Cu-like Ions Research Articles

Wavelengths and transition probabilities for n = 4 → n′ = 4 transitions in heavy Cu-like ions (70 ⩽ Z ⩽ 92)

Wavelengths and transition probabilities have been calculated for the n = 4 → n′ = 4 allowed transitions in the heavy Cu-like ions with Z = 70–92. Fully relativistic multiconfiguration Dirac–Fock (MCDF) calculations were carried out. They take into account the correlations within the n = 4 complex, the core-valence n = 3 → n′ = 4 virtual excitations, and quantum electrodynamics effects. The present results are compared to and agree well with recent electron–beam ion–trap (EBIT) measurements in ytterbium, tungsten, osmium, gold, lead, bismuth, thorium, and uranium.

QED corrections to the4p−4dtransition energies of copperlike heavy ions

Quantum electrodynamic (QED) corrections to 4p-4d transition energies of several copper-like ions with Z = 70-92 are calculated non-perturbatively in strong external fields to all orders in binding corrections. Dirac-Kohn-Sham potentials are used to account for screening and core-relaxation effects. For the 4p{sub 1/2}-4d{sub 3/2} transition in copperlike bismuth, thorium and uranium, results are in good agreement with empirical QED corrections deduced from differences between transition energies obtained from recent high-precision electron-beam ion-trap (EBIT) measurements and those calculated with the relativistic many-body perturbation theory (RMBPT). These comparisons provide sensitive tests of QED corrections for high angular momentum states in many-electron heavy ions and illustrate the importance of core-relaxation corrections. Comparisons are also made with other theories and with experiment on the 4s-4p transition energies of high-Z Cu-like ions as accuracy checks of the present RMBPT and QED calculations.

Soft-X-ray spectra of highly charged Os, Bi, Th, and U ions in an electron beam ion trap

Systematic variation of the electron-beam energy in an electron-beam ion trap has been employed to produce soft-X-ray spectra of Os, Bi, Th, and U with the highest charge states ranging up to Ni-like ions. Guided by relativistic atomic structure calculations, the strongest lines have been identified with Δn = 0 (n = 4 to n′ = 4) transitions in Rb- to Cu-like ions. The rather weak 4p–4d transitions are much less affected by QED contributions than the dominant 4s–4p transitions. Our wavelength measurements consequently provide benchmarks with and (almost) without QED. Because the radiative corrections are not very sensitive to the number of electrons in the valence shell, our data, moreover, provide benchmarks for the evaluation of electron–electron interactions. PACS Nos.: 32.30.Rj, 39.30.+w, 31.50.+w

EUV spectroscopy of highly charged xenon ions

At the Berlin Electron Beam Ion Trap facility we investigated the radiation of highly charged xenon ions in the extreme ultraviolet wavelength range using a 2m grazing incidence spectrometer. For Rb-like Xe17+ to Cu-like Xe25+ ions 37 individual lines have been registered in the range between 90 and 240Å and identified by performing atomic structure calculations with the HULLAC code. The 4s–4p resonance lines of Cu-like and Zn-like Xe ions are found to be in good agreement with measurements at tokamaks and MCDF calculations. The experimental wavelengths for ions involving a larger number of electrons in the n=4 shell deviate slightly from the predicted values. Several lines observed with the BerlinEBIT had been previously seen but not identified at the tokamak and can now be classified.

Wavelengths of the4s1∕2−4p3∕2resonance lines inCu- andZn-like heavy ions

The euv resonance lines 4s{sub 1/2}-4p{sub 3/2} of the Cu- and Zn-like ions of Os, Bi, Th, and U (Z=76-92) have been observed in an electron beam ion trap, and their wavelengths measured using a high-resolution flat-field spectrometer. Our experiments achieve a spectral resolution three to six times better than earlier measurements and remove potential systematic errors from line blends encountered in earlier work. Our results for Cu-like ions are in good agreement only with recent ab initio calculations that include quantum electrodynamical effects. Our experimental results for Zn-like ions have a similarly high accuracy. However, theoretical predictions for Zn-like ions of a quality comparable to those available for Cu-like ions are lacking.

Dielectronic Recombination Used As a Tool for Spectroscopic Studies of Highly Charged Ions

Systematic studies of electron–ion recombination for Li-like, Na-like, and Cu-like ions have been made during the last few years at the CRYRING facility. The main purpose has been to measure recombination spectra with such high resolution and accuracy that stringent tests of advanced atomic calculations of doubly excited states can be made. From the comparison with theory it is possible to obtain energy positions, as well as radiative and nonradiative decay rates for the doubly excited states. In addition, for heavy, highly charged ions it is possible to deduce radiative corrections for energy splittings with very high accuracy.

