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Recent experimental progress in cooling, trapping, and quantum logic spectroscopy of highly-charged ions (HCIs) made HCIs accessible for high resolution spectroscopy and precision fundamental studies. Based on these achievements, we explore a possibility to develop optical clocks using transitions between the ground and a low-lying excited state in the Cf$^{15+}$ and Cf$^{17+}$ ions. Using a high-accuracy relativistic method of calculation we predicted the wavelengths of clock transitions, calculated relevant atomic properties, and analyzed a number of systematic effects (such as the electric quadrupole-, micromotion-, and quadratic Zeeman shifts of the clock transitions) that affect the accuracy and stability of the optical clocks. We also calculated magnetic dipole hyperfine-structure constants of the clock states and the blackbody radiation shifts of the clock transitions., Comment: 9 pages, 2 figures

We calculate and measure the magic wavelengths for the $6s^2{}\,^1S_0-6s6p\,{}^3P_1$ intercombination transition of the neutral ytterbium atom. The calculation is performed with the \textit{ab initio} configuration interaction (CI) + all-order method. The measurement is done with laser spectroscopy on cold atoms in an optical dipole trap. The magic wavelengths are determined to be 1035.68(4) nm for the $\pi$ transition ($\Delta m = 0$) and 1036.12(3) nm for the $\sigma$ transitions ($|\Delta m| = 1$) in agreement with the calculated values. Laser cooling on the narrow intercombination transition could achieve better results for atoms in an optical dipole trap when the trap wavelength is tuned to near the magic wavelength.

Energy levels, wavelengths, magnetic-dipole and electric-quadrupole transition rates between the low-lying states are evaluated for W$^{51+}$ to W$^{54+}$ ions with $3d^n$ (n = 2 to 5) electronic configurations using an approach combining configuration interaction with 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 first 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., Comment: 11 pages

We calculate the g-factor of the 6s6p 3P0 state of 199 and 201 mercury isotopes using a relativistic high-precision all-order method that combines the configuration interaction and the coupled-cluster approaches. Our values $g(199Hg) = -0.9485(49)*10^{-3}$ and $g(201Hg) = -0.3504(18)*10^{-3}$ are in agreement with the experimental measurements within the 0.5% theoretical uncertainty. We also calculate the hyperfine quenching rate of the 6s6p 3P0 state in 199Hg and 201Hg and determine its lifetime to be 1.3 and 1.9 s, respectively., Comment: 6 pages, the text was slightly revised and noted misprints were corrected

We carried out a systematic high-precision relativistic study of the forbidden magnetic-dipole and electric-quadrupole transitions in Ca+, Rb, Sr+, Cs, Ba+, Fr, Ra+, Ac2+, and Th3+. This work is motivated by the importance of these transitions for tests of fundamental physics and precision measurements. The relative importance of the relativistic, correlation, Breit correction, and contributions of negative-energy states is investigated. Recommended values of reduced matrix elements are presented together with their uncertainties. The matrix elements and resulting lifetimes are compared with other theoretical values and with experiment where available., 9 pages, 6 tables

Energy levels of 30 low-lying states of Lu2+ and allowed electric-dipole matrix elements between these states are evaluated using a relativistic all-order method in which all single, double and partial triple excitations of Dirac-Fock wave functions are included to all orders of perturbation theory. Matrix elements are critically evaluated for their accuracy and recommended values of the matrix elements are given together with uncertainty estimates. Line strengths, transition rates and lifetimes of the metastable 5d(3/2) and 5d(5/2) states are calculated. Recommended values are given for static polarizabilities of the 6s, 5d and 6p states and tensor polarizabilities of the 5d and 6p(3/2) states. Uncertainties of the polarizability values are estimated in all cases. The blackbody radiation shift of the 6s(1/2)-5d(5/2) transition frequency of the Lu2+ ion is calculated with the aid of the recommended scalar polarizabilities of the 6s(1/2) and 5d(5/2) states. Finally, A and B hyperfine constants are determined for states of 175Lu2+ with n, 9 pages, 10 tables

