He-like Ions Research Articles

Multiconfiguration Dirac–Hartree–Fock calculations of energy levels, wavelengths, weighted oscillator strengths, transitions probabilities and lifetimes of Cd XLVII

Abstract Energy levels, wavelengths, weighted oscillator strengths, transition probabilities and lifetimes are calculated for all levels of 1s 2 and 1snl (n = 2–6) configurations of He-like cadmium ion (Cd XLVII). The calculations were carried out using three codes GRASP2018, FAC and AMBiT in order to provide theoretically the most accurate data. Transition probabilities are reported for all the E1, E2, M1 and M2 transitions. Breit interactions and quantum electrodynamics effects are included in the RCI calculations. Comparisons were made with other calculations and a good agreement was found which confirms the reliability of our results. We present some missing data for the He-like cadmium in this paper for the first time.

Debye-screening effect on electron-impact excitation of helium-like Al11+ and Fe24+ ions

Debye-screening effects on the electron-impact excitation (EIE) processes for the dipole-allowed transition 1s2 1 S → 1s2p 1P in He-like Al11+ and Fe24+ ions are investigated using the fully relativistic distorted-wave methods with the Debye–Hückel (DH) model potential. Debye-screening effects on the continuum-bound (CB) interaction and target ion are discussed, both of which result in reduction of EIE cross sections. This reduction due to screening on the CB interaction is dominant. The non-spherical and spherical DH potentials are adopted for considering the screening effect on the CB interaction. It is found that the spherical DH potential could significantly overestimate the influence of plasma screening on EIE cross sections for multielectron He-like ions.

Redshift of the isolated atomic emission line in dense plasma

We have shown recently that the redshifts of the isolated emission lines of the H-like and He-like ions subject to outside dense plasma environment could be estimated by carefully examining the spatial and temporal criteria of the classical Maxwell-Boltzmann statistics based on the Debye-Hückel (DH) approximation with the nucleus charge Z approximately between 6 and 18. The theoretical results are obtained with the input of the atomic data generated from the detailed non-relativistic and relativistic multi-configuration atomic structure calculations. Qualitatively, starting from the quasi-hydrogenic picture, we are able to show that the redshifts of these emission lines could be expressed in terms of a general expression as a function of an ad hoc parameter, i.e. reduced Debye length and, in turn, linking directly to the ratio between the electron density and the temperature of the dense plasma. Based on our earlier calculation, the results of our estimated redshifts are in good agreement with the most recent experimental measurements.

Variations of the Hartree-Fock fractional-spin error for one electron.

Fractional-spin errors are inherent in all current approximate density functionals, including Hartree-Fock theory, and their origin has been related to strong static correlation effects. The conventional way to encode fractional-spin calculations is to construct an ensemble density that scales between the high-spin and low-spin densities. In this article, we explore the variation of the Hartree-Fock fractional-spin (or ghost-interaction) error in one-electron systems using restricted and unrestricted ensemble densities and the exact generalized Hartree-Fock representation. By considering the hydrogen atom and H+ 2 cation, we analyze how the unrestricted and generalized Hartree-Fock schemes minimize this error by localizing the electrons or rotating the spin coordinates. We also reveal a clear similarity between the Coulomb hole of He-like ions and the density depletion near the nucleus induced by the fractional-spin error in the unpolarized hydrogen atom. Finally, we analyze the effect of the fractional-spin error on the Møller-Plesset adiabatic connection, excited states, and functional- and density-driven errors.

Ground State Energies of Helium-Like Ions Using a Simple Parameter-Free Matrix Method

This study aims to use hydrogenic orbitals within an analytic and numeric parameter-free truncated-matrix method to solve the projected Schrödinger equation of some Helium-like ions (3 ≤ Z ≤ 10). We also derived a new analytical expression of the ion ground state energies, which was simple and accurate and improved the accuracy of the analytic calculation, numerically using Mathematica. The standard matrix method was applied, where the wave function of the ions was expanded in a finite number of eigenvectors comprising hydrogenic orbitals. The Hamiltonian of the systems was calculated using the wave function and diagonalized to obtain their ground state energies. The results showed that a simple analytic expression of the ground state energies of He-like ions was successfully derived. Although the analytic expression was derived without involving any variational parameter, it was reasonably accurate with a 0.12% error for Ne8+ ion. From this method, the accuracy of the analytic energies was also numerically improved to 0.10% error for Ne8+ ion. The results clearly showed that the energies obtained using this method were more accurate than the hydrogenic perturbation theory and the uncertainty principle-variational approach. In addition, for Z > 4, our results were more accurate than those from the geometrical model.