Relativistic many-body calculations of excitation energies and transition rates from core-excited states in copperlike ions

Energies of (3s2 3p6 3d9 4l4l'), (3s2 3p5 3d10 4l4l'), and (3s 3p6 3d10 4l4l') states for Cu-like ions with Z = 30 -100 are evaluated to second order in relativistic many-body perturbation theory (RMBPT) starting from a Ni-like Dirac-Fock potential. Second-order Coulomb and Breit-Coulomb interactions are included. Correction for the frequency-dependence of the Breit interaction is taken into account in lowest order. The Lamb shift correction to energies is also included in lowest order. Intrinsic particle-particle-hole contributions to energies are found to be 20-30% of the sum of one- and two-body contributions. Transition rates and line strengths are calculated for the 3l-4l' electric-dipole (E1) transitions in Cu-like ions with nuclear charge Z = 30 - 100. RMBPT including the Breit interaction is used to evaluate retarded E1 matrix elements in length and velocity forms. First-order RMBPT is used to obtain intermediate coupling coefficients and second-order RMBPT is used to calculate transition matrix elements. A detailed discussion of the various contributions to the dipole matrix elements and energy levels is given for copperlike tungsten (Z = 74). The transition energies used in the calculation of oscillator strengths and transition rates are from second-order RMBPT. Trends of the transition rates as functions of $Z$ are illustrated graphically for selected transitions. Comparisons are made with available experimental data. These atomic data are important in modeling of M-shell radiation spectra of heavy ions generated in electron beam ion trap experiments and in M-shell diagnostics of plasmas.

Kinetics modeling of Ni-like multiple charged ions

Atomic processes affecting the population kinetics of Ni-like Ag are investigated using a collisional radiative model that includes the Cu-, Ni-, and Co-like ions. The atomic processes, which determine the steady-state ion abundance and detailed level populations, are investigated to determine the population inversion for the X-ray laser application, with several different sets of configurations. The dielectronic processes are considered by including doubly excited and inner-shell-excited states explicitly which allows one to identify the dominant channel of the dielectronic recombination from Co-like to Ni-like, and Ni-like to Cu-like ion. Further, the resonant excitation from ground state to low excited states of Ni-like ion in high-density plasmas ( n e>10 20/cm 3) is also studied.

Wavelengths of the4s1/2−4p3/2resonance lines in Cu-like heavy ions

The euv resonance lines 4s{sub 1/2}-4p{sub 3/2} of the Cu- and Zn-like ions of Os, Bi, Th, and U (Z=76-92) have been observed in an electron beam ion trap, and their wavelengths measured using a high-resolution flat-field spectrometer. Our experiments achieve a spectral resolution three to six times better than earlier measurements and remove potential systematic errors from line blends encountered in earlier work. Our results for Cu-like ions are in good agreement only with recent ab initio calculations that include quantum electrodynamical effects. Our experimental results for Zn-like ions have a similarly high accuracy. However, theoretical predictions for Zn-like ions of a quality comparable to those available for Cu-like ions are lacking.

Nuclear size effect and QED corrections to energy levels of heavy and superheavy Li-, Cu-like ions

Nuclear size effect and QED corrections to energy levels of heavy and superheavy Li-, Cu-like ions

AUGER RATES FOR Ni-, Cu-, AND Zn-LIKE IONS

Relativistic calculations of nonradiative transition rates to K-, L-, and M-shell vacancy states in Ni-, Cu-, and Zn-like ions with Z=32, 36, 42, 47, 56, 60, 66, 74, 83, and 92 are performed. Auger and Coster–Kronig transition probabilities are calculated using both Dirac–Hartree–Fock and model-potential wave functions. Tabulated data are presented for K- and L-shell Auger rates in Ni-, Cu-, and Zn-like ions, for M-shell Auger rates in Zn-like ions, and for L- and M-shell Coster–Kronig rates in Cu-like ions. Results obtained by averaging over angular momentum substates are also presented and semiempirical formulas are given for the average rates.

Soft-X-ray spectra of highly charged Au ions in an electron-beam ion trap

Systematic variation of the electron-beam energy in an electron-beam ion trap has been employed to produce soft-X-ray spectra (20 to 60 Å) of Au with well-defined maximum charge states ranging from Br- to Co-like ions. Guided by large-scale relativistic atomic structure calculations, the strongest Δn = 0 (n = 4 to n' = 4) transitions in Rb- to Cu-like ions (Au42+ – Au50+) have been identified. PACS Nos.: 32.30Rj, 39.30+w, 31.50+w, 32.20R

Investigation of a laser-produced cerium plasma by the analysis of the high-resolution x-ray spectrum

