Ab initio Calculations of Energy Levels in Be-Like Xenon: Strong Interference between Electron-Correlation and QED Effects.

The strong mixing of close levels with two valence electrons in Be-like xenon greatly complicates ab initio QED calculations beyond the first-order approximation. Because of a strong interplay between the electron-electron correlation and QED effects, the standard single-level perturbative QED approach may fail, even if it takes into account the second-order screened QED diagrams. In the present Letter, the corresponding obstacles are overcome by working out the QED perturbation theory for quasidegenerate states. The contributions of all the Feynman diagrams up to the second order are taken into account. The many-electron QED effects are rigorously evaluated in the framework of the extended Furry picture to all orders in the nuclear-strength parameter αZ. The higher-order electron-correlation effects are considered within the Breit approximation. The nuclear recoil effect is accounted for as well. The developed approach is applied to high-precision QED calculations of the ground and singly excited energy levels in Be-like xenon. The most accurate theoretical predictions for the binding and excitation energies are obtained. These results deviate from the most precise experimental value by 3σ but perfectly agree with a more recent measurement.

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.

Recoil Effect on the g Factor of Li-Like Ions.

The nuclear recoil effect on the g factor of Li-like ions is evaluated. The one-electron recoil contribution is treated within the framework of the rigorous QED approach to the first order in the electron-to-nucleus mass ratio m/M and to all orders in the parameter αZ. These calculations are performed in a range Z=3-92. The two-electron recoil term is calculated for low- and middle-Z ions within the Breit approximation using a four-component approach. The results for the two-electron recoil part obtained in the Letter strongly disagree with the previous calculations performed using an effective two-component Hamiltonian. The obtained value for the recoil effect is used to calculate the isotope shift of the g factor of Li-like ^{A}Ca^{17+} with A=40 and A=48 which was recently measured. It is found that the new theoretical value for the isotope shift is closer to the experimental one than the previously obtained value.

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.

g Factor of Light Ions for an Improved Determination of the Fine-Structure Constant.

A weighted difference of the g factors of the H- and Li-like ions of the same element is theoretically studied and optimized in order to maximize the cancellation of nuclear effects between the two charge states. We show that this weighted difference and its combination for two different elements can be used to extract a value for the fine-structure constant from near-future bound-electron g factor experiments with an accuracy competitive with or better than the present literature value.

Michelson-Morley analogue for electrons using trapped ions to test Lorentz symmetry.

All evidence so far suggests that the absolute spatial orientation of an experiment never affects its outcome. This is reflected in the standard model of particle physics by requiring all particles and fields to be invariant under Lorentz transformations. The best-known tests of this important cornerstone of physics are Michelson-Morley-type experiments verifying the isotropy of the speed of light. For matter, Hughes-Drever-type experiments test whether the kinetic energy of particles is independent of the direction of their velocity, that is, whether their dispersion relations are isotropic. To provide more guidance for physics beyond the standard model, refined experimental verifications of Lorentz symmetry are desirable. Here we search for violation of Lorentz symmetry for electrons by performing an electronic analogue of a Michelson-Morley experiment. We split an electron wave packet bound inside a calcium ion into two parts with different orientations and recombine them after a time evolution of 95 milliseconds. As the Earth rotates, the absolute spatial orientation of the two parts of the wave packet changes, and anisotropies in the electron dispersion will modify the phase of the interference signal. To remove noise, we prepare a pair of calcium ions in a superposition of two decoherence-free states, thereby rejecting magnetic field fluctuations common to both ions. After a 23-hour measurement, we find a limit of h × 11 millihertz (h is Planck's constant) on the energy variations, verifying the isotropy of the electron's dispersion relation at the level of one part in 10(18), a 100-fold improvement on previous work. Alternatively, we can interpret our result as testing the rotational invariance of the Coulomb potential. Assuming that Lorentz symmetry holds for electrons and that the photon dispersion relation governs the Coulomb force, we obtain a fivefold-improved limit on anisotropies in the speed of light. Our result probes Lorentz symmetry violation at levels comparable to the ratio between the electroweak and Planck energy scales. Our experiment demonstrates the potential of quantum information techniques in the search for physics beyond the standard model.

