Fine-structure Energy Levels Research Articles

Fine-structure energy levels and radiative rates in Al-like molybdenum

Based on relativistic wavefunctions from multiconfigurational Dirac–Hartree–Fock and configuration interaction calculations, energy levels, radiative rates, and wavelengths are evaluated for all levels of 3s23p, 3s3p2, 3s23d, 3p3, 3s3p3d, 3p23d, and 3s3d2 configurations of Al-like molybdenum ion (Mo XXX). Transition probabilities are reported for E1 and M2 transitions from the ground level. The valence–valence and core–valence correlation effects are accounted for in a systematic way. Breit interactions and quantum electrodynamics effects are estimated in subsequent relativistic configuration interaction calculations. Comparisons are made with the available data in the literature and good agreement has been found, which confirms the reliability of our results.

Dirac R-matrix calculations of photoionization cross sections of Ni XII and atomic structure data of Ni XIII

We performed R-matrix calculations for photoionization cross sections of the two ground state configuration levels and 12 excited states of Ni XII using relativistic Dirac Atomic R-matrix Codes (DARC) across the photon energy range between the ionizations thresholds of the corresponding states and well above the thresholds of the last level of the Ni XIII target ion. Generally, a good agreement is obtained between our results and the earlier theoretical photoionization cross sections. Moreover, we have used two independent fully relativistic GRASP and FAC codes to calculate fine-structure energy levels, wavelengths, oscillator strengths, transitions rates among the lowest 48 levels belonging to the configuration () in Ni XIII. Additionally, radiative lifetimes of all the excited states of Ni XIII are presented. Our results of the atomic structure of Ni XIII show good agreement with other theoretical and experimental results available in the literature. A good agreement is found between our calculated lifetimes and the experimental ones. Our present results are useful for plasma diagnostic of fusion and astrophysical plasmas.

Experimental Investigation of the Hyperfine Structure of Neutral Praseodymium Spectral Lines and Discovery of New Energy Levels

Experimental investigations of Pr I spectral lines were performed by means of laser induced fluorescence spectroscopy, using a hollow cathode discharge lamp as source of free atoms. The wavelengths for the laser excitation were found by the help of a highly resolved Fourier transform spectrum. Altogether we excited 236 unclassified lines and analysed their hyperfine structure, which led, together with the measured wavelengths of the observed fluorescence lines, to the discovery of 32 new even parity and 38 odd parity fine structure energy levels. These levels allow to classify more than 670 spectral lines of Pr I. The wave number calibrated Fourier transform spectrum allowed us to determine the energies of most of these newly discovered levels with an uncertainty of 0.015 cm-1. Angular momenta, parity, and magnetic and electric hyperfine interaction constants (A and B) of the new levels were also determined.

Fine structure of the exciton electroabsorption in semiconductor superlattices

Wannier-Mott excitons in a semiconductor layered superlattice (SL) are investigated analytically for the case that the period of the superlattice is much smaller than the 2D exciton Bohr radius. Additionally we assume the presence of a longitudinal external static electric field directed parallel to the SL axis. The exciton states and the optical absorption coefficient are derived in the tight-binding and adiabatic approximations. Strong and weak electric fields providing spatially localized and extended electron and hole states, respectively, are studied. The dependencies of the exciton states and the exciton absorption spectrum on the SL parameters and the electric field strength are presented in an explicit form. We focus on the fine structure of the ground quasi-2D exciton level formed by the series of closely spaced energy levels adjacent from the high frequencies. These levels are related to the adiabatically slow relative exciton longitudinal motion governed by the potential formed by the in-plane exciton state. It is shown that the external electric fields compress the fine structure energy levels, decrease the intensities of the corresponding optical peaks and increase the exciton binding energy. A possible experimental study of the fine structure of the exciton electroabsorption is discussed.

Laser gain calculations for soft X-ray and XUV radiation emitted from copper-like ions by electron collisional pumping

Electron impact excitation rate coefficients, level population densities, and gain coefficients for six excited ions with Z = 51, 52, 53, 54, 55, 56 in the copper isoelectronic sequence have been calculated. The electron collisional excitation rate coefficients are calculated according to the analytical formulas of Vriens and Smeets. Fine structure energy levels, transition probabilities, and oscillator strengths needed in the calculations have been calculated using Cowan atomic structure code with relativistic corrections for [Ar]3d10nl with n = 4–7 and l = 0–6. The level population densities are calculated by solving the coupled rate equations involving 30 levels. Positive gain coefficients of the possible emitted lines are obtained at three selected electron temperatures, namely 1/4, 1/2, and 3/4 of the ionization energy. The present calculated data show promising values for the production of soft X-ray and XUV laser by collisional pumping for the transitions 5p–5s and 6d–5f with wavelengths between 108 and 571 Å. The values of the maximum gain coefficient are found to increase with atomic number and their order of magnitude ranges from102to 104cm−1.

