Beryllium-like Ions Research Articles

Calculations of energies of intrashell doubly excited states of beryllium-like ions

Energy levels of doubly excited states of beryllium-like ions are calculated using the conventional configuration-interaction method. The interactions of the two outer electrons with the inert 1s2 core electrons are represented by a model potential. The resulting energies of 1s23l3l' and 1s24l4l' doubly excited states, designated in terms of the K, T and A correlation quantum numbers, are used to identify the Auger electron spectra derived from the collision of multiply charged ions with atoms and molecules. The systematics of energy levels is analysed and compared with the supermultiplet structure of doubly excited states of helium-like ions.

Relativistic distorted-wave cross sections for electron-impact excitations of berylliumlike ions.

Relativistic distorted-wave Born (RDWB) cross sections of Be-like ions for excitations from the ground state 2s/sup 2/ /sup 1/S/sub 0/ to the 2s2p /sup 3/P/sub 1/ and /sup 1/P/sub 1/ states by electron impact are reported for Ne/sup 6+/ through U/sup 88+/. Multiconfiguration Dirac-Fock wave functions were used to describe the target-ion states, and the relativistic continuum wave functions were calculated in the field of (frozen) target-ion charge distribution with the configuration-average exchange potential. We found, however, that cross sections hardly changed even if the exchange terms were omitted. In contrast, adding the 2p/sup 2/ configuration to the ground-state wave function reduced cross sections by 10--60 %. RDWB cross sections were calculated from thresholds to T = 10 keV, where T is the incident electron energy. For Zapprox. =25 and above, where Z is the nuclear charge, intermediate coupling mixes the /sup 3/P/sub 1/ and /sup 1/P/sub 1/ states such that the transition to the former becomes practically spin- and electric-dipole allowed, changing the high-T behavior of the excitation cross section. Cross sections are presented in compact fitting formulas that allow interpolations to determine cross sections with high precision for arbitrary Be-like ions (10less than or equal toZless than ormore » equal to92) and arbitrary incident energies (Tless than or equal to10 keV).« less

Electron impact excitation of n=3 states of C III: an application of a new R-matrix package

The R-matrix method is used to obtain effective collision strengths for the beryllium-like ion C III for all transitions between the six n=2 states with configurations 2s2, 2s2p and 2p2 and the six n=3 states with configurations 2s3s, 2s3p and 2s3d. In addition effective collision strengths between all pairs of these n=3 states are calculated. The calculations are carried out including the first twelve target eigenstates in the R-matrix expansion of the total wavefunction. In order to obtain converged cross sections involving the n=3 states a new no-exchange R-matrix package was developed and is described in this paper. This package, combined with the Burgess sum rule, is used to determine the high partial wave contributions, to the cross section. Results for the effective collision strengths are presented in tabular form for temperatures in the range 104-105.8 K.

Cross Sections and Rate Coefficients for Inelastic Electron Collisions with Carbon and Oxygen Ions

The cross sections and rate coefficients (averaged over a Maxwellian distribution) for excitation and ionization of hydrogen-, helium, lithium- and beryllium-like ions of carbon and oxygen are calculated in the Coulomb-Born-Exchange approximation. The numerical data are approximated in a wide range of electron energies and temperatures by analytic formulae containing two fitting parameters. These parameters are tabulated. The error of analytic approximation is given also and the numerical data of this work are compared with the numerical results of the most advanced theoretical calculations.

Relativistic and correlation effects in the 2s3p configuration of berylliumlike ions

Relativistic and correlation effects cause several inversions of the triplet and singlet J = 1 levels in the 2s3p configuration of berylliumlike ions. We have studied these effects in the range of atomic number Z = 6–54 by using both relativistic and nonrelativistic multiconfiguration wave functions. Theoretical predictions of energies of these levels with respect to the 2s21S0 ground level are compared with experimental data, and we conclude that overall the predictions for the ions having Z ≥ 15 are probably more accurate than the available measurements. Calculated oscillator strengths for these resonance transitions are also reported. Near cadmium (Z = 48), we confirm still another inversion that is due to the complete dominance of relativistic effects, which was reported previously. The 2p3s (1/2,1/2)1 level, a doubly excited state, goes below the 2s3p (1/2,3/2)1 level, owing to relativistic hydrogenic ordering. This type of level crossing due to hydrogenic ordering is anticipated in other sequences as well, contrary to our usual experience in atomic spectroscopy.