Many-electron QED corrections to the g factor of lithiumlike ions.

A rigorous QED evaluation of the two-photon exchange corrections to the g factor of lithiumlike ions is presented. The screened self-energy corrections are calculated for the intermediate-Z region, and its accuracy for the high-Z region is essentially improved in comparison with that of previous calculations. As a result, the theoretical accuracy of the g factor of lithiumlike ions is significantly increased. The theoretical prediction obtained for the g factor of (28)Si(11+) g(th) = 2.000 889 892(8) is in an excellent agreement with the corresponding experimental value g(exp) = 2.000 889 889 9(21) [A. Wagner et al., Phys. Rev. Lett. 110, 033003 (2013).

Mass-spectrometric monitoring of anesthesia adequacy.

Anesthesia adequacy was assessed with mass-spectrometric method by monitoring the ratio of mass concentrations of end-tidal CO2 and inhaled O2 in every respiratory cycle during surgery. For real-time monitoring, we used a mass spectrometer with electron ionization connected to the respiratory contour of inhalation anesthesia machine. The study has demonstrated advantages of the novel method in real-time assessment of adequacy of the total intravenous anesthesia.

Specific many-electron effects in X-ray spectra of simple metals and graphene.

In this work the influence of many-electron effects on the shape of characteristic X-ray emission bands of the simple metals Mg and Al is examined by means of ab initio calculations and semi-empirical models. These approaches are also used for the analysis of C K-emission and absorption spectra of graphene. Both the dynamical screening of the core vacancy and the Auger-effect in the valence band (VB) have been taken into account. Dynamical screening of the core vacancy by valence electrons (the so-called MND effect) is considered ab initio in the framework of density functional theory. The Auger effect in the VB was taken into account within a semi-empirical method, approximating the quadratic dependence of the VB hole level width on the difference between the level energy and the Fermi energy. All theoretical spectra are in very good agreement with available experimental data.

Test of many-electron QED effects in the hyperfine splitting of heavy high-Z ions.

A rigorous evaluation of the two-photon exchange corrections to the hyperfine structure in lithiumlike heavy ions is presented. As a result, the theoretical accuracy of the specific difference between the hyperfine splitting values of H- and Li-like Bi ions is significantly improved. This opens a possibility for the stringent test of the many-electron QED effects on a few percent level in the strongest electromagnetic field presently available in experiments.

Octupolar-excitation Penning-trap mass spectrometry for Q-value measurement of double-electron capture in (164)Er.

The theory of octupolar-excitation ion-cyclotron-resonance mass spectrometry is presented which predicts an increase of up to several orders of magnitude in resolving power under certain conditions. The new method has been applied for a direct Penning-trap mass-ratio determination of the (164)Er-(164)Dy mass doublet. (164)Er is a candidate for the search for neutrinoless double-electron capture. However, the measured Q(ϵϵ) value of 25.07(12) keV results in a half-life of 10(30) years for a 1 eV Majorana-neutrino mass.

Resonant enhancement of neutrinoless double-electron capture in 152Gd.

In the search for the nuclide with the largest probability for neutrinoless double-electron capture, we have determined the Q(ϵϵ) value between the ground states of (152)Gd and (152)Sm by Penning-trap mass-ratio measurements. The new Q(ϵϵ) value of 55.70(18) keV results in a half-life of 10(26) yr for a 1 eV neutrino mass. With this smallest half-life among known 0νϵϵ transitions, (152)Gd is a promising candidate for the search for neutrinoless double-electron capture.

Screened QED corrections in lithiumlike heavy ions in the presence of magnetic fields.

A rigorous evaluation of the complete gauge-invariant set of the screened one-loop QED corrections to the hyperfine structure and g factor in lithiumlike heavy ions is presented. The calculations are performed in both Feynman and Coulomb gauges for the virtual photon mediating the interelectronic interaction. As a result, the most accurate theoretical predictions for the specific difference between the hyperfine splitting values of H- and Li-like Bi ions as well as for the g factor of the Li-like Pb ion are obtained.

