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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 ${\mathrm{Cf}}^{15+}$ and ${\mathrm{Cf}}^{17+}$ 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.

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.

Energy levels, wavelengths, magnetic-dipole and electric-quadrupole transition rates between the low-lying states are evaluated for ${\mathrm{W}}^{51+}$ to ${\mathrm{W}}^{54+}$ ions with $3{d}^{n}$ ($n=2$ 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.

We study effective three-particle interactions between valence electrons, which are induced by the core polarization. Such interactions are enhanced when valence orbitals have strong overlap with the outermost core shell, in particular for the systems with partially filled f-shell. We find that in certain cases the three-particle contributions are large, affecting the order of energy levels, and need to be included in high-precision calculations., Comment: revtex4, 6 pages; v.2: discussion of the accuracy added and other small changes

All-electron configuration interaction theory in the framework of the Dirac-Coulomb Hamiltonian has been applied to the TaN molecule, a promising candidate in the search for Beyond-Standard-Model physics in both the hadron and the lepton sector of matter. We obtain in the first excited {$^3\Delta_1$} state a ${\cal{P,T}}$-odd effective electric field of $36.0 \left[\frac{\rm GV}{\rm cm}\right]$, a scalar-pseudoscalar ${\cal{P,T}}$-odd interaction constant of $32.8$ [kHz], and a nuclear magnetic-quadrupole moment interaction constant of $0.74$ [$\frac{10^{33} {\text{Hz}}}{e\, {\text{cm}}^2}$]. The latter interaction constant has been obtained with a new approach which we describe in detail. Using the same highly correlated all-electron wavefunctions with up to $2.5$ billion expansion terms, we obtain a parallel magnetic hyperfine interaction constant of $-2954$ [MHz] for the $\rm {^{181}{T}a}$ nucleus, a very large molecule-frame electric dipole moment of $-4.91$ [Debye], and spectroscopic constants for the four lowest-lying electronic states of the molecule., Comment: 15 pages, 2 figures

We have developed a significantly more flexible variant of the relativistic atomic method of calculation that combines configuration-interaction and coupled-cluster approaches. The new version is no longer restricted to a specific choice of the initial approximation corresponding to the self-consistent field of the atomic core. We have applied this approach to calculation of different properties of atomic lead, including the energy levels, hyperfine structure constants, electric-dipole transition amplitudes, and $E1$ parity nonconserving (PNC) amplitude for the $6{p}^{2}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}\text{\ensuremath{-}}6{p}^{2}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transition. The uncertainty of the $E1$ PNC amplitude was reduced by a factor of two in comparison with the previous most accurate calculation [V. A. Dzuba et al., Europhys. Lett. 7, 413 (1988)]. Our value for the weak charge ${Q}_{W}=\ensuremath{-}117(5)$ is in agreement with the standard-model prediction.

We have measured the hyperfine structure and isotope shifts of the 402.0- and 399.6-nm resonance lines in $^{229}\mathrm{Th}^{+}$. These transitions could provide pathways towards the excitation of the $^{229}\mathrm{Th}$ low-energy isomeric nuclear state. An unexpected negative isotope shift relative to $^{232}\mathrm{Th}^{+}$ is observed for the 399.6-nm line, indicating a strong Coulomb coupling of the excited state to the nucleus. We have developed an all-order approach to the isotope shift calculations that is generally applicable to heavy atoms and ions with several valence electrons. The theoretical calculations provide an explanation for the negative isotope shift of the 399.6-nm transition and yield a corrected classification of the excited state. The calculated isotope shifts are in good agreement with experimental values.

A high-precision relativistic calculations of Cd-like Nd$^{12+}$, Sm$^{14+}$ and Sn-like Pr$^{9+}$, Nd$^{10+}$ atomic properties is carried out using an approach that combines configuration interaction and a linearized coupled-cluster method. These ions have long-lived metastable states with transitions accessible by laser excitations, relatively simple electronic structure, high sensitivity to $\alpha$ variation, and stable isotopes. Breit and QED corrections were included into the calculations. Energies, transition wavelengths, electric- and magnetic-multipole reduced matrix elements, lifetimes, and sensitivity coefficients $q$ and $K$ to the variation of the fine-structure constant $\alpha$ were obtained. A detailed study of uncertainties was performed. Energies for similar Cd-like Ba$^{8+}$, La$^{9+}$, Ce$^{10+}$, Pr$^{11+}$ and Sn-like Ba$^{6+}$ ions were calculated and compared with experiment for further tests of the accuracy., Comment: 13 pages. arXiv admin note: text overlap with arXiv:1407.8272

