boldmath Multi-configuration Dirac-Hartree-Fock (MCDHF) calculations for Zn-like sequence from Z=48 to 54

The 4s4p excitation energies and the 4s²-4s4p E1 transitions for zinc-like ions from Z=48 to 54 are calculated by the multi-configuration Dirac-Hartree-Fock (MCDHF) method in this paper. The results for fine-structure energy levels, wavelengths and lifetimes between Z=48 (Cd) and Z=54 (Xe) are presented and compared with other theoretical and experimental results. The calculated values including core-valence correlation are found to be very similar to other theoretical and experimental values. We believe that our calculated values can guide experimentalists in identifying the fine-structure levels in their future work.     

X-ray spectroscopy of multiply-charged ions from laser plasmas

Original results are reported on the observation and identification of spectra of multiply-charged ions in the range of λ ≈ 1.5–15 Å, which corresponds to transitions with a range of principal quantum number n. The main part of the review consists of tables with about a thousand spectral lines, which have been mainly observed in laser-plasma radiation, as well as in the solar corona and other laboratory sources at an electron temperature T_e≈10⁷°K. The accuracy for the wavelengths (Δλ) is the following: Δλ is equal to ≈ 0.0005 Å for λ ≈ 2.5 Å and it is equal to ≈ 0.003 Å for λ ≈ 15 Å. The spectral lines are considered for the following transitions: 1-n type for [H]-like ions (Z = 11–16)and [He]-like ions (Z = 11–26); 2-n type for [Li]-like ions (Z = 19–26), [Be]-like ions (Z = 22–34) and [Ne]-like ions (Z = 26–42); 3-n type [Co]- and [Ni]-like ions (Z = 73). The line-list contains about four hundred wavelengths for multiply-charged iron L-ions (Fe(XVII)-Fe(XXIV)) and is presented with identification of some of the transitions. The wavelengths and intensities of satellites of the [H]-like ions and [He]-like ions, which are caused by transitions from the doubly-excited autoionization states 2l2l′ and 1s2l2L′ of [He]-like ions (Z = 11–16) and [Li]-like ions (Z = 11–26), respectively, are also considered.     

Testing of QED-Theory and Precise Measurements of the Rydberg Series for the He-Like Multicharged Ions

The wavelengths of the 1snp ¹ P ₁−1s ^{2 1} S ₀ transitions in He-like Mg XI, F VIII (n= 4–8) and Al XII (n=6,9) have been calculated in the framework of the 1/Z expansion method including relativistic effects and QED contributions. It is found that QED corrections to the ground-state ionization energy are significant at the present level of experimental accuracy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dielectronic recombination rate for the Be-sequence

The dielectronic recombination (DR) rate coefficient α^DR is explicitly calculated for the Mo, Fe, Ar, and Ox target ions of the Be-sequence with four electrons, in the isolated resonance approximation. This work extends the previous study of the Mo³⁸⁺ ions at 1.4, 2.8, and 5.6 keV electron temperatures. Both Δn≠0 and Δn = 0 transitions are considered in detail. The Δn≠0 contribution still dominates, but the Δn = 0 effect becomes quite large for heavy ions. An explicit LS coupling scheme is employed throughout for the dominant transitions calculated here, and contributions from many other intermediate states and cascade transitions are included by comparing the dominant contribution with the more complete Mo³⁸⁺ case and proportionately scaling their effect. Nonrelativistic Hartree-Fock wave functions are used in the evaluation of the Auger and radiative amplitudes, and the continuum wave functions are calculated using the Hartree-Fock direct potential and explicit nonlocal exchange potential. The scaling property of α^DR and its breakdown are examined, and an improved form of the phenomenological formula is proposed.     

