Precision Calculation of Hyperfine Constants for Extracting Nuclear Moments of

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.

Accurate Prediction of Clock Transitions in a Highly Charged Ion with Complex Electronic Structure.

We develop a broadly applicable approach that drastically increases the ability to predict the properties of complex atoms accurately. We apply it to the case of Ir^{17+}, which is of particular interest for the development of novel atomic clocks with a high sensitivity to the variation of the fine-structure constant and to dark matter searches. In general, clock transitions are weak and very difficult to identify without accurate theoretical predictions. In the case of Ir^{17+}, even stronger electric-dipole (E1) transitions have eluded observation despite years of effort, raising the possibility that the theoretical predictions are grossly wrong. In this work, we provide accurate predictions of the transition wavelengths and E1 transition rates for Ir^{17+}. Our results explain the lack of observations of the E1 transitions and provide a pathway toward the detection of clock transitions. The computational advances we demonstrate in this work are widely applicable to most elements in the periodic table and will allow us to solve numerous problems in atomic physics, astrophysics, and plasma physics.

Multipolar Polarizabilities and Hyperpolarizabilities in the Sr Optical Lattice Clock.

We address the problem of the lattice Stark shifts in the Sr clock caused by the multipolar M1 and E2 atom-field interactions and by the term nonlinear in lattice intensity and determined by the hyperpolarizability. We develop an approach to calculate hyperpolarizabilities for atoms and ions based on a solution of the inhomogeneous equation which allows us to effectively and accurately carry out complete summations over intermediate states. We apply our method to the calculation of the hyperpolarizabilities for the clock states in Sr. We also carry out an accurate calculation of the multipolar polarizabilities for these states at the magic frequency. Understanding these Stark shifts in optical lattice clocks is crucial for further improvement of the clock accuracy.

Nuclear Charge Radii of

The isotope ^{229}Th is unique in that it possesses an isomeric state of only a few electron volts above the ground state, suitable for nuclear laser excitation. An optical clock based on this transition is expected to be a very sensitive probe for variations of fundamental constants, but the nuclear properties of both states have to be determined precisely to derive the actual sensitivity. We carry out isotope shift calculations in Th^{+} and Th^{2+} including the specific mass shift, using a combination of configuration interaction and all-order linearized coupled-cluster methods and estimate the uncertainty of this approach. We perform experimental measurements of the hyperfine structure of Th^{2+} and isotopic shift between ^{229}Th^{2+} and ^{232}Th^{2+} to extract the difference in root-mean-square radii as δ⟨r^{2}⟩^{232,229}=0.299(15) fm^{2}. Using the recently measured values of the isomer shift of lines of ^{229m}Th, we derive the value for the mean-square radius change between ^{229}Th and its low-lying isomer ^{229m}Th to be δ⟨r^{2}⟩^{229m,229}=0.0105(13) fm^{2}.

Quantum Electrodynamical Shifts in Multivalent Heavy Ions.

The quantum electrodynamics (QED) corrections are directly incorporated into the most accurate treatment of the correlation corrections for ions with complex electronic structure of interest to metrology and tests of fundamental physics. We compared the performance of four different QED potentials for various systems to access the accuracy of QED calculations and to make a prediction of highly charged ion properties urgently needed for planning future experiments. We find that all four potentials give consistent and reliable results for ions of interest. For the strongly bound electrons, the nonlocal potentials are more accurate than the local potential.

Time-reversal symmetry violation in molecules induced by nuclear magnetic quadrupole moments.

Recent measurements in paramagnetic molecules improved the limit on the electron electric dipole moment (EDM) by an order of magnitude. Time-reversal (T) and parity (P) symmetry violation in molecules may also come from their nuclei. We point out that nuclear T, P-odd effects are amplified in paramagnetic molecules containing deformed nuclei, where the primary effects arise from the T, P-odd nuclear magnetic quadrupole moment (MQM). We perform calculations of T, P-odd effects in the molecules TaN, ThO, ThF+, HfF+, YbF, HgF, and BaF induced by MQMs. We compare our results with those for the diamagnetic TlF molecule, where the T, P-odd effects are produced by the nuclear Schiff moment. We argue that measurements in molecules with MQMs may provide improved limits on the strength of T, P-odd nuclear forces, on the proton, neutron, and quark EDMs, on quark chromo-EDMs, and on the QCD θ term and CP-violating quark interactions.

Highly charged ions for atomic clocks, quantum information, and search for α variation.