We carried out a detailed high-precision study of Ag-like ${\mathrm{Nd}}^{13+}$ and ${\mathrm{Sm}}^{15+}$ and In-like ${\mathrm{Ce}}^{9+}$, ${\mathrm{Pr}}^{10+}$, ${\mathrm{Nd}}^{11+}$, ${\mathrm{Sm}}^{13+}$, and ${\mathrm{Eu}}^{14+}$ highly charged ions. These ions were identified to be of particular interest for the development of ultra-accurate atomic clocks, the search for variation of the fine-structure constant $\ensuremath{\alpha}$, and quantum information [Safronova et al., Phys. Rev. Lett. 113, 030801 (2014)]. The 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, and magnetic-octupole reduced matrix elements, lifetimes, and sensitivity coefficients to $\ensuremath{\alpha}$ variation were calculated. A 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.

We calculated the dependence of the transition frequencies on the fine-structure constant $\ensuremath{\alpha}$ ($q$ factors) for Ni ii. Nickel is one of the few elements with high sensitivity to $\ensuremath{\alpha}$ variation, whose lines are observed at high redshifts. This makes it a sensitive probe for $\ensuremath{\alpha}$ variation on the cosmological time scale. The electronic structure of Ni ii ion was treated within the configuration interaction method using the Dirac-Coulomb Hamiltonian.

Highly excited eigenstates of atoms and ions with open f shell are chaotic superpositions of thousands, or even millions of Hartree-Fock determinant states. The interaction between dielectronic and multielectronic configurations leads to the broadening of dielectronic recombination resonances and relative enhancement of photon emission due to opening of thousands of radiative decay channels. The radiative yield is close to 100% for electron energy . 1 eV and rapidly decreases for higher energies due to opening of many autoionization channels. The same mechanism predicts suppression of photoionization and relative enhancement of the Raman scattering. Results of our calculations of the recombination rate are in agreement with the experimental data for W20+ and Au25+., Comment: Physical Review A

The ${}^{207}$Pb${}^{19}$F molecule possesses a pair of closely spaced levels of opposite parity due to near cancellation of the omega-type doubling and magnetic hyperfine interaction energy shifts [Alphei et al., Phys. Rev. A 83, 040501 (2011)]. We calculate the dependence of the transition frequency between these levels on the fine-structure constant $\ensuremath{\alpha}$ and the ratio of the light quark masses to the quantum chromodynamics scale $({m}_{q}/{\ensuremath{\Lambda}}_{\mathrm{QCD}})$, and find large enhancement of the relative effects of the variation of these parameters. Note that the effect of $\ensuremath{\alpha}$ variation appears mainly due to the significant difference in the relativistic correction factors for the fine and hyperfine structure. We hence suggest the ${}^{207}$Pb${}^{19}$F molecule as a candidate system for investigating the possible temporal variation of the fundamental constants.

It is known for a long time that the long range asymptotic behavior of the Hartree-Fock orbitals is different from that of the orbitals in the local potential. However, there is no consensus about observable physical effects associated with this asymptotics. Here we argue that weaker decrease of the Hartree-Fock orbitals at large distances is responsible for the positron annihilation on the inner shell electrons, which is observed experimentally., Comment: 8 pages, 3 figures, submitted to PRA

We evaluated the static and dynamic polarizabilities of the 5s^2 ^1S_0 and 5s5p ^3P_0^o states of Sr using the high-precision relativistic configuration interaction + all-order method. Our calculation explains the discrepancy between the recent experimental 5s^2 ^1S_0 - 5s5p ^3P_0^o dc Stark shift measurement \Delta \alpha = 247.374(7) a.u. [Middelmann et. al, arXiv:1208.2848 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502R (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1 % uncertainty; -0.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (7 %) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties., Comment: 9 pages

