Search

The Moskowitz-Lombardi rule gives a simple relation between the magnetic moment of an atomic nucleus and the effect of its radial distribution on the hyperfine structure - the magnetic hyperfine anomaly or "Bohr-Weisskopf" effect. It was originally formulated for mercury, for which experimental data for nuclear magnetic moments and hyperfine constants were available for a number of isotopes. While the relation for the differential effect between isotopes may be completely determined experimentally, the value for the additive constant that is needed to give the Bohr-Weisskopf (BW) effect for a single isotope has remained untested. In this work, we determine the BW effect in singly-ionized and neutral mercury from experimental muonic Hg-199 data together with our atomic calculations. We check this result by directly extracting the BW effect from the hyperfine constant for singly-ionized Hg-199 using state-of-the-art atomic many-body calculations. From this we deduce an empirical value for the additive constant in the Moskowitz-Lombardi rule, which differs significantly from the values advocated previously.

We perform a theoretical study of vacuum polarization corrections to the hyperfine structure in many-electron atoms. Calculations are performed for systems of interest for precision atomic tests of fundamental physics belonging to the alkali-metal atoms and singly-ionized alkaline earths. The vacuum polarization is considered in the Uehling approximation, and we study the many-body effects core relaxation, core polarization, and valence-core correlations in the relativistic framework. We find that for s states, the relative vacuum polarization correction may be well-approximated by that for hydrogen-like ions, though for all other states account of many-body effects -- in particular, the polarization of the core -- is needed to obtain the correct sign and magnitude of the effect.

While most scintillation-based dark matter experiments search for Weakly Interacting Massive Particles (WIMPs), a sub-GeV WIMP-like particle may also be detectable in these experiments. While dark matter of this type and scale would not leave appreciable nuclear recoil signals, it may instead induce ionization of atomic electrons. Accurate modelling of the atomic wavefunctions is key to investigating this possibility, with incorrect treatment leading to a large suppression in the atomic excitation factors. We have calculated these atomic factors for argon, krypton and xenon and present the tabulated results for use with a range of dark matter models. This is made possible by the separability of the atomic and dark matter form factor, allowing the atomic factors to be calculated for general couplings; we include tables for vector, scalar, pseudovector, and pseudoscalar electron couplings. Additionally, we calculate electron impact total ionization cross sections for xenon using the tabulated results as a test of accuracy. Lastly, we provide an example calculation of the event rate for dark matter scattering on electrons in XENON1T and show that these calculations depend heavily on how the low-energy response of the detector is modelled.

We use the radiative potential method to perform a detailed study of quantum electrodynamics (QED) radiative corrections to electric dipole (E1) transition amplitudes in heavy alkali-metal atoms Rb, Cs, Fr, and alkali-metal-like ions Sr+, Ba+, and Ra+. The validity of the method is checked by comparing with the results of rigorous QED in simple atomic potentials. We study the effects of core relaxation, polarization of the core by the E1 field, and valence-core correlations on QED, which are shown to be important in some cases. We identify several transitions for which the QED contribution exceeds the deviation between atomic theory and experiment.

Motivated by recent measurements for several alkali-metal atoms and alkali-metal-like ions, we perform a detailed study of electric dipole (E1) transition amplitudes in K, Ca+, Rb, Sr+, Cs, Ba+, Fr, and Ra+, which are of interest for studies of atomic parity violation, electric dipole moments, and polarizabilities. Using the all-orders correlation potential method, we perform high-precision calculations of E1 transition amplitudes between low-lying s, p, and d states. We perform a robust error analysis, and compare our calculations to many amplitudes for which there are high-precision experimental determinations. We find excellent agreement, with deviations at the level of ~0.1%. We also compare our results to other theoretical evaluations, and discuss the implications for uncertainty analyses. Further, combining calculations of branching ratios with recent measurements, we extract high-precision values for several E1 amplitudes of Ca+, Sr+, Cs, Fr, and Ra+.

