Two-electron One-photon Transitions Research Articles

QED calculation of two-electron one-photon transition probabilities in He-like ions

We consider theoretically the process of two-electron one-photon (TEOP) transitions to the ground state with the emission of a single ${K}_{\ensuremath{\alpha}\ensuremath{\alpha}}$ photon in a He-like sequence of atomic ions: from boron to uranium. The corresponding transition probabilities and transition energies are calculated within the QED theory. The calculations of the transition probabilities are performed in various gauges. The intensity ratios between the TEOP transitions and the other major transitions are presented.

Observation of strong two-electron–one-photon transitions in few-electron ions

We resonantly excite the $K$ series of O$^{5+}$ and O$^{6+}$ up to principal quantum number $n=11$ with monochromatic x rays, producing $K$-shell holes, and observe their relaxation by soft-x-ray emission. Some photoabsorption resonances of O$^{5+}$ reveal strong two-electron--one-photon (TEOP) transitions. We find that for the $[(1s\,2s)_1\,5p_{3/2}]_{3/2;1/2}$ states, TEOP relaxation is by far stronger than the radiative decay and competes with the usually much faster Auger decay path. This enhanced TEOP decay arises from a strong correlation with the near-degenerate upper states $[(1s\,2p_{3/2})_1\,4s]_{3/2;1/2}$ of a Li-like satellite blend of the He-like $K\alpha$ transition. Even in three-electron systems, TEOP transitions can play a dominant role, and the present results should guide further research on the ubiquitous and abundant many-electron ions where electronic energy degeneracies are far more common and configuration mixing is stronger.

Interference between dielectronic recombination with two-electron one-photon transitions and radiative recombination

We have studied two-electron one-photon transitions in dielectronic recombination with H-like ions ($Z=5--54$) within ab initio QED theory. It was found that interference between dielectonic recombination with two-electron one-photon transitions and radiative recombination is prominent for light and medium ions being large enough for experimental observation. The interference manifests itself firstly in a sharp Fano-like resonance structure and secondly in a noticeable distortion of the photon angular distribution of the radiative recombination.

Effects of electron correlation and the Breit interaction on one- and two-electron one-photon transitions in double K hole states of He-like ions (10 ≤ Z ≤ 47)**Project supported by the National Natural Science Foundation of China (Grant Nos. U1832126 and 11874051) and the National Key Research and Development Program of China (Grant No. 2017YFA0402300).

The x-ray energies and transition rates associated with single and double electron radiative transitions from the double K hole state 2s2p to the 1s2s and 1s2 configurations of 11 selected He-like ions (10 ≤ Z ≤ 47) are calculated using the fully relativistic multi-configuration Dirac–Fock method (MCDF). An appropriate electron correlation model is constructed with the aid of the active space method, which allows the electron correlation effects to be studied efficiently. The contributions of the electron correlation and the Breit interaction to the transition properties are analyzed in detail. It is found that the two-electron one-photon (TEOP) transition is correlation sensitive. The Breit interaction and electron correlation both contribute significantly to the radiative transition properties of the double K hole state of the He-like ions. Good agreement between the present calculation and previous work is achieved. The calculated data will be helpful to future investigations on double K hole decay processes of He-like ions.

Investigation of TEOP transitions in dielectronic recombination with H-like ions

SynopsisWe consider theoretically the process of dielectronic recombination (DR) with H-like ions where two-electron one-photon (TEOP) transitions take place. We focus our attention on the channel with transitions to the ground state of the He-like ions and emission of Kαα photon. Total and differential cross sections of DR with TEOP are calculated for wide range of H-like ions: from B4+ to Xe53+. The resonant Fano-like structure of the cross section is observed. The resonant energies, widths and TEOP transition probabilities are calculated.