Calculation of the energies, magnetic dipole hyperfine structure constants, $E$1 transition amplitudes between the low-lying states, and nuclear spin-dependent parity-nonconserving amplitudes for the ${}^{2}{S}_{1/2}\ensuremath{-}{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2,5/2}$ transitions in ${}^{171}$Yb${}^{+}$ ion is performed using two different approaches. First, we carried out many-body perturbation theory calculation considering Yb${}^{+}$ as a monovalent system. Additional all-order calculations are carried out for selected properties. Second, we carried out configuration interaction calculation considering Yb as a 15-electron system and compared the results obtained by two methods. The accuracy of different methods is evaluated. We find that the monovalent description is inadequate for evaluation of some atomic properties due to significant mixing of the one-particle and the hole-two-particle configurations. Performing the calculation by such different approaches allowed us to establish the importance of various correlation effects for Yb${}^{+}$ atomic properties for future improvement of theoretical precision in this complicated system.

We have calculated electric dipole polarizabilities of the $3{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0},\phantom{\rule{0.28em}{0ex}}3s3p\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}$, and $3s3p\phantom{\rule{0.16em}{0ex}}{}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ states of the ${\mathrm{Si}}^{2+}$ ion using the recently developed configuration interaction $+$ all-order method. A detailed evaluation of the uncertainties of the final results is carried out. Our value for the ground-state electric dipole polarizability 11.670(13) a.u. is in excellent agreement with the resonant excitation Stark ionization spectroscopy value 11.669(9) a.u. [Komara et al., J. Phys. B 38, 87 (2005); Mitroy, Phys. Rev. A 78, 052515 (2008)]. This paper represents a benchmark test of theory and experiment in divalent atoms. The near cancellation of the $n{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}$ ground state and the lowest $nsnp\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}$ polarizabilities previously observed in ${{\mathrm{B}}^{+},\phantom{\rule{0.28em}{0ex}}{\mathrm{Al}}^{+},\phantom{\rule{0.28em}{0ex}}{\mathrm{In}}^{+},\phantom{\rule{0.28em}{0ex}}\mathrm{Tl}}^{+}$, and ${\mathrm{Pb}}^{2+}$ is also found in the ${\mathrm{Si}}^{2+}$ ion.

We determine the sensitivity to a possible variation of the proton-to-electron mass ratio μ for torsion-wagging-rotation transitions in the ground state of methylamine (CH

We carry out a systematic study of Pb iii properties using a hybrid method that combines configuration interaction and linearized coupled-cluster approaches. The calculations start from a [Xe]$4{f}^{14}5{d}^{10}$ Dirac-Fock potential. Excitation energies and lifetimes of the $6{p}^{2}$, $6sns$, $6snp$, and $6snd$ ($n\ensuremath{\le}9$) states are evaluated. Reduced matrix elements, oscillator strengths, and transition rates are determined for allowed electric-dipole transitions including these states. Extensive comparison with other theoretical and experimental values is carried out. Electric-dipole polarizabilities of the $6{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}$, $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}$, and $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ states in Pb iii and ground state polarizability of Pb${}^{4+}$ are reported.

The aim of the present paper is to analyze a realistic model of a quantum chaotic system: the spectrum and the eigenstates of the rare-earth atom of Ce. Using the relativistic configuration-interaction method the spectra and the wave functions of odd and even levels of Ce with J=4 are calculated. It is shown that the structure of the excited states at excitation energies above 1 eV becomes similar to that of the compound states in heavy nuclei. The wave functions of the excited states are chaotic superpositions of the simple basis states (with the number of ``principal'' components N\ensuremath{\sim}100), built of the 4f, 6s, 5d, and 6p single-electron orbitals. The localization of the eigenstates on the energy scale is characterized by the spread width \ensuremath{\Gamma}\ensuremath{\sim}ND, where D is the average level spacing (D\ensuremath{\sim}0.03 eV). The emergence of chaos in the spectrum and the dependence of the N and \ensuremath{\Gamma} parameters on the excitation energy are studied. The shape of the localization is shown to be Lorenzian around the maximum (principal components), whereas outside this region the squared components display a faster decrease, in agreement with the perturbation theory treatment of the band random matrix (BRM) model. The structure of the real interaction matrix is compared with that assumed in the BRM models. A formula expressing the mean-squared values of matrix elements between the eigenstates in terms of their parameters and single-particle occupancies is derived, and its applicabilility is checked with the results of numerical calculations. The hypothesis of a Gaussian distribution of the eigenstates' components and matrix elements between the eigenstates has been checked. The existence of the statistical (dynamical) enhancement of weak perturbations in systems with dense spectra is demonstrated.