The finite distribution of the nuclear magnetic moment across the nucleus gives a contribution to the hyperfine structure known as the Bohr-Weisskopf (BW) effect. We have obtained an empirical value of -0.24(18)% for this effect in the ground and excited s states of atomic Cs-133. This value is found from historical muonic-atom measurements in combination with our muonic-atom and atomic many-body calculations. The effect differs by 0.5% in the hyperfine structure from the value found using the uniform magnetization distribution, which has been commonly employed in the precision heavy-atom community over the last several decades. We also deduce accurate values for the BW effect in other isotopes and states of cesium. These results enable cesium atomic wave functions to be tested in the nuclear region at an unprecedented 0.2% level, and are needed for the development of precision atomic many-body methods. This is important for increasing the discovery potential of precision atomic searches for new physics, in particular for atomic parity violation in cesium.

In this paper we study the influence of electron screening on the Bohr-Weisskopf (BW) effect in many-electron atoms. The BW effect gives the finite-nucleus magnetization contribution to the hyperfine structure. Relativistic atomic many-body calculations are performed for s and p_1/2 states of several systems of interest for studies of atomic parity violation and time-reversal-violating electric dipole moments -- Rb, Cs, Fr, Ba+, Ra+, and Tl. For s states, electron screening effects are small, and the relative BW correction for hydrogenlike ions and neutral atoms is approximately the same. We relate the ground-state BW effect in H-like ions, which may be cleanly extracted from experiments, to the BW effect in s and p_1/2 states of neutral and near neutral atoms through an electronic screening factor. This allows the BW effect extracted from measurements with H-like ions to be used, with screening factors, in atomic calculations without recourse to modelled nuclear structure input. It opens the way for unprecedented accuracy in accounting for the BW effect in heavy atoms. The efficacy of this approach is demonstrated using available experimental data for H-like and neutral Tl-203 and Tl-205.

In a recent Letter [B. K. Sahoo, B. P. Das, and H. Spiesberger, Phys. Rev. D 103, L111303 (2021)], a calculation of the parity violating 6S-7S E1 amplitude in Cs is reported, claiming an uncertainty of just 0.3%. In this Comment, we point out that key contributions have been omitted, and the theoretical uncertainty has been significantly underestimated. In particular, the contribution of missed QED radiative corrections amounts to several times the claimed uncertainty.

We report on our calculations of differential hyperfine anomalies in the nuclear single-particle model for a number of atoms and ions of interest for studies of fundamental symmetries violations. Comparison with available experimental data allows one to discriminate between different nuclear magnetization models, and this data supports the use of the nuclear single-particle model over the commonly-used uniform ball model. Accurate modelling of the nuclear magnetization distribution is important for testing atomic theory through hyperfine comparisons. The magnetization distribution must be adequately understood and modelled, with uncertainties well under the atomic theory uncertainty, for hyperfine comparisons to be meaningful. This has not been the case for a number of atoms of particular interest for precision studies, including Cs. Our work demonstrates the validity of the nuclear single-particle model for Cs, and this has implications for the theory analysis of atomic parity violation in this atom.

Searching for space-time variations of the constants of Nature is a promising way to search for new physics beyond General Relativity and the standard model motivated by unification theories and models of dark matter and dark energy. We propose a new way to search for a variation of the fine-structure constant using measurements of late-type evolved giant stars from the S-star cluster orbiting the supermassive black hole in our Galactic Center. A measurement of the difference between distinct absorption lines (with different sensitivity to the fine structure constant) from a star leads to a direct estimate of a variation of the fine structure constant between the star's location and Earth. Using spectroscopic measurements of 5 stars, we obtain a constraint on the relative variation of the fine structure constant below $10^{-5}$. This is the first time a varying constant of Nature is searched for around a black hole and in a high gravitational potential. This analysis shows new ways the monitoring of stars in the Galactic Center can be used to probe fundamental physics., Comment: 7 pages + 10 pages appendix, 3 figures, version accepted for publication

We report a fourfold improvement in the determination of nuclear magnetic moments for neutron-deficient isotopes of francium-207--213, reducing the uncertainties from 2% for most isotopes to 0.5%. These are found by comparing our high-precision calculations of hyperfine structure constants for the ground states with experimental values. In particular, we show the importance of a careful modeling of the Bohr-Weisskopf effect, which arises due to the finite nuclear magnetization distribution. This effect is particularly large in Fr and until now has not been modeled with sufficiently high accuracy. An improved understanding of the nuclear magnetic moments and Bohr-Weisskopf effect are crucial for benchmarking the atomic theory required in precision tests of the standard model, in particular atomic parity violation studies, that are underway in francium., Comment: Adds supplementary material

