as a function of the change in nuclear radii, using the MCDHF code, GRASP2018. The differential Breit–Rosenthal effect was found to be of the order of 0.1%fm−2, in most cases much less than the Bohr-Weisskopf effect. The results also indicate that large calculations might not be necessary, with the present accuracy of the experimental values for the hyperfine anomaly.

Hyperfine-induced effects on angular emission of the magnetic-quadrupole line 1s2p3/2 P23→1s2 S01 following electron-impact excitation of Tl79+ ions

The electron-impact excitation from the ground state to the excited $1s2{p}_{3/2}$ $^{3}P_{2}$ energy level and the subsequent magnetic-quadrupole radiative decay $1s2{p}_{3/2}\phantom{\rule{0.16em}{0ex}}^{3}P_{2}\ensuremath{\rightarrow}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ of heliumlike ${\mathrm{Tl}}^{79+}$ ions with nuclear spin $I=1/2$ have been investigated by employing the multiconfigurational Dirac-Fock method and the relativistic distorted-wave theory. Special attention has been paid to the effects of the hyperfine interaction on the angular distribution of the emitted magnetic-quadrupole line. To this end, we considered heliumlike spin-1/2 $_{81}^{187}\mathrm{Tl}^{79+}$, $_{81}^{205}\mathrm{Tl}^{79+}$, and $_{81}^{207}\mathrm{Tl}^{79+}$ ions with rather large nuclear magnetic dipole moment ${\ensuremath{\mu}}_{I}$. It is found that the hyperfine interaction lowers significantly the anisotropy of the angular distribution of the magnetic-quadrupole line emitted from these spin-1/2 ions for all considered impact electron energies, compared with the results for ${\mathrm{Tl}}^{79+}$ ions with zero nuclear spin. In particular, the angular distribution becomes first less and less anisotropic as the impact energy increases up to about 4.4 times the excitation threshold, for which it becomes fully isotropic. For even higher impact energies, the angular distribution becomes again anisotropic, although with inverse emission pattern. We also find that the angular distribution is quite sensitive to the magnetic moment ${\ensuremath{\mu}}_{I}$ with a more isotropic distribution for spin-1/2 ions with larger ${\ensuremath{\mu}}_{I}$. This ${\ensuremath{\mu}}_{I}$ sensitivity of the angular distribution may therefore (help) probe important information about the nuclear magnetic dipole moment of spin-1/2 isotopes.

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.

NMR Spin-Spin Coupling Constants Derived from Relativistic Four-Component DFT Theory-Analysis and Visualization.

An unambiguous assignment of coupling pathways plays an important role in the description and rationalization of NMR indirect spin-spin coupling constants (SSCCs). Unfortunately, the SSCC analysis and visualization tools currently available to quantum chemists are restricted to nonrelativistic theory. Here, we present the theoretical foundation for novel relativistic SSCC visualization techniques based on analysis of the SSCC densities and the first-order current densities induced by the nuclear magnetic dipole moments. Details of the implementation of these techniques in the ReSpect program package are discussed. Numerical assessments are performed on through-space SSCCs, and we choose as our examples the heavy-atom Se-Se, Se-Te, and Te-Te coupling constants in three similar molecules for which experimental data are available. SSCCs were calculated at the nonrelativistic, scalar relativistic, and four-component relativistic density functional levels of theory. Furthermore, with the aid of different visualization methods, we discuss the interpretation of the relativistic effects, which are sizable for Se-Se, very significant for Se-Te, and cannot be neglected for Te-Te couplings. A substantial improvement of the theoretical SSCC values is obtained by also considering the molecular properties of a second conformation.

NMR shielding in helium-3 atoms modified by gaseous nitrogen and oxygen.

Helium-3 nuclear magnetic resonance (3 He NMR) measurements were carried out for the gaseous mixtures of helium-3 with pure nitrogen and synthetic air as the solvents. It was found that 3 He shielding is linearly dependent on solvent density up to approx. 6 mol/L. At higher density of the gaseous solvent, the change of 3 He shielding is nonlinear and especially distinct when helium-3 atoms can interact with two O2 molecules. The interaction with paramagnetic oxygen molecules can induce two kinds of 3 He shielding changes: (1) due to the isotropic Fermi contact interaction and (2) from the dipolar magnetic interaction between unpaired O2 electrons and 3 He nuclear magnetic dipole moment. The two paramagnetic effects in helium-3 shielding cannot be experimentally separated, although for such small molecular objects, they could be presumably modeled by advanced theoretical calculations.

Gas-phase 21 Ne NMR studies and the nuclear magnetic dipole moment of neon-21.

Gas-phase 21 Ne nuclear magnetic resonance spectra were measured at the natural abundance of 21 Ne isotope for samples consisting of pressurized neon up to 60 bar at room temperature and applying the magnetic field of the strength B0 = 11.7574 T. It showed that the nuclear magnetic resonance frequency is linearly dependent on the density of gaseous neon. The resonance frequency was extrapolated to the zero-density point, and it permitted the determination of the 21 Ne nuclear magnetic moment, μ(21 Ne) = 0.6617774(10) μN . The present value of μ(21 Ne) is not influenced by the bulk magnetic susceptibility of neon and interactions between neon atoms; therefore, it is more precise and reliable than the previous result obtained for μ(21 Ne).