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.

Particle transport constraints via Bayesian spectral fitting of multiple atomic lines

Optimized operation of fusion devices demands detailed understanding of plasma transport, a problem that must be addressed with advances in both measurement and data analysis techniques. In this work, we adopt Bayesian inference methods to determine experimental particle transport, leveraging opportunities from high-resolution He-like ion spectra in a tokamak plasma. The Bayesian spectral fitting code is used to analyze resonance (w), forbidden (z), intercombination (x, y), and satellite (k, j) lines of He-like Ca following laser blow-off injections on Alcator C-Mod. This offers powerful transport constraints since these lines depend differently on electron temperature and density, but also differ in their relation to Li-like, He-like, and H-like ion densities, often the dominant Ca charge states over most of the C-Mod plasma radius. Using synthetic diagnostics based on the AURORA package, we demonstrate improved effectiveness of impurity transport inferences when spectroscopic data from a progressively larger number of lines are included.

Spectroscopic comparison method for determining the electron temperature of high-temperature plasmas of heavy element

For further development of the comparison method, the X-ray spectra of laser plasmas of light (Si, S, Cl, K, Ca, Ti) and heavy (Mo, W) elements are studied. Plasma is produced by focusing nanosecond laser radiation (λ = 0.53 μm, E L = 5 J, τ = 2 ns) onto massive solid targets. The spectra are recorded using two focusing crystal spectrometers in the wavelength range λ = 2 – 11 Å. A detailed analysis of H- and He-like ion spectra is performed to determine the dependence of the electron temperature (T e = 500 – 800 eV) on the energy of laser pulses (E L = 0.5 – 5 J). Recommendations are given for measuring T e from the spectra of light elements with maximum accuracy. The comparison method is employed to estimate the electron temperature of the plasmas of heavy elements (Mo, W), whose X-ray spectra are complex in structure.

Multiconfiguration Dirac–Hartree–Fock energy levels, weighted oscillator strengths, transitions probabilities, lifetimes, hyperfine interaction constants, Landé g-factors and isotope shifts of O VII

Energy levels, weighted oscillator strengths and transition probabilities, lifetimes, hyperfine interaction constants, Landé gJ factors and isotope shifts have been calculated for all levels of 1s2 and 1snl (n=2-8,l⩽7) configurations of He-like oxygen ion (O VII). The calculations were performed using the Multiconfigurational Dirac-Hartree–Fock (MCDHF) and the Relativistic Configuration Interaction (RCI) methods. A second set of calculations was obtained with the Many Body Perturbation Theory (MBPT) method. Transition probabilities are reported for all E1,E2,M1 and M2 transitions. Breit interactions and quantum electrodynamics effects were included in the RCI calculations. Comparisons have been made with the compiled data from the NIST ASD and other calculations and a good agreement was found which confirms the reliability of our results. The accuracy of the present calculations is high enough to facilitate identification of many observed spectral lines. For the first time, we present some missing data for the He-like oxygen ion.

A study of some atomic properties for He-like selected ions

The atomic properties have been studied for He-like ions (He atom, Li+, Be2+ and B3+ions). These properties included, the atomic form factor f(S), electron density at the nucleus , nuclear magnetic shielding constant and diamagnetic susceptibility ,which are very important in the study of physical properties of the atoms and ions. For these purpose two types of the wave functions applied are used, the Hartree-Fock (HF) waves function (uncorrelated) and the Configuration interaction (CI) wave function (correlated). All the results and the behaviors obtained in this work have been discussed, interpreted and compared with those previously obtained.