A highly stripped cerium $(Z=58)$ plasma is produced by irradiating a solid cerium target with a short pulse laser. The x-ray spectrum emitted from the plasma is recorded in the limited wavelength range 9.0--9.3 \AA{} using a high-resolution curved mica crystal spectrometer. The high-resolution spectrum, which corresponds to the $3d\ensuremath{-}5f$ transitions in Ni-, Cu-, and Zn-like cerium ions, is analyzed by means of a detailed collisional-radiative model that includes autoionization and dielectronic capture processes. The intensity ratio of the Ni-like $3d\ensuremath{-}5f$ resonant line at 9.045 \AA{} to the features emitted from satellite transitions of Cu-like ions provides an estimate for the mean electron temperature and density of 230 eV and ${10}^{22} {\mathrm{cm}}^{\mathrm{\ensuremath{-}}3},$ respectively. The deduced mean electron temperature is higher than that obtained in a similar experiment on laser-produced barium plasma. The origin of the higher mean electron temperature deduced in the present experiment is explained by the different type of transition employed for the temperature diagnostics, which might reflect a different phase of the plasma evolution.

General analytic formula for total dielectronic recombination rate coefficients of Ni-like ions

A general analytic formula for the total dielectronic recombination (DR) rate coefficients of all the ions along the NiI isoelectronic sequence with $34l~Zl~92$ is constructed on the basis of previously calculated DR data, which were obtained by relativistic ab initio level-by-level computations using the HULLAC code for ten Ni-like ions. The DR rate coefficients are given as a function of the electron temperature and of the ion charge. The results generated by this formula reproduce the previously calculated DR rate coefficients, generally to better than 5% accuracy for all electron temperatures ${\mathrm{kT}}_{e}g~{0.03E}_{I}$ ${(E}_{I}$ is the ionization energy of the Cu-like ion). As a test, the results of level-by-level DR calculations for two additional elements, barium and tungsten, are compared to those of the analytic formula. The agreement is found to be similar to that for the first ten ions. The analytic formula may be conveniently used for modeling the ion abundance distribution in hot plasmas.

Dielectronic recombination of Ni-, Cu-, and Ar-like tungsten and barium through the low inner-shell excited configurations including collision processes

Level-by-level relativistic calculations of dielectronic recombination (DR) cross sections and rate coefficients for Ni-, Cu-, and Ar- like tungsten in the ground state were performed. Similar calculations were carried out for Ni-like barium for comparison. The most important low-lying inner-shell excited configuration complexes are taken into account, namely (3p3d) 154141′ for Ni-like W and Ba, (3p3d) 154s4141′ for Cu-like W, and finally 3p 53d91, 3s3p 63d71, and 3p 54141′ for Ar-like W. These complexes give the dominant contributions to the total DR rate coefficients for kT e < 0.5 keV, and are still expected to give major contributions at higher electron temperature. Configuration mixing is taken into account when significant. The energy levels of the tungsten inner-shell excited DR channels are found to have typical j-j coupling characteristics, whereas those of Ni-like barium do not. The role of non-resonant radiative stabilizations is found to be generally minor for the Ni- and Cu-like ions. In contrast, for Ar-like tungsten these stabilizations are found to be very important. The DR rate coefficients for Cu-like tungsten are found to be very close in magnitude to those of the Ni-like ion. Some partial contributions to the DR rate coefficients are found to rise dramatically at very low electron temperature, a fact that has been observed experimentally for lighter ions. It is found that high-1 3p 53d91 configurations, that were previously neglected, may have a significant contribution to the DR of Ar-like tungsten. The effect of electron collisions with the inner-shell excited ions is shown to influence the DR rate coefficient only at very high electron densities, greater than 10 20 cm −3 for Ni-like W and greater than 10 22 cm −3 for Ar-like W. In the Ni-like case at an electron density of 10 23 cm −3 these collisions enhance the DR rate by about 30% at 5 keV, and by as much as a factor of 2 at 200 eV.

Dielectronic recombination rate coefficients for highly ionized Ni-like atoms.

