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     

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.     

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%.     

Probabilities of electric dipole transitions in the spectra of ions of the erbium isoelectronic sequence

The probabilities of the 4f ¹³6p→4f ¹³ ns (n=6 and 7) electric dipole transitions are calculated for the spectra of YbIII, LuIV, and HfV ions of the erbium isoelectronic sequence. The wave functions of the intermediate coupling scheme, which are necessary for calculating the relative line strengths, are semiempirically obtained from experimentally measured energy intervals between the fine-structure levels. To pass to the absolute values, radial integrals of transitions are used, which are evaluated with the Hartree-Fock functions.     

Oscillator strengths for selected 3dn4s−3dn4p transitions of the iron-group elements

Absolute transition probabilities are calculated for selected 3dⁿ4s?3dⁿ4p transitions of the iron-group elements; configuration interaction effevts are taken into account. Comparisons with Hartree-Fock and multi-configuration Hartree-Fock results and with experimental data show that the scaled Thomas-Fermi method for calculation radial wave functions is useful procedure.     

Hartree-Fock line strengths for the lithium,sodium and copper isoelectronic sequences

Hartree-Fock line strengths have been computed for the lowest Δn=0 transitions of ions in the lithium, sodium and copper isoelectronic sequences. Excitation energies were collected relativistically to lowest order in the Pauli approximation, and line strengths were corrected semiempirically using the Dirac correction factors of hydrogen-like ions. Systematic trends have been established and new data are presented for very highly ionized species.     

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.     

An assessment of the effective Gaunt factor approximation

Based on comparisons with recent theoretical data, it is shown that the effective Gaunt factor for Δn = 0 transitions in alkali-like ions is within 25% of unity in most cases and is a slowly varying function of energy. A more complex energy dependence is noted for some non-alkali-like spectra, and especially for Δn ≠ 0 excitations. A method for the approximation of important correlation effects in the target is discussed for transitions of the type ns²¹S-nsnp¹P⁰.     

Dielectronic recombination of positive ions—II. Rate coeffecients for Mo38+

Dielectronic recombination rate coefficients for Mo³⁸⁺ recombining to Mo³⁷⁺ are given for electron temperatures of 1.4, 2.8, and 5.6 KeV. Non-relativistic results for various transitions were obtained in the resonance approximation by direct evaluation of Auger and radiative decay probabilities A_a and A_r, respectively, as discussed in the preceding paper. It is found that a large number of transitions contribute to the total rate. Tables of selected A_a, A_r, fluorescence yields, and rates are given. Excitation of n = 2 electrons to higher shells is found to be the dominant contribution at the temperature considered.     

Transition energies, wavelengths, oscillator strengths and transition probabilities between 1s, 1sns and 1snp (2?n?9) states for He-like Silicon

Multiconfiguration Hartree-Fock calculations with Breit-Pauli relativistic corrections are reported for electric dipole transition (E1) energies, wavelengths, weighted oscillator strengths and transition probabilities between all of the 1s², 1sns and 1snp (2?n?9) states for He-like silicon. The results are found to compare very well with available other results except Δn=0 due to differences in the calculated excitation energies.     

Radiative constants in the spectra of ions of the erbium isoelectronic sequence

The probabilities of the 4f ¹³6p→4f ¹³5d lectric dipole transitions and the lifetimes of levels of the 4f ¹³6p and 4f ¹³5d configurations are calculated for spectra of ions Yb III, Lu IV, Hf V, and Ta VI of the erbium isoelectronic sequence. The wave functions of the intermediate coupling scheme, necessary for calculating the relative line strengths, are obtained semiempirically from experimentally measured energy intervals between fine-structure levels. To pass to the absolute values, the radial integrals of transitions, evaluated with the Hartree-Fock functions, are used.     

Relativistic calculation of spectra of 2-2 transitions in O- and F-like atomic ions

We have studied theoretically the structure of 1s²2s^n₁2p^n₂ levels in O- and F-like ions with z = 25 ÷ 40. Relativistic perturbation theory is used for the total interelectronic interaction. Allowance is made for Coulomb and relativistic interelectronic interactions. The first order perturbation theory for retardation of the interaction has been calculated fully. The complete calculation has also been made for the nonrelativistic correction in the second order and the Hartree-Fock part of the nonrelativistic correction in the third order. The Hartree-Fock relativistic correction in the second order has been taken into account fully for F-like ions and partially for O-like ions. Corrections to higher orders for z ? 28 have been found empirically and extrapolated to the region z = 29 ÷ 40. For energies of 2-2 transitions, calculation errors for z ? 28 do not exceed 900 cm^-1 and do not increase with z. Typical errors obtained with conventional, more cumbersome calculations are 5000 cm^-1 at z = 30.     

Term structure of 4d-electron configurations and calculated spectrum in Sn-isonuclear sequence

Theoretical calculations of term structure are carried out for the ground configurations 4d^w, of atomic ions in the Sn isonuclear sequence. Atomic computations are performed to give a detailed account of the transitions in Sn⁺⁶ to Sn⁺¹³ ions. The spectrum is calculated for the most important excited configurations 4p⁵ 4dⁿ⁺¹, 4dⁿ⁻¹ 4f¹, and 4dⁿ⁻¹ 5p¹ with respect to the ground configuration 4dⁿ, with n=8-1, respectively. The importance of 4p-4d, 4d-4f, and 4d-5p transitions is stressed, as well as the need for the configuration-interaction CI treatment of the Δn=0 transitions. In the region of importance for extreme ultraviolet (EUV) lithography around 13.4 nm, the strongest lines were expected to be 4dⁿ-4p⁵ 4dⁿ⁺¹ and 4dⁿ-4dⁿ⁻¹ 4f¹.     