We optically excite the electronic state $3s3p~^3P_{0}$ in $^{24}$Mg atoms, laser-cooled and trapped in a magic-wavelength lattice. An applied magnetic field enhances the coupling of the light to the otherwise strictly forbidden transition. We determine the magic wavelength, the quadratic magnetic Zeeman shift and the transition frequency to be 468.463(207)$\,$nm, -206.6(2.0)$\,$MHz/T$^2$ and 655 058 646 691(101)$\,$kHz, respectively. These are compared with theoretical predictions and results from complementary experiments. We also developed a high-precision relativistic structure model for magnesium, give an improved theoretical value for the blackbody radiation shift and discuss a clock based on bosonic magnesium., 5 pages, 3 figures

Iridium ions near $4f$-$5s$ level crossings are the leading candidates for a new type of atomic clocks with a high projected accuracy and a very high sensitivity to the temporal variation of the fine structure constant $\alpha$. To identify spectra of these ions in experiment accurate calculations of the spectra and electromagnetic transition probabilities should be performed. Properties of the $4f$-core-excited states in Ir$^{16+}$, Ir$^{17+}$, and Ir$^{18+}$ ions are evaluated using relativistic many-body perturbation theory and Hartree-Fock-Relativistic method (COWAN code). We evaluate excitation energies, wavelengths, oscillator strengths, and transition rates. Our large-scale calculations includes the following set of configurations: $4f^{14-k}5s^{m}5p^{n}$ with $(k+m+n)$ equal to 3, 2, and 1 for the Ir$^{16+}$, Ir$^{17+}$, and Ir$^{18+}$ ions, respectively. The $5s-5p$ transitions are illustrated by the synthetic spectra in the 180 - 200 \AA range. Large contributions of magnetic-dipole transitions to lifetimes of low-lying states in the region below 2.5 Ry are demonstrated., Comment: 10 pages

Testing the spatial variation of fine-structure constant $��$ indicated in [Webb et al., Phys. Rev. Lett. 107, 191101 (2011)] with terrestrial laboratory atomic measurements requires at least $\dot��/��\sim 10^{-19}~\textrm{y}^{-1}$ sensitivity. We conduct a systematic search of atomic systems for such a test that have all features of the best optical clock transitions leading to possibility of the frequency measurements with fractional accuracy on the level of $10^{-18}$ or better and have a factor of 100 extra enhancement of $��$-variation in comparisons to experimental frequency ratio measurement accuracy. We identify the pair of actinide Cf$^{15+}$ and Es$^{16+}$ ions as the best system for a test of spatial $��-$variation hypothesis as it satisfies both of these requirements and have sufficiently simple electronic structure to allow for high-precision predictions of all atomic properties required for rapid experimental progress., 5 pages, 2 figures

We predict a sequence of magic-zero wavelengths for the Sr excited $5s5p~ ^3P_0$ state, and provide a general roadmap for extracting transition matrix elements using precise frequency measurements. We demonstrate that such measurements can serve as a best global benchmark of the spectroscopic accuracy that is required for the development of high-precision predictive methods. These magic-zero wavelengths are also needed for state-selective atom manipulation for implementation of quantum logic operations. We also identify five magic wavelengths of the $5s^2\ ^1S_0 - 5s5p\ ^3P_0$ Sr clock transition between 350 nm and 500 nm which can also serve as precision benchmarks., Comment: 6 pages, 2 figures

Excitation energies, term designations, and $g$-factors of Th, Th$^{+}$ and Th$^{2+}$ are determined using a relativistic hybrid configuration interaction (CI) + all-order approach that combines configuration interaction and linearized coupled-cluster methods. The results are compared with other theory and experiment where available. We find some "vanishing" $g$-factors, similar to those known in lanthanide spectra. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for Th$^{2+}$. To estimate the uncertainties of our results, we compared our values with the available experimental lifetimes for higher $5f7p\ ^3G_{4}$, $7s7p\ ^3P_{0}$, $7s7p\ ^3P_{1}$, and $6d7p\ ^3F_{4}$ levels of Th$^{2+}$. These calculations provide a benchmark test of the CI+all-order method for heavy systems with several valence electrons and yield recommended values for transition rates and lifetimes of Th$^{2+}$., 13 pages

We propose 10 highly-charged ions as candidates for the development of next generation atomic clocks, quantum information, and search for $��$-variation. They have long-lived metastable states with transition frequencies to the ground state between 170-3000 nm, relatively simple electronic structure, stable isotopes and high sensitivity to $��$-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.