Electron impact excitation of N iv: calculations with the darc code and a comparison with ICFT results

There have been discussions in the recent literature regarding the accuracy of the available electron impact excitation rates (equivalently effective collision strengths $\Upsilon$) for transitions in Be-like ions. In the present paper we demonstrate, once again, that earlier results for $\Upsilon$ are indeed overestimated (by up to four orders of magnitude), for over 40\% of transitions and over a wide range of temperatures. To do this we have performed two sets of calculations for N~IV, with two different model sizes consisting of 166 and 238 fine-structure energy levels. As in our previous work, for the determination of atomic structure the GRASP (General-purpose Relativistic Atomic Structure Package) is adopted and for the scattering calculations (the standard and parallelised versions of) the Dirac Atomic R-matrix Code ({\sc darc}) are employed. Calculations for collision strengths and effective collision strengths have been performed over a wide range of energy (up to 45~Ryd) and temperature (up to 2.0$\times$10$^6$~K), useful for applications in a variety of plasmas. Corresponding results for energy levels, lifetimes and A-values for all E1, E2, M1 and M2 transitions among 238 levels of N~IV are also reported.

Relativistic electron-correlation on the 2p-2s transitions in Li-like to F-like Xe ions

Energy levels, wavelengths, transition rates and line strengths are reported for transitions in Li-like to F-like Xe ions, Xe LII-XLVI. For the calculations, a fully relativistic GRASP2k code based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) method has been adopted, Valence and core-Valence correlation effects were accounted for through single- and double-excitation expansions to increasing sets of active orbitals. The fine-structure energy levels and wavelengths are compared with experimental data and with values from other calculations. The calculated values including core-valence correlation are found to be similar and compare very well with other theoretical and experimental values for Xe ions. Our calculated wavelengths for Li-, Be- and B-like ions are much more precise than some available theoretical data and reveal significant shortcomings of the various theoretical predictions.

Multi-Configuration Dirac–Hartree–Fock (MCDHF) Calculations for B-Like Ions

Relativistic configuration interaction results are presented for several B-like ions (Ge XXVIII, Rb XXXIII, Sr XXXIV, Ru XL, Sn XLVI, and Ba LII) using the multi-configuration Dirac–Hartree–Fock (MCDHF) method. The calculations are carried out in the active space approximation with the inclusion of the Breit interaction, the finite nuclear size effect, and quantum electrodynamic corrections. Results for fine structure energy levels for 1s22s22p and 2s2p2 configurations relative to the ground state are reported. The transition wavelengths, transition probabilities, line strengths, and absorption oscillator strengths for 2s22p–2s2p2 electric dipole (E1) transitions are calculated. Both valence and core-valence correlation effects were accounted for through single-double multireference (SD-MR) expansions to increasing sets of active orbitals. Comparisons are made with the available data and good agreement is achieved. The values calculated using core–valence correlation are found to be very close to other theoretical and experimental values. The behavior of oscillator strengths as a function of nuclear charge is studied. We believe that our results can guide experimentalists in identifying the fine-structure levels in their future work.

Relativistic correlation effects on the x-ray spectra of Li-like ions

The wavelengths and rates of electric dipole transitions between states with $n=2$ and $n=1$ of doubly excited Li-like ions have been studied for some selected ions in the range $13\ensuremath{\le}Z\ensuremath{\le}54$ using fully relativistic multiconfiguration Dirac-Fock wave functions in the active space approximation with the inclusion of finite nuclear size, Breit interaction, self-energy, and vacuum polarization. A detailed discussion on the effects of intercomplex correlation around $Z=26$ and intracomplex correlation around $Z=37$ leading to irregularities and sharp discontinuities in the x-ray rates noticed for a few transitions has been provided. An unusually large contribution of Breit interaction has been found for intercomplex correlation in certain cases. The present results are compared with other available experimental and theoretical data. The errors associated with the transitions are highlighted for some experimentally available lines taking into account the uncertainties on the fine-structure energy levels and also on the line strengths.

