Multiconfiguration Dirac-Fock Method Research Articles

K-shell photoionization ofO+andO2+ions: Experiment and theory

Absolute cross sections for the single and double K-shell photoionization of carbonlike ${\mathrm{O}}^{2+}$ and nitrogenlike ${\mathrm{O}}^{+}$ ions were measured in the 526--620-eV photon energy range by employing the ion-photon merged-beam technique at the SOLEIL synchrotron radiation facility. High-resolution spectroscopy up to $E/\mathrm{\ensuremath{\Delta}}E\ensuremath{\approx}5300$ was achieved. Rich resonance structures observed in the experimental spectra are analyzed and identified with the aid of R-matrix and multiconfiguration Dirac-Fock (MCDF) methods. For these two atomic oxygen ions of particular astrophysical interest we characterized the strong $1s\ensuremath{\rightarrow}2p$ and the weaker $1s\ensuremath{\rightarrow}np\phantom{\rule{0.28em}{0ex}}(ng2)$ resonances observed. A detailed comparison of the energies of the $1s\ensuremath{\rightarrow}2p$ resonances in the first members of the oxygen isonuclear sequence measured by synchrotron based experiments and the Chandra and XMM-Newton x-ray satellites is presented.

Theoretical investigation of spectroscopic properties of W27+ ion

SynopsisAnalysis of energy levels and radiative transition probabilities for the W27+ ion is performed using multiconfiguration Dirac-Fock method. Configuration interaction strength has been used to determine the influence of correlation effects.

Energy levels and radiative transition rates for Ba XLVIII

Energy levels and radiative rates are reported for transitions in F-like Ba XLVIII. Configuration interaction has been included among 27 configurations (generating 431 levels) over a wide energy range up to 618 Rydbergs, and the fully relativistic multi-configurational Dirac–Fock method adopted for the calculations. To assess the accuracy, calculations have also been performed with the flexible atomic code, FAC. Radiative rates, oscillator strengths and line strengths are reported for all electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transitions from the lowest 3 levels, although calculations have been performed for a much larger number of levels. We have made comparisons of our results with existing available results and a good agreement has been achieved. Additionally, lifetimes for all 431 levels are listed.

Energy Levels and Transition Rates for GA-Like Ions (Xe XXIV–Pr XXIX)

Energy levels, wavelengths, transition probabilities, oscillator strengths, and line strengths have been calculated for allowed electric dipole 4s 2 4p–4s4p 2 and 4s 2 4p–4s 2 4d transitions of Gallium-like ions from Z = 54 to 59, Xe XXIV, Cs XXV, Ba XXVI, La XXVII, Ce XXVIII, and Pr XXIX. The fully relativistic multiconfiguration Dirac–Fock method, taking into account both correlations within the n = 4 complex and the quantum electrodynamic effects, has been used in the calculations. The results have been compared with the available experimental and other theoretical results.

Energies and transition rates for Be-like ions (Xe LI - Ce LV)

Energy levels, wavelengths, oscillator strengths, transition probabilities and lifetimes have been calculated for Be-like Xe, Cs, Ba, La, and Ce ions among the fine-structure levels of terms belonging to the 2s2, 2s2p, 2p2, 2s3s, 2s3p, 2s3d, and 2p3d configurations. The calculations have been performed using the fully relativistic multiconfiguration Dirac-Fock (MCDF) method, taking the quantum electrodynamic corrections (QED) into account. The results are compared with the available other theoretical results.

Atomic structure calculations for Br-like ions

Energy levels, wavefunction compositions, and lifetimes are computed for all levels of 4s24p5, 4s24p44d, and 4s4p6 configurations in Br-like ions (Z = 47–50). We use the multiconfigurational Dirac–Fock method to generate the wavefunctions. We also present the transition wavelengths, oscillator strengths, transition probabilities, and line strengths for the electric dipole (E1) transition from the ground state configuration. We compare our calculated results with the available data in the literature and good agreement is obtained, which confirms the quality of our results. Moreover, we predict some new atomic data that have not been available so far and may be important for plasma diagnostic analysis in fusion plasma.

K X-ray line energies as diagnostics of warm dense plasma

Ionization of an atom's outer shells affects the energy of K-shell photons. For atoms with Z > 40, i.e. Zr and higher, such as Mo and Ag, as used in recent high-current Z-pinches at Sandia, computations with a multi-configuration Dirac-Fock method show that the K-shell photon energy increases linearly with ionization of the particular shells farther out. The linear dependence is a convenient way to estimate the plasma's ionization.