We report results of ab initio calculation of the spin-rotational Hamiltonian parameters including P- and P,T-odd terms for the BaF molecule. The ground-state wave function of BaF molecule is found with the help of the relativistic effective core potential method followed by the restoration of molecular four-component spinors in the core region of barium in the framework of a nonvariational procedure. Core polarization effects are included with the help of the atomic many-body perturbation theory for the Barium atom. For the hyperfine constants the accuracy of this method is about 5-10 %. [S1050-2947(97)50311-8].

We report ab initio relativistic correlation calculations of potential curves and spectroscopic constants for the four lowest-lying electronic states of lead monofluoride. We also calculated parameters of the spin-rotational Hamiltonian for the ground ${}^{2}{\ensuremath{\Pi}}_{1/2}$ and the first excited $A$ ${}^{2}{\ensuremath{\Sigma}}_{1/2}^{+}$ states including P,T-odd and $P$-odd terms. In particular, we have obtained hyperfine constants of the $^{207}\mathrm{Pb}$ nucleus. For the ${}^{2}{\ensuremath{\Pi}}_{1/2}$ state, ${A}_{\ensuremath{\perp}}=\ensuremath{-}6859.6$ MHz, ${A}_{\ensuremath{\Vert}}=9726.9$ MHz and for the $A$ ${}^{2}{\ensuremath{\Sigma}}_{1/2}^{+}$ state, ${A}_{\ensuremath{\perp}}=1720.8$ MHz, ${A}_{\ensuremath{\Vert}}=3073.3$ MHz. Our values of the ground-state hyperfine constants are in good agreement with previous theoretical studies. We discuss and explain seeming disagreement with the recent experimental data of the sign of the constant ${A}_{\ensuremath{\perp}}$. The effective electric field on the electron ${E}_{\mathrm{eff}}$, which is important in the planned experiment for searching for the electric dipole moment of the electron, is found to be $3.3\ifmmode\times\else\texttimes\fi{}{10}^{10} \mathrm{V}/\mathrm{cm}$.

Two-photon transitions between atomic states of total electronic angular-momentum J{sub a}=0 and J{sub b}=1 are forbidden when the photons are of the same energy. This selection rule is analogous to the Landau-Yang theorem in particle physics that forbids decays of vector particle into two photons. It arises because it is impossible to construct a total angular-momentum J{sub 2{gamma}}=1 quantum-mechanical state of two photons that is permutation symmetric, as required by Bose-Einstein statistics. In atoms with nonzero nuclear spin, the selection rule can be violated due to hyperfine interactions. Two distinct mechanisms responsible for the hyperfine-induced two-photon transitions are identified, and the hyperfine structure of the induced transitions is evaluated. The selection rule is also relaxed, even for zero-nuclear-spin atoms, by application of an external magnetic field. Once again, there are two similar mechanisms at play: Zeeman splitting of the intermediate-state sublevels, and off-diagonal mixing of states with different total electronic angular momentum in the final state. The present theoretical treatment is relevant to the ongoing experimental search for a possible Bose-Einstein-statistics violation using two-photon transitions in barium, where the hyperfine-induced transitions have been recently observed, and the magnetic-field-induced transitions are being considered both as a possible systematic effect, and asmore » a way to calibrate the measurement.« less

In this paper we calculated the relativistic corrections to transition frequencies (q factors) of Fe I for the transitions from the even- and odd-parity states to the ground state. We also carried out isotope shift calculations in Fe I and Fe II. To the best of our knowledge, the isotope shift in Fe I was calculated for the first time., Revtex4, 7 pages, accepted to Phys. Rev. A