We propose 10 highly charged ions as candidates for the development of next generation atomic clocks, quantum information, and search for α variation. They have long-lived metastable states with transition wavelengths to the ground state between 170-3000 nm, relatively simple electronic structure, stable isotopes, and high sensitivity to α variation (e.g., Sm(14+), Pr(10+), Sm(13+), Nd(10+)). We predict their properties crucial for the experimental exploration and highlight particularly attractive systems for these applications.

Zeeman-tuned rotational level-crossing spectroscopy in a diatomic free radical.

Rotational levels of molecular free radicals can be tuned to degeneracy by 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 BaF138. 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 line shapes, transition dipole moments, and Stark shifts and to precisely determine molecular magnetic g factors. Our results constitute an initial proof of concept for use of this system to study nuclear spin-dependent parity-violating effects.

Electric dipole moment enhancement factor of thallium.

The goal of this work is to resolve the present controversy in the value of the electric dipole moment (EDM) enhancement factor of Tl. We carry out several calculations by different high-precision methods, study previously omitted corrections, as well as test our methodology on other, parity conserving, quantities. We find the EDM enhancement factor of Tl to be equal to -573(20). This value is 20% larger than the recently published result of Nataraj et al. [Phys. Rev. Lett. 106, 200403 (2011)], but agrees very well with several earlier results.

Precision calculation of blackbody radiation shifts for optical frequency metrology.

We show that three group IIIB divalent ions, B(+), Al(+), and In(+), have anomalously small blackbody radiation (BBR) shifts of the ns(2) (1)S(0)-nsnp (3)P(0)(o) clock transitions. The fractional BBR shifts for these ions are at least 10 times smaller than those of any other present or proposed optical frequency standards at the same temperature, and are less than 0.3% of the Sr clock shift. We have developed a hybrid configuration-interaction + coupled-cluster method that provides accurate treatment of correlation corrections in such ions and yields a rigorous upper bound on the uncertainty of the final results. We reduce the BBR contribution to the fractional frequency uncertainty of the Al(+) clock to 4×10(-19) at T=300 K. We also reduce the uncertainties due to this effect at room temperature to 10(-18) level for B(+) and In(+) to facilitate further development of these systems for metrology and quantum sensing.

Relativistic all-order many-body calculation of energies, wavelengths, and M1 and E2 transition rates for the 3d n configurations in tungsten ions.

Energy levels, wavelengths, magnetic-dipole and electric-quadrupole transition rates between the low-lying states are evaluated for W51+ to W54+ ions with 3d n (n = 2 to 5) electronic configurations by using an approach combining configuration interaction with the linearized coupled-cluster single-double method. The QED corrections are directly incorporated into the calculations and their effect is studied in detail. Uncertainties of the calculations are discussed. This study of such highly charged ions with the present method opens the way for future applications allowing an accurate prediction of properties for a very wide range of highly charged ions aimed at providing precision benchmarks for various applications.

A search for varying fundamental constants using hertz-level frequency measurements of cold CH molecules.

Many modern theories predict that the fundamental constants depend on time, position or the local density of matter. Here we develop a spectroscopic method for pulsed beams of cold molecules, and use it to measure the frequencies of microwave transitions in CH with accuracy down to 3 Hz. By comparing these frequencies with those measured from sources of CH in the Milky Way, we test the hypothesis that fundamental constants may differ between the high- and low-density environments of the Earth and the interstellar medium. For the fine structure constant we find Δα/α=(0.3 ± 1.1) × 10⁻7, the strongest limit to date on such a variation of α. For the electron-to-proton mass ratio we find Δµ/µ=(-0.7 ± 2.2) × 10⁻7. We suggest how dedicated astrophysical measurements can improve these constraints further and can also constrain temporal variation of the constants.

Using molecules to measure nuclear spin-dependent parity violation.

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.

Limit on the cosmological variation of mp/me from the inversion spectrum of ammonia.

We obtain the limit on the space-time variation of the ratio of the proton mass to the electron mass, mu=m(p)/m(e), based on comparison of quasar absorption spectra of NH3 with CO, HCO+ and HCN rotational spectra. For the inversion transition in NH3 (lambda approximately 1.25 cm(-1)) the relative frequency shift is significantly enhanced: deltaomega/omega=-4.46deltamu/mu. This enhancement allows one to increase sensitivity to the variation of mu using NH3 spectra for high redshift objects. We use published data on microwave spectra of the object B0218+357 to place the limit deltamu/mu=(0.6+/-1.9) x 10(-6) at redshift z=0.6847; this limit is several times better than the limits obtained by different methods and may be significantly improved. Assuming linear time dependence we obtain mu/mu=(-1+/-3) x 10(-16) yr(-1).

