Beryllium-like Ions Research Articles

Doubly Excited States of Beryllium-Like Ions ($$Z = 4$$–10) in Dense Quantum Plasmas

Doubly Excited States of Beryllium-Like Ions ($$Z = 4$$–10) in Dense Quantum Plasmas

Merits of atomic cascade computations

Atomic cascades refer—first and foremost—to the stepwise de-excitation of excited atoms owing to the emission of electrons or photons. Apart from dedicated experiments at storage rings and synchrotrons, such cascades frequently occur in astro and plasma physics, material research, surface science and at various places elsewhere. In addition, moreover, “atomic cascades” have been found a useful concept for modeling atomic behavior under different conditions, for instance, when dealing with the photoabsorption of matter, the generation of synthesized spectra, or for determining a rather wide class of (plasma) rate coefficients. We here compile and discuss several atomic cascades (schemes) that help predict cross sections, rate coefficients, electron and photon spectra, or ion distributions. We also demonstrate how readily these schemes have been implemented within JAC, the Jena Atomic Calculator. Emphasis is placed on the classification of atomic cascades and their (quite) natural breakdown into cascade computations, to deal with the electronic structure and transition amplitudes of atoms and ions, as well as the cascade simulation of those properties and spectra, that are experimentally accessible. As an example, we show and discuss the computation of dielectronic recombination plasma rate coefficients for beryllium-like gold ions. The concept of atomic cascades and its implementation into JAC can be applied for most ions across the periodic table and will facilitate the modeling and interpretation of many forthcoming observations.Graphical abstract

Energies and radiative properties of 1s22l2l′ and 1s(2l)22l′ levels in tungsten ion, W70+

Multiconfiguration Dirac–Hartree–Fock (MCDHF) calculations of energy levels, oscillator strengths and transition rates of open K-shell transitions in beryllium-like tungsten ion, W[Formula: see text], are performed using the fully relativistic GRASP2018 code. For only principal quantum number [Formula: see text], energy levels of 1[Formula: see text] 2[Formula: see text], 1[Formula: see text]2[Formula: see text], 1[Formula: see text]2[Formula: see text], 1[Formula: see text]2p, 1[Formula: see text] and 1[Formula: see text] at different angular momenta and parity ([Formula: see text] are presented. Excitations of up to four electrons from the ground level, 1[Formula: see text] 2[Formula: see text], to excited levels are allowed. Correlations up to 5l orbitals are included in the configuration state function (CSF), [Formula: see text], p, d, f and g. The fine-structure calculations of E1, E2, M1 and M2 oscillator strengths and radiative rates between intercombination transitions in W[Formula: see text] ions are evaluated. The accuracy of these results is estimated using different ways, such as the comparison with previously published results and calculating the uncertainty of the transition data. The uncertainty of the transition probabilities showed low values for most of transitions.

X-Ray Photoabsorption of Density-sensitive Metastable States in Ne vii, Fe xxii, and Fe xxiii

Metastable states of ions can be sufficiently populated in absorbing and emitting astrophysical media, enabling spectroscopic plasma-density diagnostics. Long-lived states appear in many isoelectronic sequences with an even number of electrons, and can be fed at large rates by various photonic and electronic mechanisms. Here, we experimentally investigate beryllium-like and carbon-like ions of neon and iron that have been predicted to exhibit detectable features in astrophysical soft X-ray absorption spectra. An ion population generated and excited by electron impact is subjected to highly monochromatic X-rays from a synchrotron beamline, allowing us to identify Kα transitions from metastable states. We compare their energies and natural line widths with state-of-the-art theory and benchmark level population calculations at electron densities of 1010.5 cm−3.