We calculate sensitivity coefficients to $\ensuremath{\alpha}$ variation for the fine-structure transitions (1,0) and (2,1) within ${^{3}P}_{J}[2{s}^{2}2{p}^{2}]$ multiplet of the carbonlike ions $\text{C}\text{ }\text{I}$, $\text{N}\text{ }\text{II}$, $\text{O}\text{ }\text{III}$, $\text{Na}\text{ }\text{VI}$, $\text{Mg}\text{ }\text{VII}$, and $\text{Si}\text{ }\text{IX}$. These transitions lie in the far-infrared region and are in principle observable in astrophysics for high redshifts $z\ensuremath{\sim}10$. This makes them very promising candidates for the search for possible $\ensuremath{\alpha}$ variation in a cosmological time scale. In such studies one of the most dangerous sources of systematic errors is associated with isotope shifts. We calculate isotope shifts with the help of relativistic mass shift operator and show that it may be significant for $\text{C}\text{ }\text{I}$ but rapidly decreases along the isoelectronic sequence and becomes very small for $\text{Mg}\text{ }\text{VII}$ and $\text{Si}\text{ }\text{IX}$.

Sensitivity coefficients to temporal variation of the fine-structure constant alpha for transitions between the fine-structure (FS) sub-levels of the ground states of C I, Si I, S I, Ti I, Fe I, N II, Fe II, O III, S III, Ar III, Fe III, Mg V, Ca V, Na VI, Fe VI, Mg VII, Si VII, Ca VII, Fe VII, and Si IX are calculated. These transitions lie in the mid- and far-infrared regions and can be observed in spectra of high-redshift quasars and infrared bright galaxies with active galactic nuclei. Using FS transitions to study alpha-variation over cosmological timescale allows to improve the limit on $|\Delta\alpha/\alpha|$ by several times as compared to contemporaneous optical observations ($|\Delta\alpha/\alpha| < 10^{-5}$), and to suppress considerably systematic errors of the radial velocity measurements caused by the Doppler noise. Moreover, the far infrared lines can be observed at redshifts z > 10, far beyond the range accessible to optical observations (z < 4). We have derived a simple analytical expression which relates the FS intervals and the sensitivity of the FS transitions to the change of alpha., Comment: RevTeX4, 7 pages, submitted to PRA; v2: results for light ions (Z

Transition frequencies of Fe II ion are known to be very sensitive to variation of the fine structure constant \alpha. The resonance absorption lines of Fe II from objects at cosmological distances are used in a search for the possible variation of \alpha in cause of cosmic time. In this paper we calculated the dependence of the transition frequencies on \alpha^2 (q-factors) for Fe II ion. We found corrections to these coefficients from valence-valence and core-valence correlations and from the Breit interaction. Both the core-valence correlation and Breit corrections to the q-factors appeared to be larger than had been anticipated previously. Nevertheless our calculation confirms that the Fe II absorption lines seen in quasar spectra have large q-factors of both signs and thus the ion Fe II alone can be used in the search for the \alpha-variation at different cosmological epochs., Comment: 7 pages, submitted to Phys. Rev. A

We calculate isotope mass shift for several light ions using Dirac wave functions and mass shift operator with relativistic corrections of the order of $(\alpha Z)^2$. Calculated relativistic corrections to the specific mass shift vary from a fraction of a percent for Carbon, to 2% for Magnesium. Relativistic corrections to the normal mass shift are typically smaller. Interestingly, the final relativistic mass shifts for the levels of one multiplet appear to be even closer than for non-relativistic operator. That can be important for the astrophysical search for possible $\alpha$-variation, where isotope shift is a source of important systematic error. Our calculations show that for levels of the same multiplet this systematics is negligible and they can be used as probes for $\alpha$-variation., Comment: 7 pages, 5 tables, revtex4

We use all-order relativistic many-body perturbation theory to study $5{s}^{2}nl$ configurations of $\mathrm{In}\phantom{\rule{0.2em}{0ex}}I$ and $\mathrm{Sn}\phantom{\rule{0.2em}{0ex}}II$. 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. A comprehensive review of experimental and theoretical studies of $\mathrm{In}\phantom{\rule{0.2em}{0ex}}I$ and $\mathrm{Sn}\phantom{\rule{0.2em}{0ex}}II$ properties is given. Our results are compared with other studies were available.

