Ground-State g Factor of Highly Charged

A method is proposed to determine the M1 nuclear transition amplitude and hence the lifetime of the "nuclear clock transition" between the low-lying (∼8 eV) first isomeric state and the ground state of ^{229}Th from a measurement of the ground-state g factor of few-electron ^{229}Th ions. As a tool, the effect of nuclear hyperfine mixing in highly charged ^{229}Th ions such as ^{229}Th^{89+} or ^{229}Th^{87+} is used. The ground-state-only g-factor measurement would also provide first experimental evidence of nuclear hyperfine mixing in atomic ions. Combining the measurements for H-, Li-, and B-like ^{229}Th ions has a potential to improve the initial result for a single charge state and to determine the nuclear magnetic moment to a higher accuracy than that of the currently accepted value. The calculations include relativistic, interelectronic-interaction, QED, and nuclear effects.

g Factor of Lithiumlike Silicon: New Challenge to Bound-State QED.

The recently established agreement between experiment and theory for the g factors of lithiumlike silicon and calcium ions manifests the most stringent test of the many-electron bound-state quantum electrodynamics (QED) effects in the presence of a magnetic field. In this Letter, we present a significant simultaneous improvement of both theoretical g_{th}=2.000 889 894 4 (34) and experimental g_{exp}=2.000 889 888 45 (14) values of the g factor of lithiumlike silicon ^{28}Si^{11+}. The theoretical precision now is limited by the many-electron two-loop contributions of the bound-state QED. The experimental value is accurate enough to test these contributions on a few percent level.

How to Observe the Vacuum Decay in Low-Energy Heavy-Ion Collisions.

In slow collisions of two bare nuclei with the total charge larger than the critical value Z_{cr}≈173, the initially neutral vacuum can spontaneously decay into the charged vacuum and two positrons. The detection of the spontaneous emission of positrons would be direct evidence of this fundamental phenomenon. However, the spontaneously produced particles are indistinguishable from the dynamical background in the positron spectra. We show that the vacuum decay can nevertheless be observed via impact-sensitive measurements of pair-production probabilities. The possibility of such an observation is demonstrated using numerical calculations of pair production in low-energy collisions of heavy nuclei.

Nuclear Excitation by Two-Photon Electron Transition.

A new mechanism of nuclear excitation via two-photon electron transitions (NETP) is proposed and studied theoretically. As a generic example, detailed calculations are performed for the E1E1 1s2s^{1}S_{0}→1s^{2}^{1}S_{0} two-photon decay of a He-like ^{225}Ac^{87+} ion with a resonant excitation of the 3/2+ nuclear state with an energy of 40.09(5) keV. The probability for such a two-photon decay via the nuclear excitation is found to be P_{NETP}=3.5×10^{-9} and, thus, is comparable with other mechanisms, such as nuclear excitation by electron transition and by electron capture. The possibility for the experimental observation of the proposed mechanism is thoroughly discussed.

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).

g Factor of lithiumlike silicon 28Si11+.

The g factor of lithiumlike silicon (28)Si(11+) has been measured in a triple-Penning trap with a relative uncertainty of 1.1×10(-9) to be g(exp)=2.000 889 889 9(21). The theoretical prediction for this value was calculated to be g(th)=2.000 889 909(51) improving the accuracy to 2.5×10(-8) due to the first rigorous evaluation of the two-photon exchange correction. The measured value is in excellent agreement with the theoretical prediction and yields the most stringent test of bound-state QED for the g factor of the 1s(2)2s state and the relativistic many-electron calculations in a magnetic field.

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.

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.

Theoretical study of the accuracy limits of optical resonance frequency measurements.

The principal limits for the accuracy of the resonance frequency measurements set by the asymmetry of the natural resonance line shape are studied and applied to the recent accurate frequency measurements in the two-photon 1s-2s resonance and in the one-photon 1s-2p resonance in a hydrogen atom. This limit for 1s-2s resonance is found to be approximately 10(-5) Hz compared to the accuracy achieved in experiment +/-46 Hz. In the case of a deuterium atom the limit is essentially larger: 10(-2) Hz. For 1s-2p resonance the accuracy limit is 0.17 MHz while the uncertainty of the recent frequency measurement is about 6 MHz.

