Sodiumlike Ions Research Articles

Comparison of phenomenological and supersymmetry-inspired quantum-defect methods in their relativistic and quasirelativistic formulations

The comparison of phenomenological and supersymmetry-inspired quantum-defect methods in their relativistic and quasirelativistic formulations is undertaken through a systematic study. Derivations, which emphasize similarities and differences between these approaches, are applied to evaluate oscillator strengths for low-lying and Rydberg states for lithiumlike, sodiumlike, and copperlike ions. Relativistic transition matrix elements calculated with the Dirac wave functions are gauge invariant. For the quasirelativistic formalism, an effective transition operator in the velocity gauge is proposed for the calculations. The detailed numerical results we obtained enable us to draw inferences as to the improvements and also to the limitations of these models. @S1050-2947~97!05009-9#

Integral and differential cross sections for electron-impact excitation of sodium-like ions

Excitations of Na-like ions (Al2+, Si3+, S5+ and Ca9+) by electron impact are studied theoretically using the R-matrix method. Integral and differential cross sections are obtained for the transitions from the ground state (3s) to the 3p, 3d, 4s, 4p and 4d excited states, allowing for coupling between the lowest eleven states. The asymmetry parameter A, which describes the forward-backward asymmetry of the differential cross section is calculated also. The resulting A indicates that the backward scattering dominates in the transition 3s → 3p at low incident energy, increasingly with the ionic charge.

TRANSITION RATES FOR LITHIUM-LIKE IONS, SODIUM-LIKE IONS, AND NEUTRAL ALKALI-METAL ATOMS

Third-order many-body perturbation theory is used to obtainE1 transition amplitudes for ions of the lithium and sodium isoelectronic sequences and for the neutral alkali-metal atoms potassium, rubidium, cesium, and francium. Complete angular reductions of the first-, second-, and third-order amplitudes are given. Tables of transition energies and rates are given for the 2p1/2→ 2s1/2, 2p3/2→ 2s1/2, 3s1/2→ 2p1/2, and 3s1/2→ 2p3/2transitions in the lithium isoelectronic sequence and for the corresponding 3p1/2→ 3s1/2, 3p3/2→ 3s1/2, 4s1/2→ 3p1/2, and 4s1/2→ 3p3/2transitions in the sodium sequence. For neutral alkali atoms, amplitudes ofnp1/2→ ns1/2,np3/2→ ns1/2, (n+ 1)s1/2→ np1/2, and (n+ 1)s1/2→ np3/2transitions are evaluated, wherenis the principal quantum number of the valence electron in the atomic ground state. Semi-empirical corrections for the omitted fourth- and higher-order terms in perturbation theory are given for the neutral alkali-metal atoms. Comparisons with previous high-precision calculations and with experiment are made.

Electron impact excitation rates for transitions in sodium-like ions between P V and Co XVII

Electron impact excitation rates for the Na-like ions Al III, S VI, Ti XII, Fe XVI and Ni XVIII, calculated with the R-matrix code, are used to interpolate data for the ions between P V and Co XVII. Results for all 10 transitions among the 3s 2S, 3p 2P, 3d 2D, 4s 2S and 4p 2P levels are presented in the form of polynomial fits in log Te to the effective collision strengths (γ) for each transition. These fits, which lead to results estimated to be accurate to ± 10%, are applicable over an electron temperature range of log Tmax − 0.8 ⩽ log Te ⩽ log Tmax + 0.8, where Tmax is the temperature of maximum fractional abundance in ionization equilibrium of the relevant species.

Precision measurements and identification of laser plasma emission spectra due to transitions from doubly excited levels of the sodium-like selenium ion

The spectrum of dielectronic satellites of resonance lines of the neon-like selenium ion was analyzed experimentally and theoretically. The satellite line spectrum resulting from stabilizing radiative transitions from doubly excited states of the sodium-like selenium ion to nonautoionizing states was obtained using a laser plasma and a record spectral resolution of λ/Δλ ≈ 5000–8000. A detailed analysis is given of the laser plasma x-ray emission spectrum in the range 7.2–8.8 A, more than 300 lines or compact groups of spectral lines were identified, and their wavelengths were measured with an error of ±5−10−4 A.The good agreement between the modeled and experimental spectra indicates that the emission spectrum of Na-like ions shows promise for use in high-temperature plasma diagnostics.

Hyperfine splittings of neonlike lasing lines.