Ab initio calculations of the total dielectronic recombination (DR) rate coefficients for ten ions along the Ni I isoelectronic sequence in the ground state (${\mathrm{Mo}}^{14+}$, ${\mathrm{Ag}}^{19+}$, ${\mathrm{Xe}}^{26+}$, ${\mathrm{Pr}}^{31+}$, ${\mathrm{Gd}}^{36+}$, ${\mathrm{Dy}}^{38+}$, ${\mathrm{Ta}}^{45+}$, ${\mathrm{Au}}^{51+}$, ${\mathrm{At}}^{57+}$, and ${\mathrm{U}}^{64+}$) have been performed using the HULLAC computer code package. Resonant and nonresonant stabilizing radiative transitions were included. Collisional transitions following electron capture were neglected. The present level-by-level calculations include the contributions of all the levels (over 17 000) belonging to the following Cu-like inner-shell excited configurations: 3${\mathit{d}}^{9}$4ln\ensuremath{'}l\ensuremath{'} (n\ensuremath{'}\ensuremath{\le}9), 3${\mathit{p}}^{5}$3${\mathit{d}}^{10}$4ln\ensuremath{'}l\ensuremath{'} (n\ensuremath{'}\ensuremath{\le}5), and 3s3${\mathit{p}}^{6}$3${\mathit{d}}^{10}$4ln\ensuremath{'}l\ensuremath{'} (n\ensuremath{'}\ensuremath{\le}5). The configuration complexes with a hole in the 3p inner shell contribute about 10% to the total DR rate coefficients and the complexes with the hole in the 3s inner shell about 1%. The contributions of 3${\mathit{d}}^{9}$4ln\ensuremath{'}l\ensuremath{'} for n\ensuremath{'}\ensuremath{\gtrsim}9 were evaluated by extrapolation, applying an ${\mathit{n}}^{\mathrm{\ensuremath{-}}3}$ scaling, which was checked for the specific ${\mathrm{Ta}}^{45+}$ case. It is shown that at electron temperatures higher than half the ionization energy ${\mathit{E}}_{\mathit{I}}$(Cu) of the Cu-like ion, the Burgess-Merts (BM) semiempirical formula can provide DR results with an accuracy better than \ifmmode\pm\else\textpm\fi{}20% for the relatively heavy ions (Z\ensuremath{\gtrsim}54), whereas for the lighter ions it leads to an underestimation of up to a factor 2 (for Mo). On the other hand, at low electron temperature [${\mathit{kT}}_{\mathit{e}}$0.3${\mathit{E}}_{\mathit{I}}$(Cu)] the BM approximation underestimates the DR rate coefficients by up to a few orders of magnitude and its temperature dependence is completely inadequate. \textcopyright{} 1996 The American Physical Society.

Cu-like Pd and Ag inner-shell photoionization phenomena

We have obtained results for converting focused laser radiation to X-ray line emissions in laser-heated NaF and Cu plasmas. These plasmas were used as the pump source for studying the phenomena of inner-shell photoionization of Zn-like ionic states. Soft X-ray emissions from transitions of 3d94s2 → 3d104p in Cu-like Pd and Ag ions were observed.

Excitation-autoionization cross sections and rate coefficients of Cu-like ions.

Detailed level-by-level calculations of the excitation-autoionization (EA) cross sections and rate coefficients were performed using the relativistic distorted-wave method along the Cu isoelectronic sequence for all the elements with 34\ensuremath{\le}Z\ensuremath{\le}92. While in a previous work only the 3d-4l inner-shell collisional excitations had been taken into account, the present extensive calculations include the 3${\mathit{d}}^{10}$4s-3${\mathit{d}}^{9}$4snl (n=4--7 and l=0--n-1) and the 3${\mathit{p}}^{6}$3${\mathit{d}}^{10}$4s-3${\mathit{p}}^{5}$3${\mathit{d}}^{10}$4snl (n=4,5 and l=0--n-1) excitations. An extrapolation method is used to evaluate the contribution for higher principal quantum numbers. Configuration mixing and secondary autoionization processes following radiative decay from autoionizing levels are also included. The results show that the EA processes give a dominant contribution compared to direct ionization, up to a factor of about 15 at Z=43. The additional inner-shell excitations for Z55 produce an increase in the EA effect varying from 20% to a factor of 2, with respect to the previously predicted 3d-4l EA rates. The additional excitations are the most significant for heavy elements with Z\ensuremath{\gtrsim}55, since they open EA channels, resulting in an EA rate varying typically along the sequence from 3 to 1 times the direct ionization rate. \textcopyright{} 1996 The American Physical Society.

Method for calculating the electron-impact ionization of ions of any complexity.

Relativistic distorted-wave cross sections are calculated for electron-impact ionization from the 21 subshells with n=3, 4, and 5 in several types of ions. Based on these results and the general, but very simple form for the cross section derived by Sampson and Zhang [Phys. Rev. A 45, 1657 (1992)] a very rapid, but quite accurate method using fits to the reduced cross sections is given. This applies to highly charged ions with any degree of complexity and should be very convenient for use in plasma modeling. The procedure is illustrated by application to inner-shell ionization of Cu-like gold ions, where good agreement is obtained with detailed direct relativistic distorted-wave calculations

Calculations of the screened self-energy and vacuum polarization in Li-like, Na-like, and Cu-like ions.

We present ab initio calculations of the screened self-energy and vacuum polarization for the resonance transitions of Li-like, Na-like, and Cu-like ions, for a degree of ionisation of about 10 or greater. The direct part of the Dirac-Fock potential is incorporated to all orders in the radiative corrections, and exchange effects are added in leading order. When combined with previous calculations of correlation and nuclear effects, our results agree with experiment at the level of experimental uncertainty with only a few exceptions, most notably the low-Z part of the Cu isoelectronic sequence