Nuclear Anapole Moment Research Articles

Using parity-nonconserving spin-spin coupling to measure the Tl nuclear anapole moment in a TlF molecular beam

An experiment utilizing a TlF molecular beam is being developed by the CeNTREX collaboration to search for hadronic interactions that violate both time-reversal ($\mathcal{T}$) and parity ($\mathcal{P}$) invariance. Here, we propose to use the same beam to look for a $\mathcal{T}$-invariance conserving but $\mathcal{P}$-nonconserving (PNC) effect induced by the anapole moment of the Tl nucleus, via a vector coupling of the two nuclear spins in TlF. To measure the nuclear anapole moment, the dc electric and magnetic fields in CeNTREX are replaced by rf fields resonant with a nuclear spin-flip transition. We adapt the relativistic coupled-cluster method in combination with relativistic density functional theory for the calculation of the molecular PNC spin-spin vector coupling constant that links the experimental signal with the anapole moment. The value of the $\mathcal{P}$-conserving spin-spin coupling constant calculated within the same approach is found to be in good agreement with available experimental data.

The role of QED effects in transition energies of heavy-atom alkaline earth monofluoride molecules: A theoretical study of Ba+, BaF, RaF, and E120F.

Heavy-atom alkaline earth monofluoride molecules are considered as prospective systems to study spatial parity or spatial parity and time-reversal symmetry violating effects such as the nuclear anapole moment or the electron electric dipole moment. A comprehensive and highly accurate theoretical study of the electronic structure properties and transition energies in such systems can simplify the preparation and interpretation of the experiments. However, almost no attempts to calculate quantum electrodynamics (QED) effects' contribution into characteristics of these neutral heavy-atom molecules have been performed. Recently, we have formulated and implemented such an approach to calculate QED contributions to transition energies of molecules [L. V. Skripnikov, J. Chem. Phys. 154, 201101 (2021)]. In this paper, we perform a benchmark theoretical study of the transition energies in the Ba+ cation and BaF molecule. The deviation of the calculated values from the experimental ones is of the order 10 cm-1 and is more than an order of magnitude better than the "chemical accuracy," 350 cm-1. The achievement of such an agreement has been provided, in particular, by the inclusion of the QED effects. The latter appeared to be not less important than the high-order correlation effects beyond the coupled cluster with single, double, and perturbative triple cluster amplitude level. We compare the role of QED effects for transition energies with heavier molecules-RaF and E120F, where E120 is the superheavy Z = 120 homologof Ra.

A laser cooling scheme for precision measurements using fermionic barium monofluoride (137Ba19F) molecules

We theoretically investigate the laser cooling of fermionic barium monofluoride (137BaF) molecules, which are promising candidates for precision studies of weak parity violation and nuclear anapole moments. This molecular species features two nuclear spins, resulting in a hyperfine structure that is considerably more complicated than the one found in the usual laser-cooled diatomics. We use optical Bloch equations and rate equations to show that optical cycling, sub-Doppler cooling and bichromatic forces can all be realized under realistically achievable experimental conditions.

Nuclear spin-dependent parity-violating effects in light polyatomic molecules

Measurements of nuclear spin-dependent parity-violating (NSD-PV) effects provide an excellent opportunity to test nuclear models and to search for physics beyond the Standard Model. Molecules possess closely-spaced states with opposite parity which may be easily tuned to degeneracy to greatly enhance the observed parity-violating effects. A high-sensitivity measurement of NSD-PV effects using light triatomic molecules is in preparation [E. B. Norrgard, et al., Commun. Phys. 2, 77 (2019)]. Importantly, by comparing these measurements in light nuclei with prior and ongoing measurements in heavier systems, the contribution to NSD-PV from $Z^0$-boson exchange between the electrons and the nuclei may be separated from the contribution of the nuclear anapole moment. Furthermore, light triatomic molecules offer the possibility to search for new particles, such as the postulated $Z^{\prime}$ boson. In this work, we detail a sensitive measurement scheme and present high-accuracy molecular and nuclear calculations needed for interpretation of NSD-PV experiments on triatomic molecules composed of light elements Be, Mg, N, and C. The ab initio nuclear structure calculations, performed within the No-Core Shell Model (NCSM) provide a reliable prediction of the magnitude of different contributions to the NSD-PV effects in the four nuclei. These results differ significantly from the predictions of the standard single-particle model and highlight the importance of including many-body effects in such calculations. In order to extract the NSD-PV contributions from measurements, a parity-violating interaction parameter $W_{\text{PV}}$, which depends on molecular structure, needs to be known with high accuracy. We have calculated these parameters for the triatomic molecules of interest using the relativistic coupled-cluster approach.