We have performed high-precision calculations of the hyperfine structure for n 2S_1/2 and n 2P_1/2 states of the alkali-metal atoms Rb, Cs, and Fr across principal quantum number n, and studied the trend in the size of the correlations. Our calculations were performed in the all-orders correlation potential method. We demonstrate that the relative correlation corrections fall off quickly with n and tend towards constant and non-zero values for highly-excited states. This trend is supported by experiment, and we utilize the smooth dependence on n to make high-accuracy predictions of the hyperfine constants, with uncertainties to within 0.1% for most states of Rb and Cs., Comment: references updated

We search for transient variations of the fine structure constant using data from a European network of fiber-linked optical atomic clocks. By searching for coherent variations in the recorded clock frequency comparisons across the network, we significantly improve the constraints on transient variations of the fine structure constant. For example, we constrain the variation in alpha to <5*10^-17 for transients of duration 10^3 s. This analysis also presents a possibility to search for dark matter, the mysterious substance hypothesised to explain galaxy dynamics and other astrophysical phenomena that is thought to dominate the matter density of the universe. At the current sensitivity level, we find no evidence for dark matter in the form of topological defects (or, more generally, any macroscopic objects), and we thus place constraints on certain potential couplings between the dark matter and standard model particles, substantially improving upon the existing constraints, particularly for large (>~10^4 km) objects.

We employ a technique that combines the configuration interaction method with the singles-doubles coupled-cluster method to perform calculation of the energy levels, transition amplitudes, lifetimes, g-factors, and magnetic dipole and electric quadrupole hyperfine structure constants for many low-lying states of neutral actinium. We find very good agreement with existing experimental energy levels and make accurate predictions for missing levels. It has been noted that some of the levels have been previously misidentified; our analysis supports this claim. If spectroscopy is performed with actinium-225, our calculations will lead to values for nuclear structure constants. The accuracy of this can be constrained by comparing with actinium-227.

We investigate the possibility for the direct detection of low mass (GeV scale) WIMP dark matter in scintillation experiments. Such WIMPs are typically too light to leave appreciable nuclear recoils, but may be detected via their scattering off atomic electrons. In particular, the DAMA Collaboration [R. Bernabei et al., Nucl. Phys. At. Energy 19, 307 (2018)] has recently presented strong evidence of an annual modulation in the scintillation rate observed at energies as low as 1 keV. Despite a strong enhancement in the calculated event rate at low energies, we find that an interpretation in terms of electron-interacting WIMPs cannot be consistent with existing constraints. We also demonstrate the importance of correct treatment of the atomic wavefunctions, and show the resulting event rate is very sensitive to the low-energy performance of the detectors, meaning it is crucial that the detector uncertainties be taken into account. Finally, we demonstrate that the potential scintillation event rate can be much larger than may otherwise be expected, meaning that competitive searches can be performed for GeV scale WIMPs using the conventional prompt S1 scintillation signals. This is important given the recent and upcoming very large liquid xenon detectors.

We analyze the prospects of employing a distributed global network of precision measurement devices as a dark matter and exotic physics observatory. In particular, we consider the atomic clocks of the Global Positioning System (GPS), consisting of a constellation of 32 medium-Earth orbit satellites equipped with either Cs or Rb microwave clocks and a number of Earth-based receiver stations, some of which employ highly-stable H-maser atomic clocks. High-accuracy timing data is available for almost two decades. By analyzing the satellite and terrestrial atomic clock data, it is possible to search for transient signatures of exotic physics, such as "clumpy" dark matter and dark energy, effectively transforming the GPS constellation into a 50,000km aperture sensor array. Here we characterize the noise of the GPS satellite atomic clocks, describe the search method based on Bayesian statistics, and test the method using simulated clock data. We present the projected discovery reach using our method, and demonstrate that it can surpass the existing constrains by several order of magnitude for certain models. Our method is not limited in scope to GPS or atomic clock networks, and can also be applied to other networks of precision measurement devices., Comment: See also Supplementary Information located in ancillary files