Isotope shift in the dielectronic recombination of three-electron ANd57+.

Isotope shifts in dielectronic recombination spectra were studied for Li-like (A)Nd(57+) ions with A=142 and A=150. From the displacement of resonance positions energy shifts deltaE(142 150)(2s-2p(1/2))=40.2(3)(6) meV [(stat)(sys)] and deltaE(142 150)(2s-2p(3/2))=42.3(12)(20) meV of 2s-2p(j) transitions were deduced. An evaluation of these values within a full QED treatment yields a change in the mean-square charge radius of (142 150)deltar(2)=-1.36(1)(3) fm(2). The approach is conceptually new and combines the advantage of a simple atomic structure with high sensitivity to nuclear size.

Exploring relativistic many-body recoil effects in highly charged ions.

The relativistic recoil effect has been the object of experimental investigations using highly charged ions at the Heidelberg electron beam ion trap. Its scaling with the nuclear charge Z boosts its contribution to a measurable level in the magnetic-dipole (M1) transitions of B- and Be-like Ar ions. The isotope shifts of 36Ar versus 40Ar have been detected with sub-ppm accuracy, and the recoil effect contribution was extracted from the 1s(2)2s(2)2p 2P(1/2) - 2P(3/2) transition in Ar13+ and the 1s(2)2s2p 3P1-3P2 transition in Ar14+. The experimental isotope shifts of 0.00123(6) nm (Ar13+) and 0.00120(10) nm (Ar14+) are in agreement with our present predictions of 0.00123(5) nm (Ar13+) and 0.00122(5) nm (Ar14+) based on the total relativistic recoil operator, confirming that a thorough understanding of correlated relativistic electron dynamics is necessary even in a region of intermediate nuclear charges.

Relativistic electron correlation, quantum electrodynamics, and the lifetime of the 1s(2)2s(2)2p2p0(3/2) level in boronlike argon.

The lifetime of the Ar13+ 1s(2)2s(2)2p2p0(3/2) metastable level was determined at the Heidelberg Electron Beam Ion Trap to be 9.573(4)(5). The accuracy level of one per thousand makes this measurement sensitive to quantum electrodynamic effects like the electron anomalous magnetic moment (EAMM) and to relativistic electron-electron correlation effects like the frequency-dependent Breit interaction. Theoretical predictions, adjusted for the EAMM, cluster about a lifetime that is approximately shorter than our experimental result.

QED corrections to the parity-nonconserving 6s-7s amplitude in 133Cs.

The complete gauge-invariant set of the one-loop QED corrections to the parity-nonconserving 6s-7s amplitude in 133Cs is evaluated to all orders in alphaZ using a local version of the Dirac-Hartree-Fock potential. The calculations are performed in both length and velocity gauges for the absorbed photon. The total binding QED correction is found to be -0.27(3)%. The weak charge of 133Cs, derived using two most accurate values of the vector transition polarizability beta, is Q(W)=-72.57(46) for beta=26.957(51)a(3)(B) and Q(W)=-73.09(54) for beta=27.15(11)a(3)(B). The first value deviates by 1.1sigma from the prediction of the standard model, while the second one is in perfect agreement with it.

Dual kinetic balance approach to basis-set expansions for the dirac equation.

A new approach to finite basis sets for the Dirac equation is developed. It does not involve spurious states and improves the convergence properties of basis-set calculations. Efficiency of the method is demonstrated for finite basis sets constructed from B splines by calculating the one-loop self-energy correction for a hydrogenlike ion.

High precision wavelength measurements of QED-sensitive forbidden transitions in highly charged argon ions.

We present the results of an experimental study of magnetic dipole (M1) transitions in highly charged argon ions (Ar X, Ar XI, Ar XIV, Ar XV) in the visible spectral range using an electron beam ion trap. Their wavelengths were determined with, for highly charged ions, unprecedented accuracy up to the sub-ppm level and compared with theoretical calculations. The QED contributions, calculated in this Letter, are found to be 4 orders of magnitude larger than the experimental error and are absolutely indispensable to bring theory and experiment to a good agreement. This method shows great potential for the study of QED effects in relativistic few-electron systems.

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.