Absolute photoionization cross-section measurements for a mixture of ground and metastable states of ${\mathrm{Xe}}^{4+}$, ${\mathrm{Xe}}^{5+}$, and ${\mathrm{Xe}}^{6+}$ are reported in the photon energy range of $4d\ensuremath{\rightarrow}nf$ transitions, which occur within or adjacent to the $13.5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ window for extreme ultraviolet lithography light source development. The reported values allow the quantification of opacity effects in xenon plasmas due to these $4d\ensuremath{\rightarrow}nf$ autoionizing states. The oscillator strengths for the $4d\ensuremath{\rightarrow}4f$ and $4d\ensuremath{\rightarrow}5f$ transitions in ${\mathrm{Xe}}^{q+}$ $(q=1--6)$ ions are calculated using nonrelativistic Hartree-Fock and random phase approximations. These are compared with published experimental values for ${\mathrm{Xe}}^{+}$ to ${\mathrm{Xe}}^{3+}$ and with the values obtained from the present experimental cross-section measurements for ${\mathrm{Xe}}^{4+}$ to ${\mathrm{Xe}}^{6+}$. The calculations assisted in the determination of the metastable content in the ion beams for ${\mathrm{Xe}}^{5+}$ and ${\mathrm{Xe}}^{6+}$. The experiments were performed by merging a synchrotron photon beam generated by an undulator beamline of the Advanced Light Source with an ion beam produced by an electron cyclotron resonance ion source.

We present an accurate ab initio method of calculating isotope shifts and relativistic shifts in atomic spectra. We test the method on neutral carbon and three carbon ions. The relativistic shift of carbon lines may allow them to be included in analyses of quasar absorption spectra that seek to measure possible variations in the fine structure constant $\ensuremath{\alpha}$ over the lifetime of the Universe. Carbon isotope shifts can be used to measure isotope abundances in gas clouds: isotope abundances are potentially an important source of systematic error in the $\ensuremath{\alpha}$-variation studies. These abundances are also needed to study nuclear reactions in stars and supernovae, and test models of chemical evolution of the Universe.

We present an ab initio method of calculation of the isotope and relativistic shifts in atoms with a few valence electrons. It is based on an energy calculation involving the combination of the configuration-interaction method and many-body perturbation theory. This work is motivated by analyses of quasar absorption spectra that suggest that the fine-structure constant $\ensuremath{\alpha}$ was smaller at an early epoch. Relativistic shifts are needed to measure this variation of $\ensuremath{\alpha}$, while isotope shifts are needed to resolve systematic effects in this study. The isotope shifts can also be used to measure isotopic abundances in gas clouds in the early universe, which are needed to study nuclear reactions in stars and supernovae and test models of chemical evolution. This paper shows that the isotope shift in magnesium can be calculated to very high precision using our method.

Searches for CP violating effects in atoms and molecules provide important constrains on competing extensions to the standard model of elementary particles. In particular, CP violation in an atom leads to the CP-odd (T,P-odd) polarizability $\beta^\mathrm{CP}$: a magnetic moment $\mu^\mathrm{CP}$ is induced by an electric field $\mathcal{E}_0$ applied to an atom, $\mu^\mathrm{CP} = \beta^\mathrm{CP} \mathcal{E}_0 $. We estimate the CP-violating polarizability for rare-gas (diamagnetic) atoms He through Rn. We relate betaCP to the permanent electric dipole moment (EDM) of the electron and to the scalar constant of the CP-odd electron-nucleus interaction. The analysis is carried out using the third-order perturbation theory and the Dirac-Hartree-Fock formalism. We find that, as a function of nuclear charge Z, betaCP scales steeply as Z^5 R(Z), where slowly-varying R(Z) is a relativistic enhancement factor. Finally, we evaluate a feasibility of setting a limit on electron EDM by measuring CP-violating magnetization of liquid Xe. We find that such an experiment could provide competitive bounds on electron EDM only if the present level of experimental sensitivity to ultra-weak magnetic fields [Kominis et al., Nature 422, 596 (2003)] is improved by several orders of magnitude., Comment: to appear in Phys. Rev. A; 6 pages, 2 figures

