Nuclear Magnetic Quadrupole Moment Research Articles

Faraday rotation method improves the upper limit of the electron electric-dipole-moment sensitivity.

The electron electric-dipole-moment (eEDM) is a powerful tool for exploring new particles. The candidates for eEDM search are heavy atoms and their molecules, which are well known for the obvious relativistic effect. Lead atom is considered to be the most ideal relativistic atom [Park et al., Nat. Commun. 11(1), 815 (2020)]. PbH molecule is an important representative of the Pb compound and is considered a cold candidate molecule due to the high diagonal Franck-Condon factors. We systematically investigated the (eEDM) searches of PbH using a two-component approach. The parity- and time-reversal symmetry violation constants of ground and excited states, including internal effective electric field Eeff, electron-nucleon scalar-pseudoscalar interaction constant WP,T, and nuclear magnetic quadrupole moment, were obtained and compared to other molecules. In addition, we designed two experimental methods to measure the sensitivity of the eEDM, indicating that the Faraday rotation method could greatly improve its sensitivity.

A survey of nuclear quadrupole deformation in order to estimate the nuclear MQM and its relative contribution to the atomic EDM

Measurement of a non-zero permanent electric dipole moment (EDM) in fundamental particles, such as in an electron or a neutron, or in nuclei or atoms, can help us gain a handle on the sources of Charge-Parity (CP) violation, both in the Standard Model (SM) and beyond. The nuclear magnetic quadrupole moment (MQM), the central topic of this work, is also CP, P, and T violating. Nucleons and nuclei have a non-zero MQM from sources within the SM, but the nuclear MQM is dramatically enhanced if the nuclei are structurally quadrupole deformed. Multiple sources contribute to an atomic EDM namely: (i) nuclear EDM through its Schiff moment, which is enhanced by nuclear octupole deformation, (ii) CP violating interactions between the electrons and the nuclei, and (iii) the nuclear MQM that contributes to the atomic EDM in atoms with an unpaired valence electron. Our survey of nuclear quadrupole deformation identified 48 isotopes as ideal systems in which to search for a CP violating EDM via their enhanced nuclear MQM. Of these candidates, 223,225\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{223,225}$$\\end{document}Fr, 223\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{223}$$\\end{document}Ra, 223,225,227\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{223,225,227}$$\\end{document}Ac, 229\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{229}$$\\end{document}Th, and 229\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{229}$$\\end{document}Pa also have maximally enhanced nuclear Schiff moment contribution due to their octupole deformation. Laser cooling of the isotopes of Fr and Ra, among a few others, has already been demonstrated, making 223,225\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{223,225}$$\\end{document}Fr and 223\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{223}$$\\end{document}Ra some of the best systems in which to measure an EDM.

Measuring the nuclear magnetic quadrupole moment of optically trapped ytterbium atoms in the metastable state

We propose a scheme to measure a nuclear magnetic quadrupole moment (MQM), a CP -violating electromagnetic moment that appears in the nuclear sector, using the long-lived 3P2 metastable state in neutral 173Yb atoms. Laser-cooling and trapping techniques enable us to prepare ultracold 173Yb atoms in the 3P2 state trapped in an optical lattice or an optical tweezer array, providing an ideal experimental platform with long spin coherence time. In addition, our relativistic configuration interaction calculation for the 3P2 electronic wavefunction reveals a large magnetic field gradient generated by the atomic electrons in this state, which amplifies the measurable effect of an MQM. Our scheme could lead to an improvement of more than one order of magnitude in MQM sensitivity compared to the best previous measurement (Murthy et al 1989 Phys. Rev. Lett. 63, 965).