Experimental investigation of the hyperfine spectra of Pr I-lines: discovery of new fine structure energy levels of Pr I using LIF spectroscopy with medium angular momentum quantum number between 7/2 and 13/2

We present 39 even and 60 odd parity newly discovered fine structure levels of Pr I with angular momentum quantum numbers J = 7 / 2, 9/2, 11/2 and 13/2. Spectral lines in the wavelength range of 4200 A to 7500 A were investigated experimentally using laser-induced fluorescence spectroscopy or optogalvanic spectroscopy. Free Pr atoms were produced in a hollow cathode discharge. A high resolution Fourier transform spectrum of Pr was used to extract excitation wavelengths. From an analysis of the recorded hyperfine patterns, together with excitation and fluorescence wavelengths, we were able to find the unknown levels involved in the formation of the investigated lines. More than 500 spectral lines could be classified by the new levels.

MCDHF calculations and study of plasma parameters for Li-like ions

Abstract Extensive configuration interaction calculations for several Li-like ions (Z=32, 36, 42, 46, 50, 54 and 56) are performed using the code GRASP2K based on the multiconfiguration Dirac–Hartree–Fock (MCDHF) method. Breit interaction and leading quantum electrodynamical (QED) effects are also included by applying active-space techniques to enlarge the configuration set. Results for fine-structure energy levels for 1s22p, 1s23s, 1s23p and 1s23d configurations with relative to ground states 1s22s are presented. The wavelengths, transition rates and oscillator strengths for the 1s22s 2S1/2–1s22p P 1 / 2 , 3 / 2 0 2 , 1s22p P 1 / 2 , 3 / 2 0 2 –1s23s 2S1/2, 1s22p P 1 / 2 0 2 –1s23d 2D3/2, 1s22p P 3 / 2 0 2 –1s23d 2D5/2 and 1s22s 2S1/2–1s23p P 1 / 2 , 3 / 2 0 2 transitions are reported. Our calculated results are in good agreement with previous theoretical results and compiled values of the National Institute for Standards and Technology (NIST). We have also provided the line intensity ratios and plasma parameters for optically thin plasma. Our calculated data may be useful for experimentalists in identifying the fine-structure levels, for plasma modeling, astrophysical research applications.

R-matrix calculations of photoionization cross section of Ne-like tungsten

The photoionization cross section calculation for the ground state 1s22s22p6 1S (J = 0) of Ne-like W64+has been performed in the close-coupling approximation using the Dirac–Coulomb R-matrix method. The resonance structures are analysed and described by finding the resonance energy positions of prominent Rydberg series 2s2p6(2S)np1P0for W LXV ion. To calculate fine structure energy levels, multi-configuration Dirac–Fock and relativistic distorted-wave methods have been employed. Wherever possible we have compared our work with the available data. The present results will be useful for diagnostics and modeling of plasma in ITER and other fusion devices.

Fine Structure Calculations of Atomic Data for Ar XVI

Fine structure energy levels, wavelengths, log gf and allowed transition probabilities (E1) have been calculated for Lithium-like Ar XVI. The optimized electrostatic parameters by a least square approach, have been used in the calculation to include the configuration interaction and relativistic effects. A total number of 69 Ar XVI levels having total angular momenta, 1/2 ≤ J ≤ 9/2 of even and odd parities, orbital angular momenta 2 ≤ l ≤ 4, with 546 E1 transitions for 6 ≤ n ≤ 10 are considered using the relativistic effect in the Breit-Pauli method, where n is the principal quantum number. A comparison is made with the available results in literature.

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.

Single-photon emission from simultaneous two-electron transitions in He-like ions

The electric and magnetic dipole radiations due to a double-electron jump from the ${}^{1}{S}_{0}$ state of He-like ions with an empty $K$ shell are evaluated for 21 ions with $10\ensuremath{\le}Z\ensuremath{\le}92$ using fully relativistic multiconfiguration Dirac-Fock wave functions in the active space approximation with the inclusion of a finite nuclear size, the Breit interaction, self-energy, and vacuum polarization. The contributions from correlation and higher-order corrections to the x-ray energies and rates are discussed in detail. The effects of biorthogonal and partially orthogonal spin orbitals of the initial and final states on the correlation sensitive radiative rates are analyzed. The accuracy of our computed data is judged by the uncertainties in the fine structure energy levels along with the agreement in the length and velocity forms of transition rates. The present results are compared with other available theoretical data.