Doubly excited states in hot and dense plasmas: Beryllium-like ions for [formula omitted

Effects of the hot and dense plasma on the doubly excited states (DES) of the four-electron beryllium-like ions (BLI) with Z varying from 4 to 10 have been investigated by applying the stabilization method. The Debye–Huckel model has been used to describe the effective potential in the plasma. The four-electron ions are treated as an effective three-body problem by means of the method of model potential. One, four and five DESs lying above the 1s2 2p threshold are found to exist in the ions having Z=4, Z=5 and Z=6−10 respectively. For the plasma-free case our results for the energy and width of the DESs are in agreement with the available results in the literature. A detailed study is made on the changes of energy and width of the DESs of the ions with varying plasma screening strength. Particular emphasis is given to explore the effects of the plasma on the whole sequence of ions.

Effect of the Breit interaction on inner-shell electron-impact excitation and subsequent radiative decay of highly charged berylliumlike ions

Effect of the Breit interaction on inner-shell electron-impact excitation and subsequent radiative decay of highly charged berylliumlike ions

Theoretical calculation of atomic spectrum for 1s23l4l′ states of beryllium-like ions

Using the saddle-point variation and saddle-point complex-rotation methods, energies, radiative, and Auger rates are calculated for the doubly-excited states 1s23l4l′ of beryllium-like ions. The total wave function is expanded by the restricted variation method to saturate the functional space and improve the nonrelativistic energy. Relativistic corrections and mass polarization effects are taken into account by the first-order perturbation theory. The partial Auger rates for these states are studied. The calculated Auger electron energies are compared with the experimental results which are observed in high resolution electron spectroscopy. The total radiative rates and the total Auger rates for these doubly-excited states 1s23l4l′ in the beryllium-like ions are also analyzed along with the increase of atomic number Z. Calculated results show that the total Auger rates are several orders of magnitude larger than the total radiative rates for these low-Z systems.

Relativistic calculations of the ground and inner- L -shell excited energy levels of berylliumlike ions

Large-scale relativistic configuration-interaction method combined with many-body perturbation theory is consistently applied to calculations of the energy levels of the ground and inner-L-shell excited states of berylliumlike ions in the range $10 \leq Z \leq 92$. The quantum electrodynamics, nuclear recoil, and frequency-dependent Breit corrections are taken into account. The obtained results are supplemented with the systematical estimation of the uncertainties.

Resonant and nonresonant indirect electron-impact single ionization of beryllium-like carbon ions via K-shell excitation

A joint experimental and theoretical study of electron-impact single ionization of beryllium-like carbon ions (C2+) is presented. Absolute cross sections are measured for electron-ion collision energies from the ionization onset up to 500 eV by using the animated crossed-beams method. Signatures of resonant and nonresonant indirect ionization processes involving the excitation of a K-shell electron were observed in the measured total ionization cross section. The present state-of-the-art distorted-wave–approximation calculations reproduce the experimentally observed structures well. Small remaining deviations of the theoretical data from the experimental findings show that the accurate description of many-body processes in highly correlated atomic systems remains a challenge.

Dipole Polarizabilities of the Ground States for Berylliumlike Ions**Supported by National Natural Science Foundation of China under Grant No. 11474020

Dipole polarizabilities of the ground states for berylliumlike ions with nuclear charge Z = 4 to 10 are calculated by using the Rayleigh-Ritz variational method with multiconfiguration interaction wave functions. The representative models of convergence are listed and compared with other theoretical data for nuclear charge Z = 4 to 6. The present dipole polarizabilities are in good agreement with previous accurate theoretical values available in the literature. For results with greater nuclear charge number, the present calculations may provide benchmarked data for future theoretical and experimental studies. Dynamic dipole polarizabilities of the ground state for the beryllium atom at selected frequencies are also calculated and compared with other theoretical values in the literature.