Hyperfine-induced transitions S01−D13 in Yb

Parity-violation experiment in Yb is made on the strongly forbidden $M1$ transition $6{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5d6s\phantom{\rule{0.16em}{0ex}}^{3}D_{1}$. The hyperfine mixing of the $5d6s\phantom{\rule{0.16em}{0ex}}^{3}D_{1}$ and $5d6s\phantom{\rule{0.16em}{0ex}}^{3}D_{2}$ levels opens the $E2$ channel, whose amplitude differs for $F$ sublevels of the $^{3}D_{1}$ level. This effect may be important for the experimental search for the nuclear-spin-dependent parity-violation effects predominantly caused by the nuclear anapole moment.

Nuclear anapole moment interaction in BaF from relativistic coupled-cluster theory

We present high accuracy relativistic coupled cluster calculations of the P-odd interaction coefficient $W_A$ describing the nuclear anapole moment effect on the molecular electronic structure. The molecule under study, BaF, is considered a promising candidate for the measurement of the nuclear anapole moment, and the preparation for the experiment is now underway [Altunas et al., Phys. Rev. Lett. 120, 142501 (2018)]. Influence of various computational parameters (size of the basis set, treatment of relativistic effects, and treatment of electron correlation) on the calculated $W_A$ coefficient is investigated and a recommended value of 147.7 Hz with an estimated uncertainty of 1.5% is proposed.

Enhanced nuclear-spin-dependent parity-violation effects using the HgH199 molecule

Electron interactions with the nuclear-spin-dependent (NSD) parity non-conserving (PNC) anapole moment are strongly enhanced within heteronuclear diatomic molecules. A novel, low-energy optical rotation experiment is being proposed with the aim of observing NSD PNC interactions in HgH. Based on the relativistic coupled cluster method we present a complete calculation of the circular polarization parameter $P = 2\,\textrm{Im}(E1_{PNC})/M1 \approx 3 \times 10^{-6}\; \kappa$ for the $^2\Sigma_{1/2} \to ^2\Pi_{1/2}$ optical transition of HgH, where $\kappa$ is a dimensionless constant determined by the nuclear anapole moment. This provides an improvement in sensitivity to NSD PNC by 2 -- 3 orders of magnitude over the leading atomic Xe, Hg, Tl, Pb and Bi optical rotation experiments, and shows that the proposed measurement will be sensitive enough to extract the $^{199}$Hg anapole moment and shed light on the underlying theory of hadronic parity violation.

Measuring nuclear-spin-dependent parity violation with molecules: Experimental methods and analysis of systematic errors

Nuclear spin-dependent parity violation (NSD-PV) effects in atoms and molecules arise from $Z^0$ boson exchange between electrons and the nucleus, and from the magnetic interaction between electrons and the parity-violating nuclear anapole moment. It has been proposed to study NSD-PV effects using an enhancement of the observable effect in diatomic molecules [D. DeMille $\textit{et al.}$, Phys. Rev. Lett. $\textbf{100}$, 023003 (2008)]. Here, we demonstrate measurements of this type with sensitivity surpassing that of any previous atomic PV measurement, using the test system ${^{138}\mathrm{Ba^{19}F}}$. We show that systematic errors associated with our technique can be suppressed to at least the level of the present statistical sensitivity. With $\sim\!170$ hours of data, we measure the matrix element, $W$, of the NSD-PV interaction with uncertainty $\delta W/(2\pi)<0.7$ Hz, for each of two configurations where $W$ must have different signs. This sensitivity would be sufficient to measure NSD-PV effects of the size anticipated across a wide range of nuclei.

Demonstration of a Sensitive Method to Measure Nuclear-Spin-Dependent Parity Violation.