Knowledge of the electric polarizabilities of certain energy levels of barium (not measured in previous studies [1‐10]) is useful for the analysis of experiments with Ba searching for violation of Bose-Einstein statistics for photons [11,12]. We have measured scalar and tensor polarizabilities and some hyperpolarizabilities of four even-parity states (6p 23 P2 ,6 s7d 3 D1,2, and 5d6d 3 D1) of Ba lying between 35 600 and 36 000 cm ˛1 (Fig. 1). Three of these four states have polarizabilities more than two orders of magnitude larger than might be expected from the known energy levels of Ba, implying the existence of two as-yet-unidentified close-lying states of odd parity. Looking for Stark-induced excitations of odd-parity states, we identified transitions to the 6s8p 3 P1 state and to two other states that may be the previously unidentified 6s8p 3 P0,2 states, and measured these states’ energies and polarizabilities. The existence of these states explains the unusually large polarizabilities reported here. Some of the polarizabilities determined in this work are the largest measured for any atomic states with principal quantum number n, 10, with the exception of the nearly degenerate states of hydrogen. Highly polarizable diatomic molecules [13] and Rydberg atoms [14,15] have been used to measure electric fields, for example, in noncontact circuit board testing. The states of Ba studied here could fulfill the same purpose but with a much broader dynamic range. Highly polarizable levels are also of use in experiments searching for (parity and time-reversal violating) atomic electric-dipole moments [16], although the short lifetimes of the levels studied here may limit their usefulness in this regard. Finally, this work demonstrates the use of Starkinduced transitions for the observation of previously unidentified energy levels, a technique that, to our knowledge, has not been previously used for this purpose. Pulsed lasers excite Ba atoms in an atomic beam (Fig. 2) to the even-parity states of interest via two successive E1

We perform an improved calculation of the $\ensuremath{\alpha}$ dependence $(\ensuremath{\alpha}{=e}^{2}/hc)$ of the transition frequencies for ions, which are used in a search for the variation of the fine-structure constant $\ensuremath{\alpha}$ in space-time. We use the Dirac-Hartree-Fock method as a zero approximation and then the many-body perturbation theory and configuration-interaction methods to improve the results. The important problem of level pseudocrossing (as a function of $\ensuremath{\alpha})$ is considered. Near the crossing point the derivative of the frequency over $\ensuremath{\alpha}$ varies strongly (including a change of sign). This makes it very sensitive to the position of the crossing point. We propose a semiempirical solution of the problem, which allows us to obtain accurate results.

Many-body calculation of nuclear spin-dependent parity-nonconserving amplitude for 7s,F=4-7s,F=5 transition between hyperfine sublevels of the ground state of 2 1 1 Fr is carried out. The final result is = -0.49×10 1 0 iκ a.u., where κ is the dimensionless coupling constant. This is approximately an order of magnitude larger than similar amplitude in Cs. The dominant contribution to K is associated with the anapole moment of the nucleus.

To support efforts on cooling and trapping of alkaline-earth-metal atoms and designs of atomic clocks, we performed ab initio relativistic many-body calculations of electric-dipole transition amplitudes between low-lying states of Mg, Ca, and Sr. In particular, we report amplitudes for ${}^{1}{\stackrel{\ensuremath{\rightarrow}}{{P}_{1}^{o}}}^{1}{S}_{0}{,}^{3}{S}_{1}{,}^{1}{D}_{2},$ for ${}^{3}{\stackrel{\ensuremath{\rightarrow}}{{P}_{1}^{o}}}^{1}{S}_{0}{,}^{1}{D}_{2},$ and for ${}^{3}{\stackrel{\ensuremath{\rightarrow}}{{P}_{2}^{o}}}^{1}{D}_{2}$ transitions. For Ca, the reduced matrix element $〈{4s4p}^{1}{P}_{1}^{o}||D||{4s}^{21}{S}_{0}〉$ is in good agreement with a high-precision experimental value deduced from photoassociation spectroscopy [Zinner et al., Phys. Rev. Lett. 85, 2292 (2000)]. An estimated uncertainty of the calculated lifetime of the ${3s3p}^{1}{P}_{1}^{o}$ state of Mg is a factor of 3 smaller than that of the most accurate experiment. Calculated binding energies reproduce experimental values within $0.1\ensuremath{-}0.2%.$