Shannon Entropy as a Measurement of the Information in a Multiconfiguration Dirac—Fock Wavefunction

Discrete Shannon entropy is applied to describe the information in a multiconfiguration Dirac—Fock wavefunction. The dependence of Shannon entropy is shown as enlarging the configuration space and it can reach saturation when there are enough configuration state wavefunctions to obtain the convergent energy levels; that is, the calculation procedure in multiconfiguration Dirac—Fock method is an entropy saturation process. At the same accuracy level, the basis sets for the smallest entropy are best able to describe the energy state. Additionally, a connection between the sudden change of Shannon information entropies and energy level crossings along with isoelectronic sequence can be set up, which is helpful to find the energy level crossings of interest in interpreting and foreseeing the inversion scheme of energy levels for an x-ray laser.

New spectroscopic data for atomic tungsten XIV

The thirteen times ionized tungsten is isoelectronic with PmI. Wavelengths and transition probabilities for the 5s-5p and 5p-5d transitions of WXIV, identifying the ground state as 4f13 5s2 2F7/2 were calculated. Both, a relativistic Hartree Fock approach, including core-polarization effects, and a purely relativistic multiconfiguration Dirac-Fock method were used for the calculations. Particularly, 5s-5p transitions were compared with experimental results obtained with VUV electron beam ion trap (EBIT) spectroscopy.

Theoretical study on radiative electron capture and subsequent radiative decay in collision of Xe54+ with Xe

Based on the multiconfiguration Dirac-Fock method and impulse approximation, the electron capture and following radiation decay of the projectile ion are studied theoretically for Xe atom which is bombarded by Xe54+ ion at 197 MeV/u. The radiative electron capture (REC) cross-sections and the corresponding emitted photon energies have been calculated in detail. Meanwhile, the probabilities of the radiative decay and energies of the REC final states are also calculated; combined with the calculated results in this paper, the X-ray spectra structure of radiative decay from projectile ion is further simulated. It is found that the simulated spectra are in good agreement with the newly measured results at Lanzhou Heavy-Ion Accelerator Device.

Calculation of Wavelengths, Transition Probabilities and Oscillator Strengths for E1 and M1 Transitions in Cu-Like Au Ion

Wavelengths, transition probabilities and oscillator strengths have been calculated for electric dipole (E1) transitions and magnetic dipole (M1) transitions in Cu-like Au ion. These values are obtained in the configuration interaction (CI) and using the fully relativistic multiconfiguration Dirac-Fock (MCDF) method including quantum electrodynamical (QED) effect and Breit correction. Obtained energy levels of some excited states in Cu-like Au ion from the method are generally in good agreement with valuable theoretical and experimental results. The calculation results indicate that for high-Z highly ionized atom, some forbidden transitions are very important.

Energy levels, transition rates, oscillator strengths and lifetimes in Ne-like, Ni-like, and Cu-like uranium ions

We present the fine-structure energy levels, wavelengths, oscillator strengths, transition energies, and transition rates of optically allowed inner-shell transitions of Ne-, Ni-, and Cu-like uranium ions by using the multiconfiguration Dirac–Fock method with the fully relativistic GRASP2 code (partly improved by us). In order to compare these results, we have performed other independent calculations with a fully relativistic Flexible Atomic Code (FAC). We have determined extensive configuration interaction wavefunctions to calculate the level energies of the inner-shell excited states of these three uranium ionic states. Overall, our calculated energy levels, wavelengths, transition rates, and oscillator strengths within the levels of selected configurations show better agreement with the available experimental and other theoretical results. Furthermore, we report radiative lifetimes of all the excited states of these three uranium ions. We also present many unpublished data about energy values, wavelengths, transitions rates, and oscillator strengths for inner-shell transitions. We believe that our calculated inner shell transition energies are of interest for the analysis of uranium x-ray spectra.

Multiconfigurational Dirac–Fock energy levels and radiative rates for Ni XXI

We present accurate atomic structure calculations for the lowest 200 fine structural energy levels for oxygen-like nickel, which may be a useful ion for both astrophysical and fusion plasmas. For the calculations of energy levels and radiative rates, we have used the multiconfigurational Dirac–Fock method. Our results are compared with those obtained using other numerical methods and experiments so that their accuracy can be assessed. The transition wavelengths, oscillator strengths, and radiative rates are reported for electric dipole (E1) transitions from the ground state. We have also presented the transition probabilities and transition wavelength of some forbidden transitions. Finally, we predict new energy levels, oscillator strengths, and transition probability data, where no other theoretical or experimental results are available, which may be useful for future experimental work.

Photoionization dynamics of the C2+ ion in Rydberg states

The goal of this work is to examine in detail the ionization dynamics of Be-like C ion in Rydberg states. An initial calculation has been done to output the lifetime due to spontaneous decay for unperturbed 1s 22sns (1Se) Rydberg states using the multi-configuration Dirac-Fock (MCDF) method with configuration interaction option implemented in the general-purpose relativistic atomic structure package (GRASP). Both the C2+ ground state and the C3+ target state energies have been carefully calculated. We report results from a detailed and systematic study of the behaviour of complex photoionization amplitudes, the lifetime due to spontaneous decay for unperturbed 1s 22sns (1Se) Rydberg states, the ‘resonant’ phase shift and the rapidly increasing of this shift from well below to well above the resonance position. The sum-over-state method is used to calculate the static dipole polarizability, while the frequency-dependent polarizability values of C2+ ion in these Rydberg states are obtained from two-state model calculation results.