Doubly-Excited States of Beryllium-Like Ions with Screened Coulomb Potentials

The screening effects of the interaction potentials on the lowest 1S doubly-excited states of beryllium-like ions were investigated by calculating the density of resonance states within the framework of the stabilization method. Two types of screened interaction potentials, namely static screened Coulomb potential and exponential cosine screened Coulomb potential, were taken into consideration. A model potential was used to describe the interaction between the core and outer electrons, and the Be-like ions were treated as being effectively three-body systems. Calculations were performed for Be and B+. It was possible to calculate the energy and width of one doubly-excited state of Be and four doubly-excited states of B+ lying above the 1s22p threshold. Significant changes were found to exist in the behaviour of the width with varying screening parameters. To the best of our knowledge, such an investigation on the doubly-excited states of Be-like ions under screened environments is the first reported calculation of this type in the literature.

Electron–ion Recombination Rate Coefficients of Be-like 40Ca16+

Abstract Electron–ion recombination rate coefficients for beryllium-like calcium ions in the center of mass energy from 0 to 51.88 eV have been measured by means of the electron–ion merged-beam technique at the main cooler storage ring at the Institute of Modern Physics in Lanzhou, China. The measurement energy range covers the dielectronic recombination (DR) resonances associated with the core excitations and the trielectronic recombination (TR) resonances associated with the core excitations. In addition, the AUTOSTRUCTURE code was used to calculate the recombination rate coefficients for comparison with the experimental results. Resonant recombination originating from parent ions in the long-lived metastable state ions has been identified in the recombination spectrum below 1.25 eV. A good agreement is achieved between the experimental recombination spectrum and the result of the AUTOSTRUCTURE calculations when fractions of 95% ground-state ions and 5% metastable ions are assumed in the calculation. It is found that the calculated TR resonance positions agree with the experimental peaks, while the resonance strengths are underestimated by the theoretical calculation. Temperature dependent plasma rate coefficients for DR and TR in the temperature range of 103–108 K were derived from the measured electron–ion recombination rate coefficients and compared with the available theoretical results from the literature. In the temperature range of photoionized plasmas, the presently calculated rate coefficients and the recent results of Gu & Colgan et al. are up to 30% lower than the experimentally derived ones, and the older atomic data are even up to 50% lower than the present experimental result. This is because strong resonances situated below electron–ion collision energies of 50 meV were underestimated by the theoretical calculation, which also has a severe influence on the rate coefficients in low-temperature plasmas. In the temperature range of collisionally ionized plasmas, agreement within 25% was found between the experimental result and the present calculation as well as the calculation by Colgan et al. The present result constitutes a set of benchmark data for use in astrophysical modeling.

Absolute rate coefficients for photorecombination of beryllium-like and boron-like silicon ions

We report measured rate coefficients for electron–ion recombination of Si10+ forming Si9+ and of Si9+ forming Si8+, respectively. The measurements were performed using the electron–ion merged-beams technique at a heavy-ion storage ring. Electron–ion collision energies ranged from 0 to 50 eV for Si9+ and from 0 to 2000 eV for Si10+, thus, extending previous measurements for Si10+ (Orban et al 2010 Astrophys. J. 721 1603) to much higher energies. Experimentally derived rate coefficients for the recombination of Si9+ and Si10+ ions in a plasma are presented along with simple parameterizations. These rate coefficients are useful for the modeling of the charge balance of silicon in photoionized plasmas (Si9+ and Si10+) and in collisionally ionized plasmas (Si10+ only). In the corresponding temperature ranges, the experimentally derived rate coefficients agree with the latest corresponding theoretical results within the experimental uncertainties.

Relativistic evaluation of the two-photon decay of the metastable1s22s2p3P0state in berylliumlike ions with an effective-potential model

The two-photon ${1s}^{2} 2s 2p~^3\mbox{P}_0 \rightarrow {1s}^{2} {2s}^2$ $^1\mbox{S}_0$ transition in berylliumlike ions is theoretically investigated within a full relativistic framework and a second-order perturbation theory. We focus our analysis on how electron correlation, as well as the negative-energy spectrum can affect the forbidden $E1M1$ decay rate. For this purpose we include the electronic correlation by an effective potential and within an active-electron model. Due to its experimental interest, evaluation of decay rates are performed for berylliumlike xenon and uranium. We find that the negative-energy contribution can be neglected in the present decay rate. On the other hand, if contributions of electronic correlation are not carefully taken into account, it may change the lifetime of the metastable state by 20\%. By performing a full-relativistic $jj$-coupling calculation, we found discrepancies for the decay rate of an order of 2 compared to non-relativistic $LS$-coupling calculations, for the selected heavy ions.