Dark matter may be composed of self-interacting ultralight quantum fields that form macroscopic objects. An example of which includes Q-balls, compact non-topological solitons predicted by a range of theories that are viable dark matter candidates. As the Earth moves through the galaxy, interactions with such objects may leave transient perturbations in terrestrial experiments. Here we propose a new dark matter signature: an asymmetry (and other non-Gaussianities) that may thereby be induced in the noise distributions of precision quantum sensors, such as atomic clocks, magnetometers, and interferometers. Further, we demonstrate that there would be a sizeable annual modulation in these signatures due to the annual variation of the Earth velocity with respect to dark matter halo. As an illustration of our formalism, we apply our method to 6 years of data from the atomic clocks on board GPS satellites and place constraints on couplings for macroscopic dark matter objects with radii R < 10^4 km, the region that is otherwise inaccessible using relatively sparse global networks.

We revisit the WIMP-type dark matter scattering on electrons that results in atomic ionization, and can manifest itself in a variety of existing direct-detection experiments. Unlike the WIMP-nucleon scattering, where current experiments probe typical interaction strengths much smaller than the Fermi constant, the scattering on electrons requires a much stronger interaction to be detectable, which in turn requires new light force carriers. We account for such new forces explicitly, by introducing a mediator particle with scalar or vector couplings to dark matter and to electrons. We then perform state of the art numerical calculations of atomic ionization relevant to the existing experiments. Our goals are to consistently take into account the atomic physics aspect of the problem (e.g., the relativistic effects, which can be quite significant), and to scan the parameter space: the dark matter mass, the mediator mass, and the effective coupling strength, to see if there is any part of the parameter space that could potentially explain the DAMA modulation signal. While we find that the modulation fraction of all events with energy deposition above 2 keV in NaI can be quite significant, reaching ~50%, the relevant parts of the parameter space are excluded by the XENON10 and XENON100 experiments.

Atoms and molecules can become ionized during the scattering of a slow, heavy particle off a bound electron. Such an interaction involving leptophilic weakly interacting massive particles (WIMPs) is a promising possible explanation for the anomalous 9 sigma annual modulation in the DAMA dark matter direct detection experiment [R. Bernabei et al., Eur. Phys. J. C 73, 2648 (2013)]. We demonstrate the applicability of the Born approximation for such an interaction by showing its equivalence to the semiclassical adiabatic treatment of atomic ionization by slow-moving WIMPs. Conventional wisdom has it that the ionization probability for such a process should be exponentially small. We show, however, that due to nonanalytic, cusp-like behaviour of Coulomb functions close to the nucleus this suppression is removed, leading to an effective atomic structure enhancement. Crucially, we also show that electron relativistic effects actually give the dominant contribution to such a process, enhancing the differential cross section by up to 1000 times., Comment: 7 pages, 2 figures. Added Appendix

In the recent work [Phys. Rev. D 91, 111702(R) (2015)], C. Hill concludes that the axion electromagnetic anomaly induces an oscillating electron electric dipole moment of frequency $m_a$ and strength $\sim 10^{-32}~e$ cm, in the limit $v/c \to 0$ for the axion field. Here, we demonstrate that a proper treatment of this problem in the lowest order yields $\textit{no}$ electric dipole moment of the electron in the same limit. Instead, oscillating electric dipole moments of atoms and molecules are produced by different mechanisms., Comment: 2 pages. Version accepted for publication as a Comment in Physical Review D

Studying the violation of parity and time-reversal invariance in atomic systems has proven to be a very effective means for testing the electroweak theory at low energy and searching for physics beyond it. Recent developments in both atomic theory and experimental methods have led to the ability to make extremely precise theoretical calculations and experimental measurements of these effects. Such studies are complementary to direct high-energy searches, and can be performed for just a fraction of the cost. We review the recent progress in the field of parity and time-reversal violation in atoms, molecules, and nuclei, and examine the implications for physics beyond the Standard Model, with an emphasis on possible areas for development in the near future., Comment: Review article prepared for Annual Review of Nuclear and Particle Science. 31 pages, 6 tables, 5 figures

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., Comment: 18 pages, 3 figures, 4 tables, Editor's Suggestion