Dielectronic recombination rates for ions of the magnesium sequence at low energies

The dielectronic recombination (DR) rate coefficient α^DR is explicitly calculated for the Si, Ar, Fe and Mo target ions of the Mg isoelectronic sequence with twelve electrons. Both the 3s, Δn ≠ 0 and 3s, Δn = 0 transitions are considered in detail. An explicit LS coupling scheme was applied to all the dominant transitions of these ions. Results of α^DR with different free electron temperatures are also discussed     

Relativistic atomic level calculations with nuclei carrying additional fractional charges

One-electron energy levels and wavelengths have been calculated for Na-like ions whose nuclei carry quarks with additional charges ±e/3, ±2e/3. The calculations are based on relativistic self-consistent field procedures. The deviations from experimental values exhibit regularities which allow an extrapolation for the wavelengths of 3s-3p, 3s-4p, 3p-3d, and 3p-4s transitions for the nuclear chargeZ=11+1/3, ±2/3. A number of transitions are found in the region of visible light which could be used in an optical search for quark atoms.     

Dielectronic recombination rate coefficients for Fe23+ ion

The dielectronic recombination rate coefficients are explicitly calculated for the Li-like ion Fe²³⁺, which recombines with the continuum electron to form Fe²²⁺. Both 1s²2s and 1s²2p initial states are treated for the temperature range 1～8 keV. The rate coefficients are obtained from a direct evaluation of the Auger and radiative transition probabilities which are calculated from nonrelativistic Hartree-Fock wave functions. The L-shell electron excitation with Δn≠0 is found to be the dominant transition, while the 2s→2p excitation with Δn = 0 contributes approx. 10–25% of the Δn≠0 value. The K-shell excitation effect is about 1～30% in the temperature range considered, and the cascade effect is estimated to be a reduction in the rate of about 14%.     

A note on Δn ≠ 0 Stark transitions in hydrogenlike atoms

In a gaseous helium or hydrogen target slow muons or antiprotons are captured into orbits with a high principal quantum number (n = 15 to 50) to form (μ^? α)⁺ ions, (p α)⁺ ions, or (p p) atoms respectively. In the subsequent deexcitation process Stark mixing of the intermediary states plays an important role. The successful Mainz Cascade Model assumed Δn = 0 for the Stark transitions, although formally no such selection rule exists. This note examines the reasons why Δn ≠ 0 Stark transitions play only a negligible role in the deexcitation cascade.     

Dielectronic recombination rates for ions of the magnesium sequence—II

The dielectronic recombination (DR) rate coefficient α^DR is explicitly calculated for Ar, Fe and Mo target ions of the Mg isoelectronic sequence (12 electrons). The 2p transitions are dominant at high temperatures and are considered in detail with full LS coupling. This work extends our previous study in which both the 3s, Δn = 0 and 3s, Δn ≠ 0 transitions are considered. Scaling of α^DR with free-electron temperature is also discussed.     

Systematic trends in the line strengths of E1 transitions in the oxygen isoelectronic sequence

Line strengthsS for the dipole allowed transitions within then=2 complex of the oxygen isoelectronic sequence have been fitted in the formZ ² S=A+B/(Z −C), whereZ is the nuclear charge of a particular ion. The constantsA, B andC are determined by using a non-linear least square method. The data forS are taken from the configuration interaction calculations which included internal, semi-internal and all external type correlations for ions in the rangeZ=8 − 25. It is shown that the values ofA obtained from the fit for all the transitions are in excellent accord with the ab-initio values obtained in the hydrogenic limitZ → ∞ provided near degeneracy effects are included in the ground state multiplet 1s²2s²2p^{4 1}S.     