We carried out detailed high-precision study of Ag-like Nd$^{13+}$, Sm$^{15+}$ and In-like Ce$^{9+}$, Pr$^{10+}$, Nd$^{11+}$, Sm$^{13+}$, Eu$^{14+}$ highly-charged ions. These ions were identified to be of particular interest to the development of ultra-accurate atomic clocks, search for variation of the fine-structure constant $��$, and quantum information [Safronova et. al. Phys. Rev. Lett. 113, 030801 (2014)]. Relativistic linearized coupled-cluster method was used for Ag-like ion calculations, and a hybrid approach that combines configuration interaction and a variant of the coupled-cluster method was used for the In-like ion calculations. Breit and QED corrections were included. Energies, transition wavelengths, electric-dipole, electric-quadrupole, electric-octupole, magnetic-dipole, magnetic-quadrupole, magnetic-octupole reduced matrix elements, lifetimes, and sensitivity coefficients to $��$-variation were calculated. Detailed study of various contributions was carried out to evaluate uncertainties of the final results. Energies for several similar "reference" ions, where the experimental values are available were calculated and compared with experiment for further tests of the accuracy., 13 pages, 2 figures

Atomic properties of the 24 low-lying ns, np, nd, nf, and ng states in Th IV ion are calculated using the high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric-dipole matrix elements, oscillator strengths, transition rates, and lifetimes. Scalar polarizabilities of the ground and six excited states (5f_j, 6d_j, 7p_j, and 7s), and tensor polarizabilities of the 5f_j, 6d_j, 7p_{3/2} states of Th IV are evaluated. The uncertainties of the recommended values are estimated. These calculations provide recommended values critically evaluated for their accuracy for a number of Th IV atomic properties for use in theoretical modeling as well as planning and analysis of various experiments including development of ultra precise nuclear clock and RESIS studies of actinide ions, 11 pages

A systematic study of Ca+ atomic properties is carried out using high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the levels up to n = 7. Recommended values and estimates of their uncertainties are provided for a large number of electric-dipole transitions. Electric-dipole scalar polarizabilities for the 5s, 6s, 7s, 8s, 4p, 5p, 3d, and 4d states and tensor polarizabilities for the 4p, 5p, 3d, and 4d states in Ca+ are calculated. Methods are developed to accurately treat the contributions from highly-excited states, resulting in significant (factor of 3) improvement in accuracy of the 3d_{5/2} static polarizability value, 31.8(3) a.u., in comparison with the previous calculation [Arora et al., Phys. Rev. A 76, 064501 (2007)]. The blackbody radiation (BBR) shift of the 4s - 3d_{5/2} clock transition in Ca+ is calculated to be 0.381(4) Hz at room temperature, T=300K. Electric-quadrupole 4s -nd and electric-octupole 4s -nf matrix elements are calculated to obtain the ground state multipole E2 and E3 static polarizabilities. The hyperfine constants A are determined for the low-lying levels up to n = 7. The quadratic Stark effect on hyperfine structure levels of 43Ca+ ground state is investigated. These calculations provide recommended values critically evaluated for their accuracy for a number of Ca+ atomic properties for use in planning and analysis of various experiments as well as theoretical modeling., Comment: 18 pages

The operation of atomic clocks is generally carried out at room temperature, whereas the definition of the second refers to the clock transition in an atom at absolute zero. This implies that the clock transition frequency should be corrected in practice for the effect of finite temperature of which the leading contributor is the blackbody radiation (BBR) shift. Experimental measurements of the BBR shifts are difficult. In this work, we have calculated the blackbody radiation shift of the ground-state hyperfine microwave transition in 87Rb using the relativistic all-order method and carried out detailed evaluation of the accuracy of our final value. Particular care is taken to accurately account for the contributions from highly-excited states. Our predicted value for the Stark coefficient, k_S=-1.240(4)\times 10^{-10}\text{Hz/(V/m)}^{2} is three times more accurate than the previous calculation [1]., Comment: 7 pages

