We propose a direct method of detection of the nuclear anapole moment. It is based on the existence of a linear Stark shift for alkali atoms in their ground state perturbed by a quadrupolar interaction potential and a magnetic field. This shift is proportional to the T-even pseudoscalar built from the quadrupolar potential symmetry axis, the directions of the applied electric and magnetic fields.It involves on the one hand the anisotropy of the hyperfine interaction induced by the quadrupolar interaction and, on the other,the static electric dipole moment arising from electroweak interactions inside the nucleus. The case of ground state cesium atoms trapped in a uniaxial (hcp) phase of solid helium-4 is examined. From an explicit evaluation of both the hyperfine structure anisotropy and the static P-odd T-even dipole deduced from recent empirical data about the cesium nuclear anapole moment, we predict the Stark shift. It is three times the experimental upper bound to be set on the T-odd Stark shift of free cesium atoms in order to improve the present limit on the electron EDM.
We demonstrate theoretically the existence of a linear dc Stark shift of the individual substates of an alkali atom in its ground state, dressed by a circularly polarized laser field. It arises from the electroweak nuclear anapole moment violating P but not T. It is characterized by the pseudoscalar equal to the mixed product formed with the photon angular momentum and static electric and magnetic fields. We derive the relevant left-right asymmetry with its complete signature in a field configuration selected for a precision measurement with cold atom beams. The 3,3 to 4,3 Cs hyperfine-transit…
Weak interactions within a nucleus generate a nuclear spin dependent parity violating electromagnetic moment; the anapole moment. In heavy nuclei, the anapole moment is the dominant contribution to spin-dependent atomic parity violation. We analyze a method to measure the nuclear anapole moment through the electric dipole transition it induces between hyperfine states of the ground level. The method requires tight confinement of the atoms to position them at the anti-node of a standing wave driving the anapole-induced E1 transiton. We explore the necessary limits in the number of atoms, excita…
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 nu…
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 sim…
Using the information on the nuclear structure of exotic neutron-rich halo nucleus $^{11}$Be, we evaluate the parity violating anapole moment in its ground state. The resulting value $κ(^{11}$Be)$=0.17$ is fifteen times bigger than the typical value of the anapole moment of a normal nucleus of the same mass, and in fact exceeds by few times anapole moments of any known neutron-odd nuclei (e.g., kappa(^{11}Be) > 2|κ(^{207}Pb)|. It is also few times bigger than the neutral current contribution to the lepton-nucleus interaction.
In this paper we present some concepts in heavy ion atomic physics for the extraction of parity violating effects. We investigate the effects of the so-called Stark-quenching, i.e., the fast decay of a meta stable state induced by a Stark field, and the superposition of one- and two-photon transitions in beryllium-like heavy ions. It turns out that the discussed theoretical phenomena for heavy ions with few electrons are beyond the scope of present day experimental possibilities because one has to require beam energies of up to 1 TeV/A, laser intensities of up to $10^{17} {\rm W/cm^2}$ and ion…
Nuclear spin-dependent parity violation arises from weak interactions between electrons and nucleons, and from nuclear anapole moments. We outline a method to measure such effects, using a Stark-interference technique to determine the mixing between opposite-parity rotational/hyperfine levels of ground-state molecules. The technique is applicable to nuclei over a wide range of atomic number, in diatomic species that are theoretically tractable for interpretation. This should provide data on anapole moments of many nuclei, and on previously unmeasured neutral weak couplings.
There are several factors which lead to a huge enhancement of parity and time invariance violating effects in the Ra atom: very close electronic levels of opposite parity, the large nuclear charge Z and the collective nature of T,P-odd nuclear moments. Experiments with Radium may be used to measure it's nuclear anapole, magnetic quadrupole and Schiff moments. Such measurements provide information about parity and time invariance violating nuclear forces and electron-nucleon interactions.
We suggest to use insulating garnets doped by rare earth ions for measurements of nuclear anapole moments. A parity violating shift of the NMR frequency arises due to the combined effect of the lattice crystal field and the anapole moment of the rare-earth nucleus. We show that there are two different observable effects related to frequency: 1) A shift of the NMR frequency in an external electric field applied to the solid. The value of the shift is about Δν_1 ~ 10^{-5} Hz with E = 10 kV/cm; 2) A splitting of the NMR line into two lines. The second effect is independent of the external electri…
Atomic parity violation has been observed in the 6s^2 1S0 - 5d6s 3D1 408-nm forbidden transition of ytterbium. The parity-violating amplitude is found to be two orders of magnitude larger than in cesium, where the most precise experiments to date have been performed. This is in accordance with theoretical predictions and constitutes the largest atomic parity-violating amplitude yet observed. This also opens the way to future measurements of neutron skins and anapole moments by comparing parity-violating amplitudes for various isotopes and hyperfine components of the transition.