On the nature of some biradicaloid and antiaromatic Vis/NIR‐chromophores

Dyes derived from the biradicalic oxyallyl and cyclopentadienylium were calculated by time‐dependent density functional theory (TDDFT) and the characteristics of the prominent low‐energy transitions revealed by graphical means. According to theoretical and experimental studies, 4‐aminophenyl‐substituted dyes absorb intensely at long wavelengths up to the near infrared. If the amino groups are removed the absorption wavelengths are changed little. As found in the previous studies on the squaraine and croconaine oxyallyl dyes, the substituents play only a minor role in the spectral excitation. Charge‐transfer‐type excitations do not occur between the donor aryl substituents and the central oxyallyl or cyclopentadienylium acceptor group. This behaviour is exceptional since donor–acceptor compounds tend to produce charge‐transfer‐ or polymethine‐type electronic transitions. The hitherto rarely used electron density difference (EDD) maps clearly unveiled the spectral excitation features. The spectral excitation of the title compounds is predominantly localized at the oxyallyl and cyclopentadienylium groups, respectively. Characteristics of simple chromophoric compounds and of conventional CT‐ and polymethine dyes are given for comparison. The biradicaloid character of these dyes is supported by the calculated low singlet–triplet splitting energies. Spin properties were characterized in terms of expectation values of the S²‐operator and antiaromatic properties in terms of nucleus‐independent chemical shifts (NICS). According to the ΔE_S/T and <S²> criteria compounds with the acyclic oxyallyl fragment are more biradicaloid. The parent compounds oxyallyl, thioxyallyl and cyclopentadienylium, display extremely large <S²> values. These compounds are triplets in the ground state. The absorption wavelengths of selected biradicaloid species were also calculated by the multi‐reference SORCI method. Copyright © 2010 John Wiley & Sons, Ltd.     

Isotope shifts of dielectronic resonances for heavy few-electron ions

Effects of the nuclear charge distribution upon the total cross-section of dielectronic recombination are investigated. We calculated isotope shifts of resonance energies for H-, He- and Li-like heavy ions in the relativistic domain from Z = 54 to Z = 94. We point out that the position of the resonances is most influenced in KLL transitions in very heavy elements and their shifts are most likely to be measurable for systems with intra-shell transitions. For these systems, dielectronic recombination experiments provide a new method to determine the parameters of the nuclear charge distribution.Received: 26 July 2004, Published online: 5 October 2004PACS: 34.80.Lx Electron-ion recombination and electron attachment - 31.30.Jv Relativistic and quantum electrodynamic effects in atoms and moleculesR. chiopu: Now at Institut für Physik, Johannes-Gutenberg-Universität, Mainz, Germany.     

Inner-shell ionization by relativistic electron impact

K-, L andM-shell ionization cross sections have been measured for 23 elements, 12≦Z≦92, after bombardment with relativistic electrons, 15≦E ₀65MeV, by means of high resolution semiconductor detectors and a recently developed gas-scintillation proportional counter. For constant electron bombarding energyE ₀ the ionization cross sections follow a power law dependence,σ∽Z ^?α, and forE ₀=50MeV we deducedα =2.45±0.02 for theK shell andα=3.00 ±0.09 for theL shell. The observedZ dependence exhibits significant systematic deviations from theoretical predictions which exceed the experimental values up to 15 % at lowZ elements for theK shell and on the average about 11% for theL andM shell. The same behaviour of too low experimental values, i.e. an overestimation by the theory, is observed for the energy dependence of the cross sections for all shells. A scaling behaviour describing theZ andE ₀ dependence for allK-, L andM-shell data points is observed which also predicts the experimental values by other groups at lower and higher energies correctly. The comparsion of the measuredLΒ/Lα, andLγ/Lα intensity ratios for highZ elements with the values obtained by other groups in the energy range 0.3≦E₀≦1,000 MeV exhibits an increase with bombarding energy that cannot merely be explained by the energy dependence of the subshellionization cross sections for theL shell. An attempt to explain this effect with the change of the Coster-Kronig transition probability is described.     

Ti-pumped Mo X-ray laser at 24 Å

We propose using the Ti XXI He- emission line to resonantly photo-pump Li-like Mo (Z=42) and produce lasing on several n=5 n=4 transitions near 24 Å. The continuum emission from Ti photoionizes the Mo to the Li-like isoelectronic sequence. Gains of 1–2 cm^–1 are calculated on these lines before the inclusion of Stark broadening which lowers the gain by as much as a factor of two.     