Effects of autoionizing resonances on electron-impact excitation rates for Be-like ions.

The effects of autoionizing resonances on the electron-impact excitation rates for n=2 to n=2 intrashell transitions in beryllium-like ions have been studied for six ions with atomic numbers Z = 30, 34, 36, 42, 47, and 54. The resonance contributions to the excitation rates were calculated in the isolated-resonance approximation. Detailed Auger and radiative rates were evaluated in the multiconfiguration Dirac-Fock model. Results are compared with background rates from the Coulomb-Born-exchange approximation. Autoionizing resonance have been found to enhance the electron-impact excitation rates by a factor of 2-4 for the electric-dipole-forbidden transitions, while for dipole-allowed transitions, the resonance effects amount to only a few percent of these rates.

Structure of hydrogenic transitions in high- Z beryllium-like ions

The structure of hydrogenic states, or low lying Rydberg states, in highly-ionized beryllium-like atoms is influenced by the effects of atomic core polarization as well as configuration interaction. Measurements have been made, using fast-ion spectroscopy, of the resolved structure of hydrogenic transitions in S XIII and Cl XIV involving 1s 22s nl and 1s 22p nl states with n = 6–11. Relativistic MCHF calculations are compared with the observed structures.

Structure of the integral cross sections for excitation in ion-atom collisions calculated in the plane-wave Born approximation.

We point out that the plane-wave Born approximation sometimes gives rise to a conspicuous minimum of the integral cross section for excitation in ion-atom collisions; for illustration we present results for a transition 1${s}^{2}$2${s}^{2}$ $^{1}s^{2}$2s3p $^{1}P$ of berylliumlike ions calculated by using configuration-mixing wave functions. The minimum of the integral cross section arises from a zero of the generalized oscillator strength.

Theoretical emission line strengths for the beryllium-like ion Sxiii compared to XUV observations of solar flares

A comparison of Skylab S082A observations for several solar flares with calculations of the electron temperature sensitive emission line ratio R1 = I(2s2p1P − 2s21S)/I(2s2p3P1 - 2s21S) = = I(256.68 A)/I(491.45 A) in Be-like SXIII reveals good agreement between theory and experiment, which provides observational support for the accuracy of the adopted atomic data. However, observed values of the electron density sensitive ratio R2 = I(2s2p1P − 2s21S)/I(2p23P2 - 2s2p3P2) = = I(256.68 A)/I(308.96 A) all lie below the theoretical high density limit, which is probably due to blending in the 308.96 A line.

The Dirac equation in the algebraic approximation. V. Self-consistent field studies including the Breit interaction

It is argued that the Breit interaction can be included in the self-consistent-field procedure of Dirac-Hartree-Fock calculations, and need not necessarily be treated as a first-order perturbation, as is widely believed. The matrix Dirac-Hartree-Fock equations including the frequency-independent Breit interaction are presented and discussed. Prototype calculations for helium-like and beryllium-like ions are presented.

New measurements of spontaneous transition probabilities for beryllium-like ions

The authors describe measurements of spectral line intensities for pairs of transitions having common upper levels and thus derive the branching ratios of their spontaneous radiative transition probabilities. These are then combined with the results of measurements of the radiative lifetimes of the upper levels by other authors to obtain values of the individual probabilities. Care was taken to avoid the effects of the trapping of resonance radiation, which could have invalidated the results. A particular feature of their measurements was the use of two spectrometers, spanning between them the wavelength range from less than 100 AA to over 7000 AA. The results are for transitions in N IV, O V and Ne VII and are given with a claimed accuracy of between 7 and 38%. These are compared with theoretically calculated values. Good agreement is found for some of the simpler electric dipole transitions. On the other hand, for some of the other transitions, which in certain cases are only possible because o configuration interaction, disparities between their measurements and theory are as large as a factor of five.

The absorption spectrum of B II, C III, N IV and O V beryllium-like ions

Energy terms, dipole oscillator strenghts and photoionization cross sections from the ground state are calculated for beryllium-like ions. Autoionizing state transition energies and line widths for the 1 P 0 resonances in the continuum are also obtained. The configuration interaction method for initial and final states is used, and the atomic orbitals are generated through angular- momentum-dependent, scaled Thomas-Fermi-Dirac potentials.