Nuclear-spin-dependent parity violation (NSD-PV) effects in atoms and molecules arise from Z^{0} boson exchange between electrons and the nucleus, and from the magnetic interaction between electrons and the parity-violating nuclear anapole moment. We demonstrate measurements of NSD-PV that use an enhancement of the effect in diatomic molecules, here using the test system ^{138}Ba^{19}F. Our sensitivity surpasses that of any previous atomic parity violation measurement. We show that systematic errors can be suppressed to at least the level of the present statistical sensitivity. We measure the matrix element W of the NSD-PV interaction with total uncertainty δW/(2π)<0.7 Hz, for each of two configurations where W must have different signs. This sensitivity would be sufficient to measure NSD-PV effects of the size anticipated across a wide range of nuclei including ^{137}Ba in ^{137}BaF, where |W|/(2π)≈5 Hz is expected.

Probing Low-Mass Vector Bosons with Parity Nonconservation and Nuclear Anapole Moment Measurements in Atoms and Molecules.

In the presence of P-violating interactions, the exchange of vector bosons between electrons and nucleons induces parity-nonconserving (PNC) effects in atoms and molecules, while the exchange of vector bosons between nucleons induces anapole moments of nuclei. We perform calculations of such vector-mediated PNC effects in Cs, Ba^{+}, Yb, Tl, Fr, and Ra^{+} using the same relativistic many-body approaches as in earlier calculations of standard-model PNC effects, but with the long-range operator of the weak interaction. We calculate nuclear anapole moments due to vector-boson exchange using a simple nuclear model. From measured and predicted (within the standard model) values for the PNC amplitudes in Cs, Yb, and Tl, as well as the nuclear anapole moment of ^{133}Cs, we constrain the P-violating vector-pseudovector nucleon-electron and nucleon-proton interactions mediated by a generic vector boson of arbitrary mass. Our limits improve on existing bounds from other experiments by many orders of magnitude over a very large range of vector-boson masses.

Enhanced spin-dependent parity-nonconservation effect in the7sS1/22→6dD5/22transition in Fr: A possibility for unambiguous detection of the nuclear anapole moment

Employing the relativistic coupled-cluster method, comparative studies of the parity non-conserving electric dipole amplitudes for the $7s \ ^2S_{1/2} \rightarrow 6d \ ^2D_{5/2}$ transitions in $^{210}$Fr and $^{211}$Fr isotopes have been carried out. It is found that these transition amplitudes, sensitive only to the nuclear spin dependent effects, are enhanced by more than 3 orders compared to the low-lying $S-D_{5/2}$ transitions in Ba$^+$ and Ra$^+$ owing to the very large contributions from the electron core-polarization effects in Fr. This translates to a relatively large and, in principle, measurable induced light shift, which would be a signature of nuclear spin dependent parity nonconservation that is dominated by the nuclear anapole moment in a heavy atom like Fr. A plausible scheme to measure this quantity using the Cyclotron and Radioisotope Center (CYRIC) facility at Tohoku University has been outlined.

Theoretical studies of the long lifetimes of the6dD3/2,5/22states in Fr: Implications for parity-nonconservation measurements

Lifetimes of the $6d^{2}D_{3/2}$ and $6d^{2}D_{5/2}$ states in Fr are determined from calculations of the radiative transition amplitudes of the allowed electric dipole $(E1)$ and the forbidden electric quadrupole $(E2)$ and magnetic dipole $(M1)$ channels which were performed using the second-order many-body perturbation theory and the coupled-cluster method at different levels of approximations in the relativistic framework. The values obtained for these two quantities are 540(10) and 1704(32) ns, respectively. These relatively long lifetimes and the large electric dipole parity-non-conserving amplitudes of $7s^{2}S_{1/2}\ensuremath{\rightarrow}6d^{2}D_{3/2,5/2}$ transitions strongly favor Fr as a leading candidate for the measurement of parity nonconservation arising from the neutral-current weak interaction and the nuclear anapole moment. In another important application, these $6D$ states in Fr can be used efficiently for resonance ionization spectroscopic techniques to carry out precise measurements of the properties of the higher excited states due to the long lifetimes of these states.