Observation of two-electron one-photon X-ray transitions in collisions of slow Xe26+ ions with beryllium surface

SynopsisTwo-Electron One-Photon (TEOP) X-ray transitions were observed for the first time in collisions of highly charged Xe ions with metallic Be surface. The intensities of TEOP X-rays are well described by performed MCDF for one-electron one-photon (OEOP) dipole-allowed transition of Paschen and Brackett series assuming constant TEOP/OEOP branching ratio. The importance of the Internal Dielectronic Excitation (IDE) in relaxation of hollow Xe ions/atoms has been evidenced and discussed.

Radiative de-excitations of the 1s2s3s configuration of Li-like ions

The fully relativistic configuration interaction method is used to study the one-electron one-photon (OEOP) and two-electron one-photon (TEOP) transitions between the 1s2s3s and the respective 1s2s2p and 1s2np (n = 2–4 ) groups of Li-like ions with 12 ≤ Z ≤ 54. The transition properties are calculated using multi-configuration Dirac–Fock wavefunctions in the active space approximation taking into account the correlated state functions that have non-negligible contributions to the mixing coefficients. The drastic variations in the level lifetimes due especially to 1s2s3s-1s2np (n = 2, 3) transitions are analyzed in detail. The OEOP transition energies are far less than those of TEOP transitions and have been taken up in this work mainly to investigate the most probable radiative decay channel and also to understand the interplay between electron–electron correlation and the low-frequency limit transverse photon interaction on the mixing coefficients of J = 3/2 states of 1s2s2p around Z = 21. The present results are compared with other available data.

Theoretical determination of two-electron one-photon transition characteristics for low- Z K -shell hollow atoms

Studying $K$-shell hollow atom spectra broadens our knowledge on femtosecond phenomena in atomic physics, chemistry, and biology. Recent synchrotron measurements of the two-electron one-photon (TEOP) transitions of low-$Z$ atoms have shown discrepancies between experiment and theoretical predictions of the TEOP relative intensities and their linewidths. The discrepancies seem to be a result of an incomplete description of an atomic response to the strong perturbation due to the $K$-shell double photoionization (DPI). A theoretical attempt, based on the multiconfiguration Dirac-Fock relativistic configuration interaction method, is presented for Mg, Al, and Si atoms. It is demonstrated that both the branching ratios and the TEOP linewidths can be closely reproduced by taking into account the influences of the core and valence electron correlations, open-shell valence configuration, and the outer-shell ionization and excitation processes following the $K$-shell DPI.

Anomalously strong two-electron one-photon X-ray decay transitions in CO caused by avoided crossing.

The unique opportunity to study and control electron-nuclear quantum dynamics in coupled potentials offered by the resonant inelastic X-ray scattering (RIXS) technique is utilized to unravel an anomalously strong two-electron one-photon transition from core-excited to Rydberg final states in the CO molecule. High-resolution RIXS measurements of CO in the energy region of 12–14 eV are presented and analyzed by means of quantum simulations using the wave packet propagation formalism and ab initio calculations of potential energy curves and transition dipole moments. The very good overall agreement between the experimental results and the theoretical predictions allows an in-depth interpretation of the salient spectral features in terms of Coulomb mixing of “dark” with “bright” final states leading to an effective two-electron one-photon transition. The present work illustrates that the improved spectral resolution of RIXS spectra achievable today may call for more advanced theories than what has been used in the past.

Two-electron one-photon transitions in Li-like ions

Two-electron one-photon transitions in Li-like ions

Radiative decay from doubly and singly excited states of He-like nickel

Fully relativistic calculations on the level energies and radiative lifetimes for all the low-lying levels of He-like Ni have been systematically carried out and attention has been paid to provide a complete tabulation of data for all the conceivable one- and two-electron one-photon transitions from levels of $2{p}^{2}$ configuration decaying sequentially to the ${}^{1}{S}_{0}$ ground state. Large-scale multiconfiguration Dirac-Fock wave functions have been applied to study the level features. The accuracy of our computed data has been highlighted in terms of the uncertainty estimates on the fine structure energy levels and also on the line strengths. The branching ratios of the emitted radiations from various transitions are evaluated. The sensitivity of transition rates to Breit interaction and quantum elctrodynamics effects are analyzed in detail. A comparison of our results with available experimental and previous computations is also made.