The hyperfine splitting of a soft-x-ray lasing line coming from neonlike niobium has recently been measured and the effect of the splitting on the gain coefficient observed, as reported earlier. In this work, the hyperfine splittings for the principal 3p\ensuremath{\rightarrow}3s neonlike lasing lines due to the coupling with the dipole magnetic moment of the nucleus are calculated for atomic numbers Z from 17 through 59 in the framework of the relativistic multiconfiguration-atomic-structure theory. The diminution of the gains due to splittings in the case of Doppler-broadened lines is calculated. The parameters for the splitting of the 2p-to-2s transitions in fluorinelike ions and the 3p-to-3s and 3d-to-3p transitions in sodiumlike ions are also presented.

Total cross sections of electron-impact ionization ofAr7+

The electron-impact single-ionization cross section of ${\mathrm{Ar}}^{7+}$ has been measured from 18 to 1186 eV using a crossed-beams technique. The present results are higher than previous measurements at the higher energies and are in good agreement with recent distorted-wave calculations that include contributions from excitation autoionization. Below the threshold for direct ionization at 144 eV, the cross section contains contributions due to space-charge modulation and excitation of metastable ions in the target beam into autoionizing states. These transitions are predominantly spin allowed and dipole forbidden. Scaling laws for sodiumlike ions are discussed.

Excitation-autoionization in highly charged sodiumlike ions.

The effects of excitation-autoionization have been studied for nine sodiumlike ions with 26{le}{ital Z}{le}92. Relativistic-distorted-wave methods were used to calculate cross sections for direct electron-impact ionization of these ions. Relativistic-distorted-wave cross sections were computed for electron-impact excitation of {ital n}=2 electrons to {ital n}=3 levels of the ions, and detailed relativistic Auger rates and radiative rates were calculated in order to obtain the excitation-autoionization cross sections. We investigated the variation of these cross sections along the Na-like isoelectronic sequence. We found that configuration interaction significantly affects some cross sections in ions where level crossings occur for some of the doubly excited intermediate states.

Spectra of Cd, In, Sb and Te in laser produced plasmas (5-9.2 Å) and survey of 2p6 nl energy levels in the sodium isoelectronic sequence (Zn XX-Nd L)

The emission spectra of plasma produced by frequency-doubled Nd: YAG laser irradiation (0.53 µm, 600 ps, 5 × 1014W cm−2) of Cd, In, Sb and Te have been photographed in the region 5.0-9.2 Å by means of a flat crystal spectrograph. The transitions from 2p6nl(n = 4-7) to 2p63l' in sodium-like ions are identified by comparison between experimental wavelengths λexp and predictions λREL of the relativistic parametric potential method. By extending these comparisons to the levels of lower-Z elements, systematic trends of Eexp - EREL = f(Z) are derived. The resulting semi-empirical energies are listed from Zn XX to Nd L and lead to recommended wavelengths and to ionization limits. Some features of magnesium-like ion spectra (Cd36+ through Te40+) which overlap sodium-like ion spectra, are briefly described.

Indirect x-ray line formation processes in highly charged barium.

We have studied indirect excitation processes contributing to the x-ray line emission of neonlike barium (Ba{sup 46+}) interacting with an electron beam. Techniques are presented which resolve the contributions due to electron capture by fluorinelike ions and inner-shell ionization of sodiumlike ions from contributions due to direct electron-impact excitation and radiative cascades. The strength of resonance excitation of the 2{ital p}--3{ital s} magnetic quadrupole line through intermediate levels 4{ital lnl}{prime} ({ital n}=5,6) is measured to equal {ital S}=(2.8{plus minus}0.8){times}10{sup {minus}19} cm{sup 2} eV.

Spectra and energy levels of sodiumlike ions from Y^28+ to Sn^39+

Spectra of ten sodiumlike ions from Y28+ to Sn39+ were observed with laser-produced plasmas and grazing-mcidence spectrographs. Wavelengths, energy levels, and ionization energies were determined for all ions of the isoelectronic sequence from Y to Sn. Revised ab initio and fitted values are given for the 3d–4f wavelengths of the sodiumlike ions K8+ and Rh34+.