Allowed and forbiddenn=2-2 transitions of highly ionised titanium

Relativistic intermediate-coupling wavefunctions are used to evaluate transition energies, line strengths and transition probabilities for all allowed and forbiddenn=2-2 transitions for beryllium-like titanium ion. We have shown that to achieve a better than 1% agreement between theory and experiment for transition energies between then=2-2 levels it is not sufficient to use the three-configuration basis composed of 2s2, 2s2p and 2p2.

Electron impact excitation of C III in a twelve-state R-matrix calculation. Effective collision strengths between the n=2 states

An R-matrix calculation for the electron impact excitation of the beryllium-like ion C III is described, in which the first twelve states formed from the 2s2, 2s2p, 2p2 and 2s3l configurations are included in the expansion of the total wavefunction. Effective collision strengths for electron temperatures between 12000 and 50000K are calculated for all transitions between the lowest six states, and are compared with those obtained in an earlier six-state R-matrix calculation. In contrast to earlier work on the beryllium-like ion O V, the effective collision strength for 2s2 1S-2s2p 3P0 in C III is not significantly affected by resonances converging to the 2s3l thresholds. However, some other dipole-forbidden transitions do show significant differences, particularly at the lowest temperatures. The biggest effect is for 2s2 1S-2p2 1S, where the twelve-state effective collision strength is double the six-state one at all temperatures considered.

Fifteen Years On - The Calculation of Atomic Transition Probabilities Revisited

An up-date is presented of a previous review by the author of atomic transition probability calculations published in 1969. Attention is again restricted, in the main, to allowed electric dipole transitions. Attention is in particular paid to the construction of accurate atomic wave-functions, to the random phase approximation and to recent progress in relativistic calculations. Comparative results for the resonance transition of beryllium-like ions are discussed by way of illustration.

Allowed and Forbidden n = 2?2 Transitions of the Elements Kr and Mo

Relativistic intermediate-coupling wavefunctions are used to evaluate transition energies, line strengths and transition probabilities for all allowed and forbidden n = 2-2 transitions for krypton and molybdenum beryllium-like ions. Our results are in very good agreement with those calculated using the relativistic multi-configuration Hartree-Fock approximation. These calculations were carried out under the same physical assumption that the dominant correlation effect is the n = 2 intra-shell correlation. We also discuss the importance of relativistic effects on the radial functions, the relativistic intermediate-coupling scheme in the variational process, the importance of radiative corrections for transition energies between states with different occupation of the 2s shell, and the relative importance of intra- versus inter-shell correlation effects.

Electron collisional excitation of beryllium-like ions: C2+, N3+, O4+and Ne6+

The Coulomb-Born and Coulomb-Born-Bely approximations have been used to calculate the cross sections of electron impact excitation for six allowed transitions in the beryllium-like ions C2+, N3+, O4+ and Ne6+. The cross sections have been obtained for electron impact energies from threshold to the high-energy region. The authors find that the Coulomb-Born-Bely calculation gives good results comparable with the distorted-wave calculation.

Spin-orbit electric dipole transmissions in beryllium-like ions

We have used configuration interaction wavefunctions to calculate energy levels, wavelengths, oscillator strengths and transition probabilities for spin-orbit electric dipole transitions between the 2s2, 2s2p, and 2p2 states in beryllium-like ions (Z = 6–10). Some significant differences with previous calculations are obtained. A common set of radial functions is used.

Resonance Transitions of Be-like Ions from Multiconfiguration Relativistic Random-Phase Approximation

Relativistic excitation energies and transition rates from the $^{1}S_{0}$ ground states to the first $^{3}P_{1}$ and $^{1}P_{1}$ excited states of berylliumlike ions are determined by using the newly developed multiconfiguration relativistic random-phase approximation (MCRRPA). Results from the MCRRPA theory are compared with those from other theories and experiments. The large discrepancies between the single-configuration RRPA predictions of excitation energies and the precise experimental values are resolved.

Erratum - Intermediate Coupling Collision Strengths for DELTAN=0 Transitions Produced by Electron Impact on Highly Charged Ions - Part Two - Transitions Between States of the 1S22S2P Configuration in Beryllium-Like Ions

Erratum - Intermediate Coupling Collision Strengths for DELTAN=0 Transitions Produced by Electron Impact on Highly Charged Ions - Part Two - Transitions Between States of the 1S22S2P Configuration in Beryllium-Like Ions