Measuring the nuclear magnetic quadrupole moment in heavy polar molecules

Theories that extend the Standard Model of particle physics often introduce new interactions that violate charge-parity (CP) symmetry. Charge-parity-violating effects within an atomic nucleus can be probed by measuring its nuclear magnetic quadrupole moment (MQM). The sensitivity of such a measurement is enhanced when using a heavy polar molecule containing a nucleus with quadrupole deformation. We determine how the energy levels of a molecule are shifted by the magnetic quadrupole moment and how those shifts can be measured. The measurement scheme requires molecules in a superposition of magnetic sub-levels that differ by many units of angular momentum. We develop a generic scheme for preparing these states. Finally, we consider the sensitivity that can be reached, showing that this method can reduce the current uncertainties on several charge-parity-violating parameters.

P,T -odd energy shifts of the YbOH173 molecule

The energy shift in molecular spectra due to interaction of nuclear magnetic quadrupole moment ($M$) with electrons is equal to $\delta E_M = MW_M P_{ M}$, where $W_M$ is a constant determined by the electronic structure of the molecule and $P_{ M}$ is a dimensionless constant. We extended the method for calculation of parity nonconservation effects in triatomic molecules developed in Ref. [A. Petrov and A. Zakharova, Phys. Rev. A ${\bf 105}$, L050801 (2022)] to the case of $P_{ M}$ constant and applied it to $^{173}$YbOH in the first excited $v=1$ bending mode. Results of our calculations are required for the extraction of the $M$ value from the YbOH experiment.

Enhanced magnetic quadrupole moments in nuclei with octupole deformation and their CP -violating effects in molecules

Nuclei with an octupole deformation have a non-zero electric octupole moment, electric dipole moment (EDM), Schiff moment and magnetic quadrupole moment (MQM) in the intrinsic frame which rotates with the nucleus. In a state with definite angular momentum in the laboratory frame, these moments are forbidden by parity (P) and time reversal invariance (T) conservation, meaning their expectation values vanish due to nuclear rotation. However, nuclei with an octupole deformation have doublets of close opposite parity rotational states with the same spin, which are mixed by T,P-odd nuclear forces. This mixing produces the orientation of the nuclear axis along nuclear spin and all moments existing in the intrinsic frame appear in the laboratory frame (provided the nuclear spin I is sufficiently large to allow such moment). Such a mechanism produces enhanced T,P-violating nuclear moments. This enhancement also takes place in nuclei with a soft octupole vibration mode. Schiff moments in such nuclei have been calculated in previous works. In the present paper we consider the magnetic quadrupole moment which appears in isotopes with nuclear spin $I \geq 1$. Magnetic interaction between the nuclear MQM and electrons produces an atomic EDM and T,P-violating nuclear spin - molecular axis interaction constants for molecules in electronic states with non-zero electron angular momentum. Measurements of these constants may be used to test CP-violation theories and search for axion dark matter in atomic, molecular and solid state experiments. Potential candidate nuclei include 153Eu, 161Dy, 221Fr, 223Fr, 223Ra, 223Rn, 225Ac, 227Ac, 229Th, 229Pa, 233U and 235U. We subsequently consider molecules containing these nuclei (EuO, EuN+, RaF, AcO, AcN+, AcF+, ThO and ThF+).

Laser-coolable AcOH+ ion for CP -violation searches

The ${\mathrm{AcOH}}^{+}$ molecular ion is identified as a prospective system to search for $\mathcal{CP}$-violation effects. According to our study ${\mathrm{AcOH}}^{+}$ belongs to the class of laser-coolable polyatomic molecular cations implying a large coherence time in the experiments to study symmetry-violating effects of fundamental interactions. We perform both nuclear and high-level relativistic coupled cluster electronic structure calculations to express the experimentally measurable $\mathcal{T},\mathcal{P}$-violating energy shift in terms of fundamental quantities such as the nuclear magnetic quadrupole moment (MQM), electron electric dipole moment ($e\mathrm{EDM}$) and dimensionless scalar-pseudoscalar nuclear-electron interaction constant. We further express nuclear MQM in terms of the strength constants of $\mathcal{CP}$-violating nuclear forces: quantum chromodynamics vacuum angle $\overline{\ensuremath{\theta}}$ and quark chromo-EDMs. The equilibrium structure of ${\mathrm{AcOH}}^{+}$ in the ground and the four lowest excited electronic states was found to be linear. The calculated Franck-Condon factors and transition dipole moments indicate that the laser cooling using an optical cycle involving the first excited state is possible for the trapped ${\mathrm{AcOH}}^{+}$ ions with the Doppler limit estimated to be $\ensuremath{\sim}$4 nK. The lifetime of the ($0,{1}^{1},0$) excited vibrational state considered as a working one for MQM and $e\mathrm{EDM}$ search experiments is estimated to be $\ensuremath{\sim}0.4$ s.