Compact X-ray laser amplifier in the “Water Window”

Spectroscopy and microscopy in the so-called “water-window” is a holy grail of modern molecular biology. A pulsed source of coherent X-rays within this spectral window, falling between 2.3 nm and 4.4 nm, provides a unique tool for time-resolved imaging of bio-systems in their naturally water-rich state. Within this spectral range, water is mostly transparent, while proteins are mostly opaque. This results in a high-contrast image on the sub-cellular level. Here we present, for the first time, generation of a very high gain of G≈ 60/cm in He-like CV ions via transitions to the ground state at 4.03 nm in a table-top device.

Confined atoms in plasma environment: variational Monte Carlo calculations

Hydrogen (H) and Helium (He) atoms restricted by an impenetrable spherical box within plasma environment sight are investigated. The effect of compression and the presence of the plasma environment on the energy of H and He in the ground state is investigated. The plasma effect is considered by utilising Debye screening potential. The Schrödinger equation is solved using the variational Monte Carlo method with a compact trial wave function depending on many variational parameters. Our results are compared with the most recent accurate values. The obtained results are in agreement with the latest results. These results could be extended to incorporate He-like ions up to Z = 10 with good precision.

Variational Calculation of the Doubly-Excited States Nsnp of He-Like Ions via the Modified Atomic Orbitals Theory

In this paper, we have declined the formalism of the method of the Modified Atomic Orbital Theory (MAOT) applied to the calculations of energies of doubly excited states 2snp, 3snp, and 4snp Helium-like systems. Then we also applied the variational procedure of the Modified Atomic Orbital Theory to the computations of total energies, excitation energies of doubly-excited states 2snp, 3snp, 4snp types of Helium-like systems. The results obtained in this work are in good agreement with the experimental and theoretical values available.

Analytical Calculation of Cl$$^{15+}$$ Ion Immersed in Dense Plasmas

A method of analytically calculating energy levels of He-like ions in an environment of dense plasma is given by using the angular momentum coupling theory and irreducible tensor theory under Hartree–Fock approximation. In order to obtain higher calculation precision, relativistic correction terms of the non-relativistic energy including corrections caused by relativistic mass, one- and two-body Darwin effect, spin–spin contact interaction and orbit–orbit interaction, are calculated. The binding energies of the ground state $$1s^2$$ $$^1S$$ and excited state 1snp $$^1P$$ (n = 1 − 4) of He-like Cl ions and the transition energy between two energy levels in an environment of dense plasma are calculated. The scaling relationship between the energy shift of plasma and its temperature and density is given. According to our study, the energy shift of plasma conforms very well with the recent high-precision experimental result (Phys Rev A 100:012511, 2019).

Measuring the oscillator strength of intercombination lines of helium-like V ions in a laser-produced-plasma

We present results of measurements of the oscillator strength of intercombination lines of He-like Vanadium ions in high energy density (HED) laser-produced-plasmas and compare them with the simulations from commonly used codes and data from the NIST database. Whilst not yet sufficiently accurate to constrain different trusted atomic-physics models for the particular system studied, our results are in agreement with the available data within experimental error bars, yet differ from cruder approximations of the oscillator strength used in certain atomic-kinetics packages, suggesting that this general method could be further extended to be used as a measurement of the oscillator strength of additional atomic transitions under the extreme conditions that are achieved in HED experiments.

PyAtomDB: Extending the AtomDB Atomic Database to Model New Plasma Processes and Uncertainties

The AtomDB project provides models of X-ray and extreme ultraviolet emitting astrophysical spectra for optically thin, hot plasma. We present the new software package, PyAtomDB, which now underpins the entire project, providing access to the underlying database, collisional radiative model calculations, and spectrum generation for a range of models. PyAtomDB is easily extensible, allowing users to build new tools and models for use in analysis packages such as XSPEC. We present two of these, the kappa and ACX models for non-Maxwellian and Charge-Exchange plasmas respectively. In addition, PyAtomDB allows for full open access to the apec code, which underlies all of the AtomDB spectra and has enabled the development of a module for estimating the sensitivity of emission lines and diagnostic line ratios to uncertainties in the underlying atomic data. We present these publicly available tools and results for several X-ray diagnostics of Fe L-shell ions and He-like ions as examples.