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…
Nuclear-spin-dependent (NSD) parity violating (PV) effects can be strongly enhanced in diatomic molecules containing heavy atoms. Future measurements are anticipated to provide nuclear anapole moments and strength constants for PV nuclear forces. In light molecules, the NSD electroweak electron-nucleus interaction may also be detected. Here we calculate NSD PV effects for molecular ions. Our calculations are motivated by rapid developments in trapping techniques for such systems at low temperatures.
We perform calculations of s-d_5/2 nuclear-spin-dependent parity nonconservation amplitudes for Rb, Cs, Ba+, Yb+, Fr, Ra+ and Ac++. These systems prove to be good candidates for the use in atomic experiments to extract the so-called anapole moment, a P-odd T-even nuclear moment important for the study of parity violating nuclear forces. We also extend our previous works by calculating the missed spin-dependent amplitudes for the s-d_3/2 transitions in the above systems.
We show that the interaction of an axion field, or in general a pseudoscalar field, with the axial-vector current generated by an electron through a derivative-type coupling can give rise to a time-dependent mixing of opposite-parity states in atomic and molecular systems. Likewise, the analogous interaction of an axion field with the axial-vector current generated by a nucleon can give rise to time-dependent mixing of opposite-parity states in nuclear systems. This mixing can induce oscillating electric dipole moments, oscillating parity non-conservation effects and oscillating anapole moment…
Rotational levels of molecular free radicals can be tuned to degeneracy using laboratory-scale magnetic fields. Because of their intrinsically narrow width, these level crossings of opposite-parity states have been proposed for use in the study of parity-violating interactions and other applications. We experimentally study a typical manifestation of this system using $^{138}$BaF. Using a Stark-mixing method for detection, we demonstrate level-crossing signals with spectral width as small as 6 kHz. We use our data to verify the predicted lineshapes, transition dipole moments, and Stark shifts,…
We have developed a relativistic coupled-cluster theory to incorporate nuclear spin-dependent interaction Hamiltonians perturbatively. This theory is ideal to calculate parity violating nuclear spin-dependent electric dipole transition amplitudes, $E1_{\rm PNC}^{\rm NSD}$, of heavy atoms. Experimental observation of which is a clear signature of nuclear anapole moment, the dominant source of nuclear spin-dependent parity violation in atoms and ions. We apply the theory to calculate $E1_{\rm PNC}^{\rm NSD}$ of Cs, which to date has provided the best atomic parity violation measurements. We also…
Parity (P) and time (T) invariance violating effects in the Ra atom are strongly enhanced due to close states of opposite parity, the large nuclear charge Z and the collective nature of P,T-odd nuclear moments. We have performed calculations of the atomic electric dipole moments (EDM) produced by the electron EDM and the nuclear magnetic quadrupole and Schiff moments. We have also calculated the effects of parity non-conservation produced by the nuclear anapole moment and the weak charge. Our results show that as a rule the values of these effects are much larger than those considered so far i…
We study the chirality of ground-state alkali atoms in E and B fields, dressed with a circularly-polarized laser beam close-detuned from an E-field-assisted forbidden transition, such as 7S-8S in Fr. We predict a parity violating energy shift of their sublevels, linear in E, and the weak nuclear charge Q_W$. A dressing beam of 10 kW/cm$^2$ at 506 nm produces a shift of $\sim100 μ$Hz at E=100 V/cm, B $\gtrsim$30 mG. It should be observable with $\sim 10^4$ Fr atoms confined in an optical dipole trap. We discuss optimal conditions, parameter reversals and a calibration procedure to measure $Q_W$…
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 heavie…
The anisotropic effect of a hcp 4He solid matrix on cesium atoms has been proposed as a tool to reveal the parity violating anapole moment of its nucleus. It should also result in splitting the D2 optical excitation line in a way depending on the light polarization. An experimental investigation has been set up using oriented hcp helium crystals in which cesium metal grains are embedded. Atoms are created by laser sputtering from this grains. Optical absorption spectra of the D2 line have been recorded in the temperature range of 1.0 to 1.4 K at liquid/solid coexistence pressure by monitoring …
We present a detailed description of the observation of parity violation in the 1S0-3D1 408-nm forbidden transition of ytterbium, a brief report of which appeared earlier. Linearly polarized 408-nm light interacts with Yb atoms in crossed E- and B-fields. The probability of the 408-nm transition contains a parity violating term, proportional to (Elight . B)[(E x Elight) . B], arising from interference between the parity violating amplitude and the Stark amplitude due to the E-field (Elight is the electric field of the light). The transition probability is detected by measuring the population o…
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 nonc…
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 s…
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 ${^2}Σ$ 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 $…