We present results of the first-principles calculation of Cs dipole static polarizabilities for the Ns (N = 6 - 12), Np_j (N = 6 - 10), and Nd_j (N = 5 - 10) states using the relativistic all-order method. In our implementation of the all-order method, single and double excitations of Dirac-Fock wave functions are included to all orders in perturbation theory. Additional calculations are carried out for the dominant terms and the uncertainties of our final values are estimated for all states. A comprehensive review of the existing theoretical and experimental studies of the Cs polarizabilities is also carried out. Our results are compared with other values where they are available. These calculations provide a theoretical benchmark for a large number of Cs polarizabilities., 19 pages

We use all-order relativistic many-body perturbation theory to study 5s^2 nl configurations of In I and Sn II. Energies, E1-amplitudes, and hyperfine constants are calculated using all-order method, which accounts for single and double excitations of the Dirac-Fock wave functions., Comment: 10 pages, accepted to PRA; v2: Introduction changed, references added

We present an experimental and theoretical investigation of the polarizabilities and hyperfine constants of D_J states in 133Cs for J=3/2 and J=5/2. New experimental values for the hyperfine constant A are obtained from level-crossing signals of the (7,9,10)D_5/2 states of 133Cs and precise calculations of the tensor polarizabilities alpha_2. The results of relativistic many-body calculations for scalar and tensor polarizabilities of the (5-10)D_3/2 and (5-10)D_5/2 states are presented and compared with measured values from the literature. Calculated values of the hyperfine constants A for these states are also presented and checked for consistency with experimental values., 12 pages, revtex4, 11 figure files

Black-body radiation (BBR) shift is an important systematic correction for the atomic frequency standards realizing the SI unit of time. Presently, there is a controversy over the value of the BBR shift for the primary $^{133}$Cs standard. At room temperatures the values from various groups differ at $3 \times 10^{-15}$ level, while the modern clocks are aiming at $10^{-16}$ accuracies. We carry out high-precision relativistic many-body calculations of the BBR shift. For the BBR coefficient $\beta$ at $T=300K$ we obtain $\beta=-(1.708\pm0.006) \times 10^{-14}$, implying $6 \times 10^{-17}$ fractional uncertainty. While in accord with the most accurate measurement, our 0.35%-accurate value is in a substantial, 10%, disagreement with recent semi-empirical calculations. We identify an oversight in those calculations., Comment: 4 pages

A relativistic many-body method is developed to calculate energy and transition rates for multipole transitions in many-electron ions. This method is based on relativistic many-body perturbation theory (RMBPT), agrees with MCDF calculations in lowest-order, includes all second-order correlation corrections and includes corrections from negative energy states. Reduced matrix elements, oscillator strengths, and transition rates are calculated for electric-multipole (dipole (E1), quadrupole (E2), and octupole (E3)) and magnetic-multipole (dipole (M1), quadrupole (M2), and octupole (M3)) transitions between 3l5l' excited and ground states in Ni-like ions with nuclear charges ranging from Z = 30 to 100. The calculations start from a 1s22s22p63s23p63d10} Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. A detailed discussion of the various contributions to the dipole matrix elements and energy levels is given for nickellike tungsten (Z = 74). The contributions from negative-energy states are included in the second-order E1, M1, E2 M2, E3, and M3 matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations. These atomic data are important in modeling of M-shell radiation spectra of heavy ions generated in electron beam ion trap experiments and in M-shell diagnostics of plasmas., Comment: 21 pages, 8 figures, 11 tables

Energies of np (n=6-9), ns (n=7-9), nd (n=6-8), and nf (n=5-6) states in Tl I and Pb II are obtained using relativistic many-body perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the 72 possible electric-dipole transitions. Electric-quadrupole and magnetic-dipole matrix elements are evaluated to obtain np(3/2) - mp(1/2) (n,m=6,7) transition rates. Hyperfine constants A are evaluated for a number of states in 205Tl. First-, second-, third-, and all-order corrections to the energies and matrix elements and first- and second-order Breit corrections to energies are calculated. In our implementation of the all-order method, single and double excitations of Dirac-Fock wave functions are included to all orders in perturbation theory. These calculations provide a theoretical benchmark for comparison with experiment and theory., twelve tables, no figures