Enhanced sensitivity to the time variation of the fine-structure constant and m{p}/m{e} in diatomic molecules.

Sensitivity to temporal variation of the fundamental constants may be strongly enhanced in transitions between narrow close levels of different nature. This enhancement may be realized in a large number of molecules due to cancellation between the ground state fine-structure omega{f} and vibrational interval omega{v} [omega=omega{f}-nomega{v} approximately 0, delta omega/omega=K(2delta alpha/alpha+0.5 delta mu/mu), K>>1, mu=m{p}/m{e}]. The intervals between the levels are conveniently located in microwave frequency range and the level widths are very small. Required accuracy of the shift measurements is about 0.01-1 Hz. As examples, we consider molecules Cl(+)(2), CuS, IrC, SiBr, and HfF(+).

Proposal for a sensitive search for the electric dipole moment of the electron with matrix-isolated radicals.

We propose using matrix-isolated paramagnetic diatomic molecules to search for the electric dipole moment of the electron (eEDM). As was suggested by Shapiro in 1968, the eEDM leads to a magnetization of a sample in the external electric field. In a typical condensed matter experiment, the effective field on the unpaired electron is of the same order of magnitude as the laboratory field, typically about 10(5) V/cm. We exploit the fact that the effective electric field inside heavy polar molecules is on the order of 10(10) V/cm. This leads to a huge enhancement of the Shapiro effect. Statistical sensitivity of the proposed experiment may allow one to improve the current limit on eEDM by 3 orders of magnitude in a few hours accumulation time.

Enhancement of the electric dipole moment of the electron in PbO.

The a(1) state of PbO can be used to measure the electric dipole moment of the electron d(e). We discuss a semiempirical model for this state, which yields an estimate of the effective electric field on the valence electrons in PbO. Our final result is a lower limit on the measurable energy shift, which is significantly larger than was anticipated earlier: 2/W(d)/d(e)>or=2.4x10(25) Hz[d(e) divided by e cm].

High-accuracy calculation of 6s --> 7s parity-nonconserving amplitude in Cs.

We calculated the parity-nonconserving (PNC) 6s-->7s amplitude in Cs. In the Dirac-Coulomb approximation our result is in good agreement with other calculations. Breit corrections to the PNC amplitude and to the Stark-induced amplitude beta are found to be -0.4% and -1%, respectively. The weak charge of 133Cs is Q(W) = -72.5+/-0.7 in agreement with the standard model.

Fluorescence and excitation Escherichia coli RecA protein spectra analyzed separately for tyrosine and tryptophan residues.

The method for separation of emission (EM) and excitation (EX) spectra of a protein into EM and EX spectra of its tyrosine (Tyr) and tryptophan (Trp) residues was described. The method was applied to analysis of Escherichia coli RecA protein and its complexes with Mg(2+), ATPgammaS or ADP, and single-stranded DNA (ssDNA). RecA consists of a C-terminal domain containing two Trp and two Tyr residues, a major domain with five Tyr residues, and an N-terminal domain without these residues (R. M. Story, I. T. Weber, and T. A. Steitz (1992) Nature (London) 355, 374-376). Because the fluorescence of Tyr residues in the C-terminal domain was shown to be quenched by energy transfer to Trp residues, Trp and Tyr fluorescence of RecA was provided by the C-terminal and the major domains, respectively. Spectral analysis of Trp and Tyr constituents revealed that a relative spatial location of the C-terminal and the major domains in RecA monomers was different for their complexes with either ATPgammaS or ADP, whereas this location did not change upon additional interaction of these complexes with ssDNA. Homogeneous (that is, independent of EX wavelength) and nonhomogeneous (dependent on EX wavelength) types of Tyr and Trp fluorescence quenching were analyzed for RecA and its complexes with nucleotide cofactors and ssDNA. The former was expected to result from singlet-singlet energy transfer from these residues to adenine of ATPgammaS or ADP. By analogy, the latter was suggested to proceed through energy transfer from high vibrational levels of the excited state of Trp and Tyr residues to the adenine. In this case, for correct calculation of the overlap integral, Trp and Tyr donor emission spectra were substituted by the spectral function of convolution of emission and excitation spectra that resulted in a significant increase of the overlap integral and gave an explanation of the nonhomogeneous quenching of Trp residues in the C-terminal domain.