Static-field ionization model of He-like ions for diagnostics of light-field intensity

We study static-field ionization of He-like ions with nuclear charge number in the range of $2\le Z \le 36$. Both the tunneling and over-the-barrier regimes are considered. We calculate the ionization rates by three approximate methods: a fitting formula based on the Perelemov-Popov-Terent'ev (PPT) formula, a perturbative expansion in powers of $1/Z$, and a single-active electron approximation, and compare them with reference ionization rates computed by the multiconfiguration time-dependent Hartree-Fock (MCTDHF) approach. The relative deviation of the rates computed by the PPT-based fitting formula and the third-order perturbation theory from the rates computed by the MCTDHF approach is found to be around 10\%. We discuss quantitatively the contribution from the exchange interaction during the ionization by comparing the single-active electron rates and the reference rates in which multielectron effects are included. We find that a single-active electron approximation, where the exchange interaction is neglected, results in the overestimation of the ionization rates by 30\% for He and 2\% for He-like Kr, showing that the magnitude of the effect of the exchange interaction scales approximately as $1/Z$.

MCDHF/RCI extended calculations of energy levels, radiative properties, [formula omitted], [formula omitted] hyperfine interaction constants, and Landé [formula omitted]-factors for [formula omitted][formula omitted

Energy levels, weighted oscillator strength, transition probabilities, AJ, BJ hyperfine interaction constants, and Landé gJ-factors have been calculated for all levels of 1s2 and 1snl (n=1−7, 0≤l≤n−1) configurations of He-like Argon ion (ArXVII). Multiconfigurational Dirac-Hartree-Fock (MCDHF) method has been adopted for calculating the mentioned parameters. Transition probabilities are reported for all allowed and forbidden transitions (E1, E2, M1 and M2) from the ground level. Breit interactions and quantum electrodynamics effects are estimated in subsequent relativistic configuration interaction calculations (RCI). The present calculations, namely MCDHF/RCI, have been compared with other theoretical results. Our results are in reasonable agreement with the published experimental data and theoretical values. Also, lifetimes for all excited levels were calculated. Most of the data presented here are published for the first time.

Stripping of relativistic uranium-ion beams by foils

The dynamics of relativistic uranium-ion beams stripped by foils from Be to Au is investigated in the 100–500 MeV/u energy range. Calculations of the charge-state distributions of uranium fractions as a function of foil thickness are performed using the BREIT code, based on the analytical solution of the balance rate equations for the ion charge-state fractions. Relativistic electron-loss and electron-capture cross sections, required for BREIT as input data, are calculated for interactions of Uq+ ions, q = 65–92, colliding with Be, C, Al, Ti, Cu, Mo, W, and Au atoms. The beam energy losses are found to be rather small, less than 20%, and are not accounted for in calculations. Calculated charge-state distributions are compared with available experimental data, obtained at the GSI (Gesellschaft für Schwerionenforschung) and BEVALAC (Bevatron Linear Accelerator) facilities, and with calculations by the GLOBAL code created at GSI.The optimal conditions are predicted for production of bare, H-like, He-like and Li-like uranium ions with the largest probabilities. Dependencies of the equilibrium thicknesses for uranium charge-state fractions on the initial charge of incident ions are investigated.

Linear polarization of anisotropically excited x-ray lines from the n = 2 complex in He-like Ar16+

High-resolution x-ray spectra were recorded at the National Institute of Standards and Technology electron beam ion trap (EBIT) using two Johann-type crystal spectrometers, with their dispersion planes oriented parallel and perpendicular to the beam direction. The linear polarizations of the 1s2 − 1s2l transitions in He-like argon ions were determined from the measured spectra at electron beam energies of 3.87 and 7.91 keV. The theoretical analysis was performed using detailed collisional-radiative modeling of the non-Maxwellian EBIT plasma with the NOMAD code modified to account for magnetic sublevel atomic kinetics. Effects influencing the polarizations of the observed 1s2 − 1s2l lines were investigated, including radiative cascades, the 1s2 1S0 − 1s2s 1S0 two-photon transition, and the charge exchange recombination of H-like argon ions. With these included, the measured polarizations of the resonance (1s2 1S0 − 1s2p 1P1), intercombination (1s2 1S0 − 1s2p 3P1), and forbidden lines (1s2 1S0 − 1s2s 3S1, 1s2 1S0 − 1s2p 3P2 ) were found to be in good agreement with the calculations.