Energy levels and spectral lines in the X-ray spectra of highly charged W XLIV

The multi-configuration Dirac-Hartree-Fock method is employed to calculate the fine-structure energy levels, wavelengths, transition probabilities, and oscillator strengths for electric dipole allowed (E1) and forbidden (M1, E2, M2) lines for the 4s 24p and 4s4p 2 configurations of W XLIV. The valence-valence and core-valence correlation effects are accounted for in a systematic way. Breit interactions and quantum electrodynamics (QED) effects are estimated in subsequent relativistic configuration interaction (CI) calculations. The present results are in good agreement with other available theoretical and experimental values, and we predict new data for several levels where no other theoretical and/or experimental results are available, precise measurements are clearly needed here.

Photoionization of Al X from ground state using the relativistic R-matrix close-coupling method

The relativistic R-matrix method is used to calculate the total photoionization cross sections from the ground state 1s22s2 1S0 of Al X for photon energies ranges from the first ionization threshold to just above the eighth threshold of the residual ion Al XI. In this work, the relativistic distorted-wave method is employed to calculate the fine-structure energy levels and radial functions. The lowest eight level target states of Al XI are used in the photoionization calculations of Al X and should provide a reasonably complete database for practical application for photoionization cross section for Al X. The resonance energy levels and widths of 18 Rydberg series have been investigated.

Atomic Data for S XIV for 6≤ n ≤10

Energy levels, wavelengths, log gf and transition rates for E1 have been calculated for S XIV. Configuration interaction and relativistic effects have been included in the calculations. 69 fine structure energy levels and 545 transition rates have been listed for 6≤n≤10. The calculations are in a good agreement with the other literatures.

Fine-structure calculations of energy levels, oscillator strengths, and transition probabilities for sulfur-like iron, Fe XI

Energy levels, oscillator strengths, and transition probabilities for transitions among the 14 LS states belonging to configurations of sulfur-like iron, Fe XI, have been calculated. These states are represented by configuration interaction wavefunctions and have configurations 3s23p4, 3s3p5, 3s23p33d, 3s23p34s, 3s23p34p, and 3s23p34d, which give rise to 123 fine-structure energy levels. Extensive configuration interaction calculations using the CIV3 code have been performed. To assess the importance of relativistic effects, the intermediate coupling scheme by means of the Breit–Pauli Hamiltonian terms, such as the one-body mass correction and Darwin term, and spin–orbit, spin–other-orbit, and spin–spin corrections, are incorporated within the code. These incorporations adjusted the energy levels, therefore the calculated values are close to the available experimental data. Comparisons between the present calculated energy levels as well as oscillator strengths and both experimental and theoretical data have been performed. Our results show good agreement with earlier works, and they might be useful in thermonuclear fusion research and astrophysical applications.

Fine-structure energy levels, oscillator strengths and lifetimes in Al-like chromium

We have performed large scale calculations of excitation energies from ground state for 97 fine-structure levels as well as of oscillator strengths and radiative rates for all electric-dipole-allowed and intercombination transitions among the fine-structure levels of the terms belonging to the (1s22s22p6)3s23p, 3s3p2, 3s23d, 3p3, 3s3p3d, 3p23d, 3s3d2, 3s24s, 3s24p, 3s24d, 3s24f and 3s3p4s configurations of Al-like chromium. These states are represented by very extensive configuration-interaction wave functions obtained with the configuration-interaction version 3 computer code of Hibbert. The important relativistic effects in intermediate coupling are included through the Breit-Pauli approximation. Small adjustments to the diagonal elements of Hamiltonian matrices have been made so that energy splittings are as close as possible to the energy values of the National Institute of Standards and Technology. From the radiative rates, we have also calculated radiative lifetimes of fine-structure levels. Generally, the calculated excitation energies, oscillator strengths and the radiative rates are found to be in good agreement with those obtained from other sophisticated calculations. However, significant differences between present calculated lifetimes and those from the calculation of Fischer and co-workers for a few fine-structure levels are noted and discussed. Also the present calculated lifetime for level 3s24s(2S0.5) is found to be in excellent agreement with the experimental value given by Thornbury and co-workers. With this calculation, we also predict new data for several fine-structure levels, where no other theoretical and/or experimental results are available.