Proof-of-principle experiment for a hot electron pumped XUV amplifier

An X-ray laser scheme was recently proposed based on the pumping of neon-like 3s-3p transitions using inner-shell ionization of sodium-like ions by suprathermal electrons. Since this laser operates in principle with no population in the neon-like charge-state power requirements can be reduced from the standard collisionally driven amplifier, and the problem of line-trapping can be ameliorated. Model calculations using a quasi-steady state collisional-radiative model indicated that measurable gains could be obtained in practical experiments. We propose a proof-of-principle experiment to demonstrate the pumping of neon-like excited states by hot electrons. A ~ 1 ns long, 0.53 µ laser beam, will be focussed on a solid dot target of dilute (5%) bromine, to create a cool, dense plasma. The pulse and target will be optimized to produce as much sodium-like population as possible in the corona. This low-fluence green pulse does not produce suprathermals. A second, ~ 100 ps, 1.06 µm pulse of 1015 W/cm2 will be "piggybacked" on the first, to create hot electrons. The timing of the red beam will be optimized with respect to the sodium-like fraction of the cool plasma. The hot electrons create a transient population of neon-like ions, coincident with the red beam, that are detected by their characteristic n=3-n=2 resonant X-ray emission. If, as expected while the red beam is present, the neon-like excited states are produced by inner-shell ionization (as opposed to collisional excitation), n = 3-2 line ratios will carry a distinctive signature indicating a statistical feeding mechanism. The same signature will imply the existence of a population inversion. Proposed detection systems include space and time resolving crystal X-ray spectrometers for measuring the neon-like lines, and an array of filtered X-ray diodes to measure suprathermal electron temperature and number.

Relativistic many-body calculations of oscillator strengths for sodium-like ions

Relativistic many-body perturbation theory is applied to calculate oscillator strengths for the components of the resonant 3p-3s doublets in sodium-like ions with nuclear charges ranging from Z = 11−29. The present calculations of the multiplet averaged oscillator strengths are in excellent agreement with previous nonrelativistic MCHF calculations. Discrepancies of order ten percent between measured oscillator strengths and ab initio Dirac-Hartree-Fock calculations for highly-ionized members of the sequence are resolved, but a one-percent discrepancy between theory and experiment remains for neutral sodium.

S-Matrix formalism calculation of atomic transition probabilities with inclusion of polarization effects

A universal, semi-empirical procedure is proposed for including polarization of the core by the outer electrons of an atom in calculations of radiative transition probabilities based on the S-matrix approach. A calculation was carried out of dipole transition probabilities between low lying configurations of sodium-like ions for nuclear charges Z = 16 to 40 and for aluminum-like ions with nuclear charges Z = 21 to 40.

High-resolution bent-crystal spectrometer for the ultrasoft x-ray region

A multichannel vacuum Bragg-crystal spectrometer has been developed for high-resolution measurements of the line emission from tokamak plasmas in the wavelength region between 4 and 25 Å. The spectrometer employs a bent crystal in Johann geometry and a microchannel-plate-intensified photodiode diode array. The instrument is capable of measuring high-resolution spectra (λ/Δλ≊3000) with fast time resolution (4 ms per spectrum) and good spatial resolution (3 cm). The spectral bandwidth is Δλ/λ0=15% at λ0=8 Å. A simple tilt mechanism allows access to different wavelength intervals. In order to illustrate the utility of the new spectrometer, time- and space-resolved measurements of the n=3–2 spectrum of selenium from the Princeton Large Torus tokamak plasmas are presented. The data are used to determine the plasma transport parameters and to infer the radial distribution of fluorinelike, neonlike, and sodiumlike ions of selenium in the plasma. The new ultrasoft x-ray spectrometer has thus enabled us to demonstrate the utility of high-resolution L-shell spectroscopy of neonlike ions as a fusion diagnostic.

Electron-impact excitation of Al2+

Detailed calculations of the electron-impact excitation of the sodiumlike ion ${\mathrm{Al}}^{2+}$ were performed using both the unitarized Coulomb-Born approximation and the close-coupling approach. Calculations were undertaken at both the five-state (3s, 3p, 3d, 4s, and 4p) and nine-state (+4d\ifmmode\bar\else\textasciimacron\fi{}, 4f\ifmmode\bar\else\textasciimacron\fi{}, 5s\ifmmode\bar\else\textasciimacron\fi{}, and 5p\ifmmode\bar\else\textasciimacron\fi{}) levels of approximation. Calculations using Hamiltonians both with and without (semiempirical) core-polarization potentials were completed. Particular attention was paid to the resonance (3s-3p) excitation. The inclusion of core-polarization potentials resulted in cross sections for the resonance excitation that are 10% smaller in magnitude. As an additional check on the calculations, binding energies of ${\mathrm{Al}}^{+}$ bound states, and oscillator strengths for ${\mathrm{Al}}^{2+}$ transitions, were also computed and compared with the results of measurements and other calculations.