Nuclear spin-dependent interactions: searches for WIMP, axion and topological defect dark matter, and tests of fundamental symmetries

We calculate the proton and neutron spin contributions for nuclei using semi-empirical methods, as well as a novel hybrid \emph{ab initio}/semi-empirical method, for interpretation of experimental data. We demonstrate that core-polarisation corrections to \emph{ab initio} nuclear shell model calculations generally reduce discrepancies in proton and neutron spin expectation values from different calculations. We derive constraints on the spin-dependent P,T-violating interaction of a bound proton with nucleons, which for certain ranges of exchanged pseudoscalar boson masses improve on the most stringent laboratory limits by several orders of magnitude. We derive a limit on the CPT and Lorentz-invariance-violating parameter $|\tilde{b}_{\perp}^p| < 7.6 \times 10^{-33}$ GeV, which improves on the most stringent existing limit by a factor of 8, and demonstrate sensitivities to the parameters $\tilde{d}_{\perp}^p$ and $\tilde{g}_{ D\perp}^p$ at the level $\sim 10^{-29} - 10^{-28}$ GeV, which is a one order of magnitude improvement compared to the corresponding existing sensitivities. We extend previous analysis of nuclear anapole moment data for Cs to obtain new limits on several other CPT and Lorentz-invariance-violating parameters: $\left|b_0^p \right| < 7 \times 10^{-8}$ GeV, $\left|d_{00}^p \right| < 8 \times 10^{-8}$, $\left|b_0^n \right| < 3 \times 10^{-7}$ GeV and $\left|d_{00}^n \right| < 3 \times 10^{-7}$.

Ab initiostudy of radium monofluoride (RaF) as a candidate to search for parity- and time-and-parity–violation effects

Relativistic ab initio calculations have been performed to assess the suitability of RaF for experimental search of P- and T,P-violating interactions. The parameters of P- and T,P-odd terms of the spin-rotational Hamiltonian have been calculated for the ${^2}\Sigma$ electronic ground state of RaF molecule. They include the parameter $W_a$, which is critical in experimental search for nuclear anapole moment and the parameters $W_d$ and $W_{\rm SP}$ required to obtain restrictions on the electric dipole moment of the electron and T,P-odd scalar-pseudoscalar interactions, respectively. The parameter $X$ corresponding to the "volume effect" in the T,P$-$odd interaction of the $^{223}$Ra nuclear Schiff moment with electronic shells of RaF has also been computed. Spectroscopic and hyperfine structure constants for $^{223}$RaF and $^{223}$Ra$^+$ have been computed as well, demonstrating the accuracy of the methods employed.

Parity-violating interactions of cosmic fields with atoms, molecules, and nuclei: Concepts and calculations for laboratory searches and extracting limits

We propose methods and present calculations that can be used to search for evidence of cosmic fields by investigating the parity-violating effects, including parity nonconservation amplitudes and electric dipole moments, that they induce in atoms. The results are used to constrain important fundamental parameters describing the strength of the interaction of various cosmic fields with electrons, protons, and neutrons. Candidates for such fields are dark matter (including axions) and dark energy, as well as several more exotic sources described by standard-model extensions. Existing parity nonconservation experiments in Cs, Dy, Yb, and Tl are combined with our calculations to directly place limits on the interaction strength between the temporal component, b_0, of a static pseudovector cosmic field and the atomic electrons, with the most stringent limit of |b_0^e| < 7*10^(-15) GeV, in the laboratory frame of reference, coming from Dy. From a measurement of the nuclear anapole moment of Cs, and a limit on its value for Tl, we also extract limits on the interaction strength between the temporal component of this cosmic field, as well as a related tensor cosmic-field component d_00, with protons and neutrons. The most stringent limits of |b_0^p| < 4*10^(-8) GeV and |d_00^p| < 5*10^(-8) for protons, and |b_0^n| < 2*10^(-7) GeV and |d_00^n| < 2*10^(-7) for neutrons (in the laboratory frame) come from the results using Cs. Axions may induce oscillating P- and T-violating effects in atoms and molecules through the generation of oscillating nuclear magnetic quadrupole and Schiff moments, which arise from P- and T-odd intranuclear forces and from the electric dipole moments of constituent nucleons. Nuclear-spin-independent parity nonconservation effects may be enhanced in diatomic molecules possessing close pairs of opposite-parity levels in the presence of time-dependent interactions.

Strongly enhanced atomic parity violation due to close levels of opposite parity

We present calculations of nuclear-spin-dependent and nuclear-spin-independent parity violating amplitudes in Ba, Ra, Ac+, Th and Pa. Parity nonconservation in these systems is greatly enhanced due to the presence of very close electronic energy levels of opposite parity, large nuclear charge, and strong nuclear enhancement of parity-violating effects. The presented amplitudes constitute several of the largest atomic parity-violating signals predicted so far. Experiments using these systems may be performed to determine values for the nuclear anapole moment, a P-odd T-even nuclear moment given rise to by parity-violating nuclear forces. Such measurements may prove to be valuable tools in the study of parity violation in the hadron sector. The considered spin-independent transitions could also be used to measure the ratio of weak charges for different isotopes of the same atom, the results of which would serve as a test of the standard model and also of neutron distributions. Barium, with seven stable isotopes, is particularly promising in this regard.