Measurements of relative line strengths in N I multiplets for transition arrays 3s-np (n=3, 4, 5)

Applying the emission method, intensities of 60 spectral lines of neutral nitrogen (N I) belonging to 15 multiplets originating from 3s-np (n=3, 4, 5) transition arrays have been measured. A wall-stabilized arc, operated at atmospheric pressure in helium with some admixture of nitrogen was applied as the excitation source. From measured line intensities, relative line strengths within multiplets have been evaluated. For transitions with Δn=1 and 2, significantly larger discrepancies from LS coupling results are found if compared to transitions 3s-3p (Δn=0). The measured relative line strengths within 3s-3p multiplets are compared with older measurements, recent calculations and with the new data recommended by NIST.     

Theoretical study on 2s2p6np Rydberg states of Cu19+ ion

We report on the calculations of transition wavelengths and weighted oscillator strengths for 2s²2p⁶-2s2p⁶ⁿp (4 ≤ n ≤ 20) electric dipole (E1) transitions of Cu¹⁹⁺ ion. The flexible atomic code (FAC) has been adopted for the calculations. Comparisons are made with the experimental data available, showing that the present results for 4 ≤ n ≤ 6 are more accurate than the previous calculated values. Furthermore, combining the quantum defect theory (QDT) with the transition energies of 2s²2p⁶-2s2p⁶np, the quantum defects for 2s2p⁶np Rydberg series of Cu¹⁹⁺ ion are determined. In addition, the energies of any highly excited states (n > 20) for this series can be reliably predicted using the QDT and the given quantum defects. The ionization energies for Cu¹⁹⁺ and Cu²⁰⁺ ions are also calculated and they excellently accord with previous experimental and calculated values.     

Laser gain by electron collisional pumping of Ar VII–V XII

Gain coefficients have been calculated for transitions of singlet levels ns–np of orbital n=4 and n=5 in magnesium-like ions with atomic numbers Z=18, 19, 20, 21, 22 and 23. Population inversions for 4p and 5p levels in these ions were also calculated, via electron collisional excitation, for electron temperature range of 93–231 eV and electron density range of 10¹⁶–10¹⁷ cm⁻³. Under these plasma conditions, the maximum gain that occurred for 4s–4p transition was at electron temperature of 231 eV and electron density of 4×10¹⁷ cm⁻³. Scaling of the maximum gain coefficients with atomic number Z and the plasma parameters is also presented.     

Isovector magnetic dipole sum rules in (d s)- shell

Linear-energy weighted sum-rules (LEWSR) are calculated for isovector magnetic dipole transitions from the ground state in some (d s)-shell nuclei. It is found that the well-known Kurath sum rule is inadequate to explain the experimental transition strengths in these nuclei. A significant contribution to the sum-rule is seen to arise from the two-body part of the Hamiltonian. The calculations are made using the spectral distribution methods.     

Double <Emphasis Type="Italic">K</Emphasis>-shell ionization of atoms by a single photon

We investigate the double K-shell ionization of heliumlike ions by a single photon. A fast convergence of QED perturbation theory with respect to the parameter 1/Z is demonstrated in the entire nonrelativistic domain for moderate nuclear charge numbers Z≥2. The ratio of double-to-single photoionization cross sections is calculated for light heliumlike ions, taking into account the leading orders of 1/Z and αZ expansions. A comparison of our results with the available experimental data for a number of neutral atoms is presented.     

Vergleich von klassischen und BORN-Wirkungsquerschnitten bei Elektronenstößen am H-Atom

Comparison of Classical and BORN Cross Sections for Electron-H-Collisions In Part I first BORN approximation cross-sections σ(n → n + Δn) for collision-induced transitions n = 10, 20, 30; Δn = 1 are calculated by Monte-Carlo methods. It is shown that the simplier circular orbit approximation (i.e. taking into account the highest momenta (? n ?1) only) approximates the exact results by BORN quite well. Circular orbit approximation cross-sections are tabulated up to n = 150 and Δn = 1. In Part II cross-sections are calculated classically in the adiabatic approximation [1, 2]. This method yields quite accurate cross-sections for small projectile energies where usual momentum approximations (binary encounter approximations) work not so well. In the paper is also presented a selection rule according to which for high n and l dipole-transitions in the H-atom are possible only for Δn = 1.