Potential energy curves for excited states of the hydrogen-antihydrogen system.

The potential energy curves for the hydrogen-antihydrogen (HH) system in states with a leptonic orbital angular momentum projection Lambda=0, 1, 2, 6, and 30 are presented. Within the framework of the adiabatic picture, explicitly correlated Gaussians are used as basis functions which describe accurately the hydrogen-antihydrogen interaction. The critical internuclear distances where the system transforms into positronium and protonium atoms are found. Adiabatic corrections to the potential energy curves are also estimated.

g-Factor of heavy ions: a new access to the fine structure constant.

A possibility for a determination of the fine structure constant in experiments on the bound-electron g-factor is examined. It is found that studying a specific difference of the g-factors of B- and H-like ions of the same spinless isotope in the Pb region to the currently accessible experimental accuracy of 7 x 10(-10) would lead to a determination of the fine structure constant to an accuracy which is better than that of the currently accepted value. Further improvements of the experimental and theoretical accuracy could provide a value of the fine structure constant which is several times more precise than the currently accepted one.

Double ionization of lithiumlike ions by Compton scattering of high-energy photons.

The double ionization of lithiumlike ions by Compton scattering of photons is investigated in the asymptotic high-energy region. To leading order of the nonrelativistic perturbation theory, the total cross section for double Compton effect is calculated, taking into account the channels of simultaneous and sequential emission of two electrons. Relationships between the cross sections for double ionization of He- and Li-like ions with the same nuclear charge Z are established. This can open wide perspectives for experimental investigations of ionization processes involving low-lying excited states. The universal scaling is found for the ratio of double-to-single ionization in the lithium isoelectronic sequence.

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.

Nuclear-polarization correction to the bound-electron g factor in heavy hydrogenlike ions.

The influence of nuclear polarization on the bound-electron g factor in heavy hydrogenlike ions is investigated. Numerical calculations are performed for the K- and L-shell electrons taking into account the dominant virtual nuclear excitations. This determines the ultimate limit for tests of QED utilizing measurements of the bound-electron g factor in highly charged ions.

Asymmetry of the natural line profile for the hydrogen atom.

The asymmetry of the natural line profile for transitions in hydrogenlike atoms is evaluated within a QED framework. For the Lyman- alpha 1s-2p absorption transition in neutral hydrogen this asymmetry results in an additional energy shift of 2.929 856 Hz. For the 2s(1/2)-2p(3/2) transition it amounts to -1.512 674 Hz. As a new feature this correction turns out to be process dependent. The quoted numbers refer to the Compton-scattering process.

Hyperfine structure of highly charged 23892U ions with rotationally excited nuclei

The hyperfine structure (hfs) of electron levels of 23892U ions with the nucleus excited in the low-lying rotational 2(+) state with an energy E(2(+)) = 44.91 keV is investigated. In hydrogenlike uranium, the hfs splitting for the 1s(1/2) ground state of the electron constitutes 1.8 eV. The hyperfine-quenched (hfq) lifetime of the 1s2p 3P0 state has been calculated for heliumlike 23892U and was found to be 2 orders of magnitude smaller than for the ion with the nucleus in the ground state. The possibility of a precise determination of the nuclear g(r) factor for the rotational 2(+) state by measurements of the hfq lifetime is discussed.

Dynamical casimir effect at finite temperature

Thermal effects on the creation of particles under the influence of time-dependent boundary conditions are investigated. The dominant temperature correction to the energy radiated by a moving mirror is derived by means of response theory. For a resonantly vibrating cavity the thermal effect on the number of created photons is obtained nonperturbatively. Finite temperatures can enhance the pure vacuum effect by several orders of magnitude. The relevance of finite-temperature effects for the experimental verification of the dynamical Casimir effect is addressed.