Photoinduced K-shell hollow atoms

The mechanisms leading to the production of hollow K shell atoms via single photon impact were investigated for a variety of light elements with 12≤Z≤23. The double 1s vacancy states were produced by irradiating the samples with intense monoenergetic synchrotron radiation beams. The double-to-single K-shell photoionization probabilities PKK and the absolute double K-shell photoionization cross sections σ2+ were determined by measuring with a high-resolution bent von Hamos crystal spectrometer the Kαh hypersatellite X-ray emission of the samples. The measurements were performed over a wide range of incoming photon energies from threshold up to energies beyond the broad maximum of the double-to-single photoionization cross section ratios. The PKK and σ2+ were determined from the relative yields of the resolved Kαh hypersatellite lines. For Mg, Al and Si, the two-electron one-photon (TEOP) Kααh transitions which represent an alternative but much weaker decay channel for double 1s vacancy states could be also observed, using a highly efficient flat crystal wavelength dispersive spectrometer. This observation of single photon-induced TEOP transitions has shown that the I(Kαh)/I(Kααh) branching ratios are very poorly reproduced by most of existing theoretical models. Besides the relative yields of the hypersatellite and TEOP transitions, the energies and natural linewidths of the Kαh and Kααh X-ray lines were also determined. The energies are found to be in good agreement with different theoretical predictions, whereas the linewidths are significantly underestimated by the calculations, except if non-lifetime broadening effects such as the outer-shell ionization and the open valence configuration are taken into consideration.

First Observation of Two-Electron One-Photon Transitions in Single-PhotonK-Shell Double Ionization

Experimental evidence for the correlated two-electron one-photon transitions (1s(-2)→2s(-1)2p(-1)) following single-photon K-shell double ionization is reported. The double K-shell vacancy states in solid Mg, Al, and Si were produced by means of monochromatized synchrotron radiation, and the two-electron one-photon radiative transitions were observed by using a wavelength dispersive spectrometer. The two-electron one-photon transition energies and the branching ratios of the radiative one-electron to two-electron transitions were determined and compared to available perturbation theory predictions and configuration interaction calculations.

Two-electron one-photon transitions in atoms with 12 ⩽ Z ⩽ 80

Relativistic configuration interaction results are presented for the Kαα x-rays arising from the decay of doubly ionized K shell of atoms with 12 ⩽ Z ⩽ 80. The x-ray energies and dipole rates are calculated in the active space approximation using multi-configuration Dirac–Fock wavefunctions with the inclusion of the Breit interaction and quantum electrodynamics corrections. The calculations include all single and double excitations from core-valence interactions. The resulting length and velocity gauge transition rates are well converged and are in good agreement with the allowed transition, while the intercombination line rate is seen to be gauge dependent. Conclusions concerning the relative importance of correlation and the Breit interaction on the intensity ratios are obtained in some detail. The sensitivity of the relative intensities of the fine structure lines to the coupling variations in both length and velocity gauges is analysed. The calculated results are compared with previous experimental and theoretical data.

The effect of a 2s vacancy on two-electron–one-photon lines: Relativistic approach

Energies and rates for two-electron–one-photon transitions and their satellites have been calculated using multiconfiguration Dirac–Fock method for a number of atoms having nuclear charges within Z = 12 – 20 . In addition, the energies and transition rates of the K α hypersatellite lines have been computed for these atoms. From these rates, the branching ratios between the K α hypersatellite and two electron one photon lines are evaluated and compared with existing experimental and theoretical results.