Relativistically prolonged lifetime of the 2s2p 3P0 level of zero nuclear-spin beryllium-like ions

The E1M1 transition rate of the line in beryllium-like ions has been calculated within the framework of relativistic second-order perturbation theory. Both multiconfiguration and quantum-electrodynamical computations have been carried out independently to better understand and test for all major electron–electron correlation contributions in the representation of the initial, intermediate and final states. By comparing the results from these methods, which agree well for all ions along the beryllium isoelectronic sequence, the lifetime of the metastable 2s2p 3P0 level is found to be longer by about 2–3 orders of magnitude for all medium and heavy elements than was estimated previously. This makes the 3P0 level of beryllium-like ions to one of the longest living (low-lying) electronic excitations of a tightly bound system with potential applications for atomic clocks and in astro physics and plasma physics.

Ionization energies along beryllium isoelectronic sequence

Ionization energies for the ground state of berylliumlike ions with nuclear charge numbers in the range Z=16-96 are rigorously evaluated. The calculations merge the ab initio QED treatment in the first and second orders of the perturbation theory in the fine-structure constant $\alpha$ with the third- and higher-order electron-correlation contributions evaluated within the Breit approximation. The nuclear recoil and nuclear polarization effects are taken into account. The accuracy of the ionization energies obtained has been significantly improved in comparison with previous calculations.

Isotope Shift Calculations of Stable and Short-Lived Beryllium Isotopes**Supported by the Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant No 14JK1402.

The isotope shifts of the 2s2 1S0 to 2s2p 1P1 and 3P1 transitions in the four-electron beryllium atom are calculated by using the multi-configuration Dirac–Hartree–Fock method and the relativistic configuration interaction approach for the stable and short-lived beryllium isotopes. The results provided herein can be employed for the consistency check with the nuclear rms charge radii from the experimental isotope shifts by using the corresponding transitions for the short-lived nuclei7,10–12Be and 14Be. The analogous isotope shift results could also be obtained for the beryllium-like ions by the methods used here.

QED calculation of the ground-state energy of berylliumlike ions

The calculations of the ground-state binding energies and ionization potentials for berylliumlike ions were performed in the range 18\ensuremath{\le}Z\ensuremath{\le}96 including the QED corrections up to the second order in $\ensuremath{\alpha}$ and the electron-correlation effects to all orders in 1/Z.

Polarization of M2 line emitted from highly-charged beryllium-like ions following electron-impact excitation

The contributions of the Breit interaction to the linear polarization of the 1s2s22p3/2 J=2 → 1s22s2 J=0 magnetic quadrupole (M2) line following electron-impact excitation have been investigated systematically for the beryllium isoelectronic sequence with 42 ≤ Z ≤ 92. It is found that the Breit interaction depolarizes significantly the linear polarization of the M2 fluorescence radiation and that these depolarization effects increase as the incident electron energy and/or the atomic number is enlarged.

Theoretical study of inner-shell electron-impact excitation of highly charged ions: Alignment and angular distribution of electron emission

The influence of the Breit interaction, typically appears as a relativistic correction to the Coulomb repulsion acting among the electrons, on the alignment (i.e. the population of the magnetic sublevels) and the angular distribution of electron emission from the excited state have been investigated systematically. Detailed calculations have been carried out for the electron-impact excitation cross sections from the ground state to the individual magnetic sublevels of highly charged beryllium-like ions by using a fully relativistic distorted-wave (RDW) method. A remarkable change in the alignment and the electron angular distribution due to the Breit interaction is found, especially for the cases with high-energetic incident electron and high-Z target ions.