Development of an experimental database of EUV spectra from highly charged ions of medium to high Z elements in the Large Helical Device plasmas

We are developing an experimental database of extreme ultraviolet spectra from highly charged ions using optically thin high-temperature plasmas produced in the Large Helical Device. Spectra from a variety of elements with atomic numbers ranging from 36 to 83 have been systematically recorded in the range of 1–20 nm by a grazing incidence spectrometer. For higher Z elements from tin onward, discrete or quasicontinuum spectral features from n=4 (N-shell) ions are mainly observed depending upon the plasma temperature, which leads to some new experimental identifications of spectral lines. On the other hand, major emitters are n=3 (M-shell) ions for medium Z elements from krypton to ruthenium. The calculated wavelengths for Δn≠0 transitions agree well with the measurements and the calculated wavelengths are systematically shifted to shorter wavelengths for Δn=0 transitions associated with inner-subshell excited configurations.     

Compton profiles of multiply ionized oxygen atoms

We have calculated Compton profiles of multiply ionized oxygen atoms with electronic configurations 1s^m2sⁿ2p^q, m=1−2,n=0−2,q=0−4. The values of the Compton profiles from the present calculation can be used to determine the doubly differential electron production cross sections in recent ion-atom collision experiments with oxygen ions in the rest frame of the target atoms. The calculations have been performed in impulse approximation using numerical Hartree-Fock wave functions. Compton profiles of neutral oxygen atoms, available in the literature, are in excellent agreement with the present calculation. The variation of Compton profile with the degree of ionization is investigated.     

Radiative transition probabilities in ions of the silver isoelectronic sequence

The wave functions of one-electron states above the 4d ¹⁰ core have been calculated within the relativistic perturbation theory with a zero-order model potential. The wavelengths and probabilities of electric dipole transitions in an Ag-like ion have been calculated for the 5s-5p, 5p-5d, 5d-5f, and 4f-5d transitions. The data obtained are compared with the results of calculations by the relativistic Hartree-Fock method and within the relativistic many-body perturbation theory. The theoretical results are compared with experimental data on the lifetimes of energy levels in Ag-like ions.     

Electron momentum distribution in multiply-ionized neon atoms

We present momentum-space properties of multiply ionized neon atoms as a function of the degree of ionization of the atom. In particular, we have calculated the Compton profiles of all possible ionized states of neon atoms with electronic configurations 1s^m2sⁿ2p^q, m=1-2, n=0-2, q=0-6. The radial single-electron radial wave functions, obtained from the Hartree-Fock atomic model, were converted into momentum space wave functions by applying appropriate Fourier transformation. The values of the Compton profiles from the present calculation can be used to interpret experimental cross sections of variously ionized neon atoms colliding with other atoms. Compton profiles of neutral neon atoms, available in the literature, are in excellent agreement with the present calculation.     

Properties of the quasiparticle excitations in 207Pb and 209Pb from an extrapolation of the optical-model potential

A previously developed dispersion relation approach is used to calculate the shell-model potential in the case of neutrons in ²⁰⁸Pb, in the energy domain (-50 MeV, 0). This potential contains a dispersive contribution besides a Hartree-Fock type component, and thereby includes correlation and polarization effects. The shell-model and the Hartree-Fock type potentials are assumed to have Woods-Saxon shapes with diffuseness a_v = 0.70 fm; the energy dependence of their depths and radii is calculated. The energy dependence of the shell-model potential is characterized by the effective mass, whose dependence upon radial distance and neutron energy is determined. The effective mass is a sensitive function of energy, in contrast to its Hartree-Fock type component which is nearly independent of energy. Attention is drawn to the fact that the effective mass in nuclear matter cannot be straightforwardly identified with the effective mass at the nuclear centre. The effective mass presents a sharp peak at the nuclear surface near the Fermi energy and a dip at the surface for energies 10 to 20 MeV away from the Fermi energy. The spectroscopic factors of single-particle excitations in ²⁰⁷Pb and ²⁰⁹Pb are calculated from the difference between the effective mass and its Hartree-Fock type component. The predicted values of the valence single-particle wave functions at large radial distances are in fair agreement with experimental values deduced from analyses of sub-Coulomb pickup reactions. It is shown that the dispersive contribution increases the level density parameter by about 25%, in agreement with previous microscopic or semi-phenomenological models; the calculated level density parameter is in good agreement with the empirical value.     

Scattering of Light Exotic Atoms in Excited States

The scattering of light exotic atoms in excited states (n = 2–5) from hydrogen has been calculated in a close-coupling model. For the first time, the absorption cross sections for hadronic atoms due to Stark collisions have been calculated by taking the shifts and widths of the nS states into account in a self-consistent quantum mechanical framework. A classical-trajectory Monte Carlo method has been used to calculate the scattering of exotic atoms from molecular hydrogen for n≥8. The Coulomb transitions with Δn>1 are found to be the dominant deexcitation mechanism at the initial stage of the cascade.     

Kβ X-ray emission from He-like ions

Relativistic calculations on the energies and electric dipole rates of K_β X-rays from 1s3p(¹P₁,³P₁)-1s² (¹S₀) transitions for He-like ions in the range Z=14–54 are carried out using multi-configuration Dirac–Fock (MCDF) wave functions in the active space interaction approach. The contributions from Breit interaction and quantum electrodynamics have also been included in the calculation. An attempt has been made to find a scaling expression for Breit energy in terms of Zα .The scaled Breit energies are in good agreement with the earlier accurate relativistic results and this ensures the reliability of our scaling procedure. The behavior of MCDF wavefunctions for a given J in the non-relativistic limit has also been studied. The calculated K_β X-ray energies and rates agree well with other available experimental and theoretical values.