Experimental and theoretical determination of the Kα2/Kα1 intensity ratio for zinc

X-ray intensity ratios, such as the Kα2/Kα1 ratio, are parameters with a large application in atomic physics and related scientific and technological areas. Despite the measurements carried out for several elements since 1969, available data are scarce for some elements. In this work, we present experimental and theoretical values for the intensity ratio Kα2/Kα1 that were obtained within a collaboration between an experimental and a theoretical group. The value of Kα2/Kα1 for zinc was measured using a double-crystal spectrometer. Calculations were performed within the Multiconfiguration Dirac–Fock method, including relativistic and QED corrections. Results show a very good agreement between the experiment and theory (1.2%).

Theoretical determination of K X-ray transition energy and probability values for highly charged ions of lanthanum and cerium

We provide, for the first time to our knowledge, accurate theoretical data for the the transition energy and probability values related to the decay of the most important excited states in He- through C-like lanthanum and cerium ions leading to the emission of K X-ray lines. We employed the multiconfiguration Dirac-Fock method, including QED corrections, to obtain the wave functions and energy values of each level involved in the X-ray analyzed transitions. The presented data may be used, among others, in the diagnostic of laboratory plasmas, such as the ones obtained in EBIT and ECRIS sources.

Wavelengths, transition probabilities, and oscillator strengths for M-shell transitions in Co-, Ni-, Cu-, Zn-, Ga-, Ge-, and Se-like Au ions

Wavelengths, transition probabilities, and oscillator strengths have been calculated for M-shell electric dipole transitions in Co-, Ni-, Cu-, Zn-, Ga-, Ge-, and Se-like Au ions. The fully relativistic multiconfiguration Dirac–Fock method, taking quantum electrodynamical effects and the Breit correction into account, was used in the calculations. Calculated energy levels of M-shell excited states for Cu-, Zn-, Ga-, Ge-, and Se-like Au ions from the method were compared with available theoretical and experimental results, and good agreement with them was achieved.

Atomic structure calculations for F-like tungsten

Energy levels, wavefunction compositions and lifetimes have been computed for all levels of 1s22s22p5, 1s22s2p6, 1s22s22p43s, 1s22s22p43p, and 1s22s22p43d configurations in highly charged F-like tungsten ion. The multiconfigurational Dirac—Fock method (MCDF) is adopted to generate the wavefunctions. We have also presented the transition wavelengths, oscillator strengths, transition probabilities, and line strengths for the electric dipole (E1) and magnetic quadrupole (M2) transition from the 1s22s22p5 ground configuration. We have performed parallel calculations with the flexible atomic code (FAC) for comparing the atomic data. The reliability of present data is assessed by comparison with other theoretical and experimental data available in the literature. Good agreement is found between our results and those obtained using different approaches confirm the quality of our results. Additionally, we have predicted some new atomic data for F-like W that were not available so far and may be important for plasma diagnostic analysis in fusion plasma.

Diagnostics of plasma based on K, L and M x-ray line positions

Ionization can affect the energy of characteristic x-ray lines sufficiently for a single line to be of value in plasma diagnostics. Recently, the ionization of a hot, dense tungsten plasma was determined from a detailed analysis of a single, highly resolved L x-ray line, and in an iridium plasma the change in energy of a single K x-ray line confirmed the theoretical estimate of the ionization. Diagnosing plasmas by these ionization energy shifts depends essentially on computations that can now be performed with sufficient accuracy, e.g. with the multi-configuration Dirac–Fock method. Besides extending earlier computations on the influence of outer-shell ionization on the energy of tungsten's K and L x-ray lines, this paper also presents the effect of ionization on the lower-energy M x-ray lines and a discussion of their relative merits for plasma diagnostics.

Polarization and Angular Distribution of Lℓ X-Ray Following Inner-Shell 2p3/2 Photoionization of Magnesium-Like Ions

The inner-shell 2p3/2 photoionization and the subsequent decay of Mg-like Fe14+, Cd36+, W62+ and U80+ ions are studied theoretically within the multiconfiguration Dirac—Fock method and the density matrix theory. Special attention is paid to exploring the influence of the non-dipole terms which arise from the multipole expansion of the electron-photon interaction in the photoionization process. The results show that the non-dipole contribution to the total cross section, the magnetic sublevels cross section of the photoionization process, the degree of linear polarization and angular distribution of the subsequent characteristic x-ray radiation become more important with the increase of photons energy and atomic nuclear Z. Especially for the cross section and the degree of linear polarization, the non-dipole contribution arrives at 50% for U80+ at four time energy threshold units. However, for the angular distribution, the maximum contribution does not exceed 4%, even for U80+ ions.