We derive the relativistic factor for splitting of the $g$-factors of a fermion and its anti-fermion partner, which is important for placing constraints on dimension-5, $CPT$-odd and Lorentz-invariance-violating interactions from experiments performed in a cyclotron. From existing data, we extract limits (1$\sigma$) on the coupling strengths of the temporal component, $f^0$, of a background field (including the field amplitude), which is responsible for such $g$-factor splitting, with an electron, proton, and muon: $|f^0_e|< 2.3 \times 10^{-12} ~\mu_{\textrm{B}}$, $|f^0_p|< 4 \times 10^{-9} ~\mu_{\textrm{B}}$, and $|f^0_\mu|< 8 \times 10^{-11} ~\mu_{\textrm{B}}$, respectively, in the laboratory frame. From existing data, we also extract limits on the coupling strengths of the spatial components, $d^{\perp}$, of related dimension-5 interactions of a background field with an electron, proton, neutron, and muon: $| {d}_e^{\perp} | \lesssim 10^{-9} ~\mu_{\textrm{B}}$, $| {d}_p^{\perp} | \lesssim 10^{-9} ~\mu_{\textrm{B}}$, $| {d}_n^{\perp} | \lesssim 10^{-10} ~\mu_{\textrm{B}}$, and $| {d}_\mu^{\perp} | \lesssim 10^{-9} ~\mu_{\textrm{B}}$, respectively, in the laboratory frame., Comment: 6 pages. Minor corrections and new references added

We propose methods for extracting limits on the strength of P-odd interactions of pseudoscalar and pseudovector 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. Calculations of parity nonconserving amplitudes and atomic electric dipole moments induced by these fields are performed for H, Li, Na, K, Rb, Cs, Ba+, Tl, Dy, Fr, and Ra+. From these calculations and existing measurements in Dy, Cs and Tl, we constrain the interaction strengths of the parity-violating static pseudovector cosmic field to be 7*10^(-15) GeV with an electron, and 3*10^(-8) GeV with a proton., Comment: 6 pages, 1 figure

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., Comment: 15 pages, 19 tables, 0 figures

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., Comment: 8 pages

We present a detailed study of the effect of the double core polarization (the polarization of the core electrons due to the simultaneous action of the electric dipole and parity-violating weak fields) for amplitudes of the s-s and s-d parity non-conserving transitions in Rb, Cs, Ba +, La 2+, Tl, Fr, Ra +, Ac 2+ and Th 3+ as well as electron EDM enhancement factors for the ground states of the above neutral atoms and Au. This effect is quite large and has the potential to resolve some disagreement between calculations in the literature. It also has significant consequences for the use of experimental data in the accuracy analysis., Comment: 6 pages

Parity nonconservation amplitudes are calculated for the 7s-6d transitions of the francium isoelectronic sequence (Fr, Ra +, Ac 2+, Th 3+, Pa 4+, U 5+ and Np 6+) and for the 6s-5d transitions of the cesium isoelectronic sequence (Cs, Ba +, La 2+, Ce 3+ and Pr 4+). We show in particular that isotopes of La 2+, Ac 2+ and Th 3+ ions have strong potential in the search for new physics beyond the standard model - the PNC amplitudes are large, the calculations are accurate and the nuclei are practically stable. In addition, 232-Th 3+ ions have recently been trapped and cooled [C. J. Campbell et al., Phys. Rev. Lett. 102, 233004 (2009)]. We also extend previous works by calculating the s-s PNC transitions in Ra + and Ba +, and provide new calculations of several energy levels, and electric dipole and quadrupole transition amplitudes for the Fr-like actinide ions., Comment: 7 pages, 1 figure. calculations expanded

We use previously developed radiative potential method to calculate quantum electrodynamic (QED) corrections to energy levels and electric dipole transition amplitudes for atoms which are used for the study of the parity non-conservation (PNC) in atoms. The QED shift in energies and dipole amplitudes leads to noticeable change in the PNC amplitudes. This study compliments the previously considered QED corrections to the weak matrix elements. We demonstrate that the QED corrections due to the change in energies and dipole matrix elements are comparable in value to those due to change in weak matrix elements., Comment: 5 pages, 1 figure