Ritz variational calculation for two-electron–one-photon transitions in helium

Variational calculations for the energy levels of doubly excited $3dnf$ $(^{1,3}D^{\ensuremath{\circ}})$ states $(n=4--12)$ for helium have been performed using the extended Hylleraas basis set. No previous calculations for the energy eigen-values for the $3dnf$ $(^{1,3}D^{\ensuremath{\circ}})$ states for $(n=7--12)$ exist. Prediction of two-electron--one-photon peaks at 12.220, 12.649, 12.859, 12.978, 13.054, 13.110, 13.141, 13.168 and $13.213\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ corresponding to the transitions $2{p}^{2}$ $(^{3}P^{\mathrm{e}})\ensuremath{\rightarrow}3dnf$ $(^{3}D^{\ensuremath{\circ}})$ $(n=4--12)$, respectively, is reported here. Highly precise energy eigenvalues of doubly excited $2pnd$ states $(^{1,3}D^{\ensuremath{\circ}})$ $(n=3--8)$ for helium are also reported and the upper bound energies are the lowest yet obtained. The effective quantum numbers $({n}^{*})$ of the above mentioned states are calculated using quantum defect theory.

High precision measurements of forbidden transitions in highly charged ions at the Heidelberg EBIT

Few-electron ions, which can be produced and studied at rest in electron beam ion traps (EBITs) are very well suited for the study of nuclear size effects and QED in strong fields, but the various contributions are usually entangled. Therefore, combinations of experiments with ions in different charge states are required to separate those contributions. In order to achieve this, several spectroscopic techniques have been recently implemented at the Heidelberg EBIT, aiming at high resolution and accuracy. In the optical region the most accurate wavelengths ever reported for highly charged ions [Draganić et al., Phys. Rev. Lett. 91 (2003) 183001] have been obtained, the results being sensitive to isotopic shifts [Tupitsyn et al., Phys. Rev. A 68 (2003) 022511] at the 0.01meV level. The forbidden transitions of B-like ArXIV and Be-like ArXV ions studied here are especially interesting, since the QED contributions are as large as 0.2%. Improved atomic structure calculations allow to determine their values with growing accuracy, although the theoretical accuracy still lags three to four orders of magnitude behind the experimental one. In a different experiment, the lifetime of the corresponding metastable level has also been measured with an uncertainty of less than 0.2% thus becoming sensitive to the influence of the bound electron anomalous magnetic moment, an almost experimentally unexplored QED effect so far. A new laser spectroscopic setup aims at facilitating future studies of the hyperfine structure of heavy hydrogenic ions. Through the study of the dielectronic recombination, information on rare processes, such as two-electron–one-photon transitions in Ar16+ [Zou et al., Phys. Rev. A 67 (2003) 42703] at energies of around 2keV, or the interference effects between dielectronic and radiative recombination in Hg77+ at 50keV, and accurate values for the excitation energies of very heavy HCI have been obtained. A novel X-ray crystal spectrometer allowing absolute X-ray wavelength measurements in the range up to 15keV with very high precision and reproducibility is currently used to study the Lyman series of H-like ions of medium-Z ions and the 2s–2p transitions of very heavy Li-like ions.

Relativistic calculation of two-electron one-photon and hypersatellite transition energies for 12 ⩽ Z ⩽ 30 elements

Energies of two-electron one-photon transitions from initial double K-hole states were computed using the Dirac–Fock model. The transition energies of competing processes, the Kα hypersatellites, were also computed. The results are compared with experiment and to other theoretical calculations.

Observation of dielectronic recombination through two-electron–one-photon correlative stabilization in an electron-beam ion trap

Dielectronic recombination (DR) for He-like ${\mathrm{Ar}}^{16+}$ through both one-electron--one-photon and two-electron--one-photon (TEOP) stabilizations of Li-like states was studied with an electron-beam ion trap (EBIT). It turned out that this is an excellent method to investigate TEOP transitions. Its advantages are a high branching ratio for the TEOP transition and clean conditions under which spectator electrons are controlled. Further, state- and configuration-resolved KLL DR cross sections were obtained due to the unsurpassed electron energy resolution achieved in the EBIT in the energy range around 2 keV.

Two-electron one-photon transition relativistic calculations for low-Z elements

Energies of two-electron one-photon transitions from initial double K-hole states and the transition energies of competing processes, namely Kα hyper-satellites, were computed for low-Z elements, using the multi-configuration Dirac–Fock method. Transition rates are also evaluated.