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.

Search for CP-violating nuclear magnetic quadrupole moment using the LuOH+ cation

The time-reversal and spatial parity violating interaction of the nuclear magnetic quadrupole moment (MQM) of the 175Lu and 176Lu nuclei with electrons in the molecular cation LuOH+ is studied. The resulting effect is expressed in terms of fundamental parameters, such as quantum chromodynamics angle θ¯, quark electric dipole moment (EDM), and chromo-EDM. For this, we have estimated the magnetic quadrupole moments of 175Lu and 176Lu nuclei and calculated the molecular constant that characterizes the interaction of the MQM with electrons in the considered molecules. Additionally, we predict the hyperfine structure constants for the ground electronic state of LuOH+. In the molecular calculations, both the correlation and relativistic effects including the Gaunt interaction have been considered. According to the calculated expressions in terms of the fundamental constants, we conclude that LuOH+ can be a promising system to measure the nuclear MQM.

Electronic structure parameter of nuclear magnetic quadrupole moment interaction in metal monofluorides.

The electronic structure parameter (WM) of the nuclear magnetic quadrupole moment (MQM) interaction in numerous open-shell metal monofluorides (viz., MgF, CaF, SrF, BaF, RaF, and PbF) is computed in the fully relativistic coupled-cluster framework. The electron-correlation effects are found to be very important for the precise calculation of WM in the studied molecular systems. The molecular MQM interaction parameter scales nearly as Z2 in the alkaline earth metal monofluorides, where Z is the nuclear charge of metal. Our study identifies 223RaF as a good candidate for the experimental search of the nuclear MQM, which can help unravel the physics beyond the standard model in the hadron sector of matter.

Atomic and molecular transitions induced by axions via oscillating nuclear moments

The interaction of standard model's particles with the axionic Dark Matter field may generate oscillating nuclear electric dipole moments (EDMs), oscillating nuclear Schiff moments and oscillating nuclear magnetic quadrupole moments (MQMs) with a frequency corresponding to the axion's Compton frequency. Within an atom or a molecule an oscillating EDM, Schiff moment or MQM can drive transitions between atomic or molecular states. The excitation events can be detected, for example, via subsequent fluorescence or photoionization. Here we calculate the rates of such transitions. If the nucleus has octupole deformation or quadrupole deformation then the transition rate due to Schiff moment and MQM can be up to $10^{-16}$ transition per molecule per year. In addition, an MQM-induced transition may be of M2-type, which is useful for the elimination of background noise since M2-type transitions are suppressed for photons.

Role of electron correlation in the P,T -odd effects of CdH: A relativistic coupled-cluster investigation

We investigate the parity ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) symmetry violating effects in the CdH molecule and perform the relativistic coupled-cluster calculation of the molecular parameters- $E_\text{eff}$, $W_\text{s}$ and $W_\text{M}$ related to the electric dipole moment of electron (eEDM) interaction, the scalar-pseudoscalar (S-PS) nucleus-electron neutral current coupling and the nuclear magnetic quadrupole moment (MQM) interaction with electrons, respectively. We also compute the molecular dipole moment and the magnetic hyperfine structure coupling constant of CdH. The value of $E_\text{eff}$, $W_\text{s}$ and $W_\text{M}$ obtained by us in the said molecule are 12.2 GV/cm, 14.0 kHz and $0.82\times$10$^{33}$ Hz/e cm$^2$, respectively, within an uncertainty of 10\%. Furthermore, we study the trend of electron-correlation in the computed properties of CdH and that of the $\mathcal{P,T}$-odd parameters in the group-12 monohydrides (i.e., ZnH, CdH, and HgH).

