g Factor of Lithiumlike Silicon and Calcium: Resolving the Disagreement between Theory and Experiment.

The bound-electron g factor is a stringent tool for tests of the standard model and the search for new physics. The comparison between an experiment on the g factor of lithiumlike silicon and the two recent theoretical values revealed the discrepancies of 1.7σ [Glazov et al. Phys. Rev. Lett. 123, 173001 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.173001] and 5.2σ [Yerokhin et al. Phys. Rev. A 102, 022815 (2020)PLRAAN2469-992610.1103/PhysRevA.102.022815]. To identify the reason for this disagreement, we accomplish large-scale high-precision computation of the interelectronic-interaction and many-electron QED corrections. The calculations are performed within the extended Furry picture of QED, and the dependence of the final values on the choice of the binding potential is carefully analyzed. As a result, we significantly improve the agreement between the theory and experiment for the g factor of lithiumlike silicon. We also report the most accurate theoretical prediction to date for lithiumlike calcium, which perfectly agrees with the experimental value.

Breakdown of the electric dipole approximation at Cooper minima in direct two-photon ionisation.

We predict breakdown of the electric dipole approximation at nonlinear Cooper minimum in direct two-photon K-shell atomic ionisation by circularly polarised light. According to predictions based on the electric dipole approximation, we expect that tuning the incident photon energy to the Cooper minimum in two-photon ionisation results in pure depletion of one spin projection of the initially bound 1s electrons, and hence, leaves the ionised atom in a fully oriented state. We show that by inclusion of electric quadrupole interaction, dramatic drop of orientation purity is obtained. The low degree of the remaining ion orientation provides a direct access to contributions of the electron-photon interaction beyond the electric dipole approximation in the two-photon ionisation of atoms and molecules. The orientation of the photoions can be experimentally detected either directly by a Stern-Gerlach analyzer, or by means of subsequent Kα fluorescence emission, which has the information about the ion orientation imprinted in the polarisation of the emitted photons.

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.

Ab initio QED Treatment of the Two-Photon Annihilation of Positrons with Bound Electrons.

The process of a positron-bound-electron annihilation with simultaneous emission of two photons is investigated theoretically. A fully relativistic formalism based on an ab initio QED description of the process is worked out. The developed approach is applied to evaluate the annihilation of a positron with K-shell electrons of a silver atom, for which a strong contradiction between theory and experiment was previously stated. The results obtained here resolve this longstanding disagreement and, moreover, demonstrate a sizable difference with approaches so far used for calculations of the positron-bound-electron annihilation process, namely, Lee's and the impulse approximations.

g Factor of Boronlike Argon

We have measured the ground-state g factor of boronlike argon ^{40}Ar^{13+} with a fractional uncertainty of 1.4×10^{-9} with a single ion in the newly developed Alphatrap double Penning-trap setup. The value of g=0.663 648 455 32(93) obtained here is in agreement with our theoretical prediction of 0.663 648 12(58). The latter is obtained accounting for quantum electrodynamics, electron correlation, and nuclear effects within the state-of-the-art theoretical methods. Our experimental result distinguishes between existing predictions that are in disagreement, and lays the foundations for an independent determination of the fine-structure constant.

Maximum Elliptical Dichroism in Atomic Two-Photon Ionization.

Elliptical dichroism is known in atomic photoionization as the difference in the photoelectron angular distributions produced in nonlinear ionization of atoms by left- and right-handed elliptically polarized light. We theoretically demonstrate that the maximum dichroism |Δ_{ED}|=1 always appears in two-photon ionization of any atom if the photon energy is tuned in so that the electron emission is dominantly determined by two intermediate resonances. We propose the two-photon ionization of atomic helium in order to demonstrate this remarkable phenomenon. The maximum elliptical dichroism could be used as a sensitive tool for analyzing the polarization state of photon beams produced by free-electron lasers.

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.

Spectral shape of the two-photon decay of the 2 1S0 state in he-like tin.

The spectral distribution of the 1s2s {1}S{0}-->1s{2} 1S0 two-photon decay of He-like tin was measured using a novel approach at the gas-jet target of the ESR storage ring. Relativistic collisions of Li-like projectiles with low-density gaseous matter have been exploited to selectively populate the desired 1s2s state. Compared to conventional techniques, this approach results in a substantial gain in statistical and systematic accuracy, which allowed us to achieve for the first time a sensitivity to relativistic effects on the two-photon decay spectral shape as well as to discriminate the measured spectrum for Sn from theoretical shapes for different elements along the He-isoelectronic sequence.

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.

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.

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.