Relativistic study of nuclear-anapole-moment effects in diatomic molecules

Nuclear-spin-dependent (NSD) parity violating effects are studied for a number of diatomic molecules using relativistic Hartree-Fock and density functional theory and accounting for core polarization effects. Heavy diatomic molecules are good candidates for the successful measurement of the nuclear anapole moment, which is the dominant NSD parity violation term in heavy elements. Improved results for the molecules studied in our previous publication [Borschevsky et al., Phys. Rev. A 85, 052509 (2012)] are presented along with the calculations for a number of new promising candidates for the nuclear anapole measurements.

Investigation of parity violation in nuclear spin-rotation interaction of fluorooxirane

When it comes to the question of how signatures from parity violation in chiral molecules can be revealed, then ultra-high resolution spectroscopy techniques play a crucial role in attempts to detect such effects via line shifts. A prerequisite for this approach towards molecular parity violation is a detailed understanding of the corresponding conventional spectroscopy, including even small effects that are often neglected. Nuclear spin-rotation (NSR) interaction is one such effect that becomes appreciable only at high to ultra-high resolution and is often masked by nuclear electric quadrupole interactions (NQI) if nuclei are present with nuclear spin quantum number I larger than 1/2. Herein, NSR interactions are studied theoretically for the chiral molecules fluorooxirane and bromochlorofluoromethane (CHBrClF). For the latter molecule, NSR interactions are compared to nuclear electric quadrupole coupling contributions. The former molecule is devoid of I > 1/2 nuclei such that NSR interactions are not masked by NQI. Parity-odd contributions to NSR of 19F are computed that give rise to additional line shifts in hyperfine transitions. A detection of these nuclear spin-dependent P-odd terms could in principle give information on the nuclear anapole moment in fluorine, which arises due to parity violating interactions within the nucleus.

Calculation of parity-nonconserving optical rotation in iodine at 1315 nm

We examine the feasibility of a parity non-conserving (PNC) optical rotation experiment for the $^2$P$_{3/2}\rightarrow ^2$P$_{1/2}$ transition of atomic iodine at 1315 nm. The calculated $E1_{\rm PNC}$ to $M1$ amplitude ratio is $R=0.80(16)\times 10^{-8}$. We show that very large PNC rotations (greater than 10 $\mu$rad) are obtained for iodine-atom column densities of $\sim 10^{22}$ cm$^{-2}$, which can be produced by increasing the effective interaction pathlength by a factor of $\sim 10^4$ with a high-finesse optical cavity. The simulated signals indicate that measurement of the nuclear anapole moment is feasible, and that a 1% PNC precision measurement should resolve the inconsistency between previous measurements in Cs and Tl.

New Limit on Possible Long-Range Parity-Odd Interactions of the Neutron from Neutron-Spin Rotation in LiquidHe4

Various theories beyond the standard model predict new particles with masses in the sub-eV range with very weak couplings to ordinary matter. A parity-odd interaction between polarized nucleons and unpolarized matter proportional to g(V)g(A)s · p is one such possibility, where s[over →] and p[over →] are the spin and the momentum of the polarized nucleon, and g(V) and g(A) are the vector and axial vector couplings of an interaction induced by the exchange of a new light vector boson. We report a new experimental upper bound on such possible long-range parity-odd interactions of the neutron with nucleons and electrons from a recent search for parity violation in neutron spin rotation in liquid ^{4}He. Our constraint on the product of vector and axial vector couplings of a possible new light vector boson is g(V) g(A)(n) ≤ 10(-32) for an interaction range of 1 m. This upper bound is more than 7 orders of magnitude more stringent than the existing laboratory constraints for interaction ranges below 1 m, corresponding to a broad range of vector boson masses above 10(-6) eV. More sensitive searches for a g(V) g(A)(n) coupling could be performed using neutron spin rotation measurements in heavy nuclei or through analysis of experiments conducted to search for nucleon-nucleon weak interactions and nuclear anapole moments.