Enhanced P,T-violating nuclear magnetic quadrupole moment effects in laser-coolable molecules.

Nuclear magnetic quadrupole moments (MQMs), such as intrinsic electric dipole moments of elementary particles, violate both parity and time-reversal symmetry and, therefore, probe physics beyond the standard model. We report on accurate relativistic coupled cluster calculations of the nuclear MQM interaction constants in BaF, YbF, BaOH, and YbOH. We elaborate on estimates of the uncertainty of our results. The implications of experiments searching for nonzero nuclear MQMs are discussed.

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.

Enhanced molecular yield from a cryogenic buffer gas beam source via excited state chemistry

We use narrow-band laser excitation of Yb atoms to substantially enhance the brightness of a cold beam of YbOH, a polyatomic molecule with high sensitivity to physics beyond the standard model (BSM). By exciting atomic Yb to the metastable 3P1 state in a cryogenic environment, we significantly increase the chemical reaction cross-section for collisions of Yb with reactants. We characterize the dependence of the enhancement on the properties of the laser light, and study the final state distribution of the YbOH products. The resulting bright, cold YbOH beam can be used to increase the statistical sensitivity in searches for new physics utilizing YbOH, such as electron electric dipole moment and nuclear magnetic quadrupole moment experiments. We also perform new quantum chemical calculations that confirm the enhanced reactivity observed in our experiment and compare reaction pathways of Yb(3P) with the reactants H2O and H2O2. More generally, our work presents a broad approach for improving experiments that use cryogenic molecular beams for laser cooling and precision measurement searches of BSM physics.

Theoretical study of YbOH173 to search for the nuclear magnetic quadrupole moment

CP-violating interaction of the nuclear magnetic quadrupole moment (MQM) with electrons in the ytterbium mono-hydroxide molecule, $^{173}$YbOH, is considered. Both the magnetic quadrupole moment (MQM) of the $^{173}$Yb nucleus and the molecular interaction constant WM are estimated. Electron correlation effects are taken into account within the relativistic Fock-space coupled cluster method. Results are interpreted in terms of the strength constants of CP-violating nuclear forces, neutron EDM, QCD vacuum angle $\theta$, quark EDM and chromo-EDM.

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.

Time reversal violating magnetic quadrupole moment in heavy deformed nuclei

The existence of permanent electric dipole moments (EDMs) and magnetic quadrupole moments (MQMs) violate both time reversal invariance ($T$) and parity ($P$). Following the $CPT$ theorem they also violate combined $CP$ symmetry. Nuclear EDM are completely screened in atoms and molecules while interaction between electrons and MQM creates atomic and molecular EDM which can be measured and used to test CP-violation theories. Nuclear MQM are produced by the nucleon-nucleon $T,P$-odd interaction and by nucleon EDM. In this work we study the effect of enhancement of the nuclear MQM due to the nuclear deformation. Using the Nilsson model we calculate the nuclear MQMs for deformed nuclei of experimental interest and the resultant MQM energy shift in diatomic molecules of experimental interest $^{173}$YbF , $^{177,179}$HfF$^+$, $^{181}$TaN, $^{181}$TaO$^+$, $^{229}$ThO and $^{229}$ThF$^+$.

Evaluation of CP violation in HfF+

CP violation effects produced by the nuclear magnetic quadrupole moment (MQM), electron electric dipole moment (EDM) and scalar$-$pseudoscalar nucleus$-$electron neutral current (SP) interaction in $^{177}$Hf$^{19}$F$^+$ and $^{179}$Hf$^{19}$F$^+$ are calculated. The role of the hyperfine interaction is investigated. It is shown that the MQM shift can be distinguished from the electron EDM and SP ones due to the implicit dependence of MQM shift on the hyperfine sublevel. The MQM effect is expressed in terms of the proton (EDM), QCD vacuum angle $\theta$ and quark chromo-EDMs.