Many-body perturbation-theory calculations of energy levels along the sodium isoelectronic sequence.

Energies of 3s and 3p states of sodiumlike ions are calculated from Z=11 to Z=92 starting from a Dirac-Fock potential and including second- and third-order Coulomb correlation corrections, the lowest-order Breit interaction with retardation treated exactly, second- and third-order correlation corrections to the Breit interaction, and corrections for reduced mass and mass polarization. The calculated energies are compared to measured energies to determine the size of the omitted quantum electrodynamics corrections.

LOW LYING ODD PARITY AUTOIONISING STATES IN THE 2p-SUBSHELL ABSORPTION SPECTRUM OF A1 III AND Si IV

The photoabsorption spectrum of an aluminum plasma and of a silicon plasma were photographed in the E W region. The absorption technique used utilises two laser plasmas, one produces the background continuum, the other generates the absorbing medium. Under appropriate experimental conditions the 2p-subshell excitation spectra of the sodium-like ions ARIII and Si IV were observed. The observed spectra are interpreted with the help of multiconfiguration Dirac-Fock type calculations. The study of photoabsorption spectra of atoms and ions provide valuable information relevant to several different areas such as astrophysics or short wavelength laser studies for example. For purpose of systematising, absorption studies should ideally be carried out over extended isoelectronic and isonuclear sequences. However, when using conventional atomic or ionic absorption techniques, one encounters severe difficulties obtaining the spectra of highly refractory and/or corrosive elements in the vapor phase and also the spectra of multiply charged ions. The dual laser-plasma absorption technique1 presents some advantages that overcome these difficulties. The latest development based on this techniquez is characterised by a great versatility which allows time resolved absorption studies over a wide range of ionisation stages as well as neutral species. In this paper we present wavelength measurements of inner-shell transitions in the sodium-like ions ARIII and SiIV. The corresponding spectra are due to the excitation of a 2p-subshell electron into outer shells. Similar studies were carried out in NaI by several groups over the past years 3*4 s5 and In MgII by Esteva and Mehlman6. In the following, we will first describe briefly the experimental technique used, outline the main features of the 2p spectrum of Na-like species, and then present and comment on our results. The experimental technique consisted of equally dividing the output of a 1.55, 30 nanos., Q-switched ruby laser between a cylindrical lens and a spherical lens combination. Two different solid targets in vacuo were positioned at the foci such that a line plasma was formed at the surface of one and a point plasma at the surface of the other. The line plasma (aluminium or silicon) constituted the absorbing medium, the point plasma (tungsten or hafnium) acted as a source of quasi Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987934

3s–3p, 3p–3d, and 3d–4f transitions of sodiumlike ions

New measurements have been made for wavelengths of the 3s–3p, 3p–3d, and 3d–4f transitions of the sodiumlike ions Cu18+, Zn19+, Ga20+, Ge21+, As22+, Se23+, Br24+, Kr25+, Y28+, Zr29+, Nb30+, Mo31+, Ru33+, Rh34+, Pd35+, Ag36+, and Sn39+. The measurements were made by photographing laser-produced plasmas and tokamak plasmas with grazing-incidence spectrographs. The energies of the transitions were also calculated with Dirac–Fock computer codes. By fitting the differences between the observed and calculated wave numbers to simple formulas, least-squares-fitted wavelengths for all sodiumlike ions from Ar7+ to Xe43+ were determined. The estimated uncertainty of the fitted wavelengths is ±0.007 Å, which makes them useful as reference values. The wavelengths range from 9 to 713 Å.

Mechanisms for creating population inversions in Ne-like ions.

We investigate the effects of inner-shell ionization of sodiumlike ions on the kinetics of neonlike selenium, using a simple model that separates the calculation of the excited-state kinetics from that of the ionization balance. Our model includes collisional and radiative transitions between the neonlike states, inner-shell ionization of sodiumlike states, and dielectronic recombination from fluorinelike ions. By examining the relative importance of these various population mechanisms, we demonstrate that inner-shell ionization of sodiumlike ions has a significant effect on the inversion kinetics of neonlike selenium, although it is not sufficient alone to account for the discrepancy with experimental observation.