Reduced population and gain coefficient calculations for soft X-ray laser emission from Eu

Energy levels, transition probabilities and effective collision strengths for the 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰, and the 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁹ 4l (l=s, p, d, and f) states of nickel-like Eu are used in the determination of the reduced population for 55 fine structure levels over a wide range of electron densities (from 10⁺²⁰ to 4×10⁺²² cm⁻³) and at various electron plasma temperatures.The gain coefficients for those transitions with positive population inversion factor are determined and plotted against the electron density.     

Soft X-ray laser emission from W46+

Using published atomic data, the populations of the excited states 1s²2s²2p⁶3s²3p⁶3d⁹4l (l= s, p, d, and f) – 1s²2s²2p⁶3s²3p⁶3d¹⁰of Ni-like W have been calculated for electron densities in the range 10²⁰–10²³ cm^-3and electron temperatures in the range 0.5–1 keV. For those transitions with positive population inversion factor, the gain coefficients are determined and plotted against the electron density.     

Extreme ultraviolet and soft x-ray laser emission from Ni-like Nd ions

We use the energy levels, transition probabilities, and effective collision strengths for the states 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ and 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁹ 4 l (l = s, p, d, and f) of a nickel-like Nd ion to determine reduced population for 55 fine-structure levels over a wide range of electron density values (from 10²⁰ to 4 · 10²² cm ⁻³) at various electron plasma temperatures in the range of 1–2 keV. We find the gain coefficients for those transitions with the positive population inversion factor and show their dependences on the electron density.     

Energy Levels, Transition Probabilities, Collision Strength, and Reduced Population Calculations for High Gain Predictions in Neon-Like Krypton

We calculate the atomic structure, energy levels, oscillator strengths, transition probabilities, and collision strengths for Kr XXVII. The data refer to the 157 fine-structure levels belonging to the configurations (1s²) 2s² 2p⁶, 2s²2p⁵3l, 2s¹2p⁶3l, 2s²2p⁵4l, 2s¹2p⁶4l, 2s²2p⁵5l, and 2s¹2p⁶5l, where l?=?s, p, d, f, and the calculations are performed using the fully relativistic atomic structure program FAC. We use the obtained data to calculate the level populations and gain coefficients employing the MATLAB R2012a computer program for solving simultaneously the coupled rate equations. Finally, we determine the 157 fine-structure population levels and gain coefficients for those transitions with a positive inversion factor and plot the electron density in wide range from 10¹⁹ to 10²³.     

Energy levels of ions of silver and rhodium isoelectronic sequences with <Emphasis Type="Italic">Z</Emphasis> < 86

The method of extrapolation of the parameter of a model potential for states of one electron (4f, 5s, 5p, 5d, 5f) above the core 1s ²2s ²2p ⁶3s ²3p ⁶3d ¹⁰4s ²4p ⁶4d ¹⁰ and one vacancy (4d ⁹) in the same core is applied to calculate the energy levels in the silver and rhodium isoelectronic sequences with the maximum nuclear charge Z = 86. The energy levels of Ag-and Rh-like ions were used for the calculation of the energies of resonance transitions to the ground state ¹ S ₀ in Pd-like ions. Good agreement between the theoretical and calculated energies of the resonance transitions in Pd-like ions indicates the reliability of the results obtained.     

Fine- and hyperfine structure analysis of the odd configurations in the lead atom

The fine- and hyperfine structure (hfs) analysis, on the basis of available experimental data for the configuration 6s ²6p6d+6s ²6p7s+6s ²6p8s in PbI has been performed. The Slater integrals, spin-orbit parameters and the effective hfs one-electron parameters have been determined. We find an off-diagonal core-polarization effect in the 6p6d+6p7s-space. Using the calculated radial parameters, the values of the quadrupole moment for stable and radioactive Pb-nuclei have been determined from measuredB-factors of the 6p7s ³P₁ state. In addition, a repulsion effect on the hfs sublevels with the same quantum numberF has been investigated.     

Experimentally determined transition probabilities of the systems 6p2→6p6d, 6p7s, 6p8s of neutral lead

Branching ratio measurements have been performed for all of the observed transitions from eight levels in neutral lead (6p²→6p6d, 6p²→ 6p7s, 6p²→6p8s) excited in a hollow cathode discharge in the 200–730 nm spectral range. From the relative emission intensity data, a set of absolute transition probabilities is derived for 28 lines, including lines for which transition probabilities have not been previously published. The absolute scales are obtained by averaging the measured lifetimes of the ³P⁰_1,2, ¹P_1⁰(6p7s), ³F^0_2,3, ³D^0_1,2(6p6d) levels.     

Hyperfine-structure and isotope-shift measurements in the 6s 5d↔6p 5d transitions of Ba I in the far-red spectral region

Measurements of the hyperfine structures in the 6p5d ¹ D ₂,³ D ₁ and³ F _{2, 3, 4} states of¹³⁵Ba and¹³⁷Ba, and isotope-shifts in several far-red transitions between the 6s 5d and 6p 5d configurations, as well as the transition 6s ^{2 1} S ₀→6s6p ³ P ₁ at 7,911 Å have been performed using high-resolution laser spectroscopy on a collimated atomic beam of natural barium. An analysis of the magnetic-dipole interaction in the 6p 5d configuration using effective one- and two-body hyperfine operators is presented. In particular the contact interaction was studied with respect to the correlation between the two valence electrons. Effects of strong configuration interaction were found. From a King-plot analysis of the isotope shift term- andJ-dependence of the field shift have been evaluated for the transitions between the 6s 5d and 6p 5d configurations. Relativistic Hartree-Fock (RHF) calculations have been performed of electron densities at the nucleus for six different configurations in Ba I and Ba II. The RHF calculations reproduce the experimental King-plot slopes quite well, while the absolute values, of the changes in electron density at the nucleus for the studied transitions, are found to be 9% lower than the results derived from a muonic experiment.     

类铷W37+离子双电子复合速率系数的理论研究

 利用全相对论组态相互作用理论方法,研究了类铷W³⁷⁺离子从基组态3s²3p⁶3d¹⁰4s²4p⁶4d经过双激发态(3s²3p⁶3d¹⁰4s²4p⁶4d)^-1nln′l′(n,n′=4,5)的双电子复合过程,得到了该离子在温度为1~5×10⁴ eV范围内的总双电子复合速率系数。分析比较了不同电子激发的双电子复合速率系数,结果表明:4p电子激发的双电子复合速率系数在低温时给出了主要贡献,而3d的贡献在高温时突出。由于强组态相互作用,两电子一光子跃迁对双电子复合速率系数的贡献不可忽略,其中辐射跃迁4p⁵4d5d5f-4p⁶4f5d的贡献是双激发态4p⁵4d5d5f总的双电子复合速率系数的5%。对双电子复合、辐射复合以及三体复合速率系数的比较表明,在所研究的温度范围内双电子复合速率系数最大。     

Eine Hyperfeinstruktur-Analyse der Grundkonfigurationen 5d 8 6s 2 und 5d 9 6s des Pt-I Spektrums

The hyperfine structure of the ground configurations 5d ⁸ 6s ² and 5d ⁹ 6s of the stable Platin isotopes 194, 195, 196, 198 was analyzed. For the isotope 195 a complete set of the magnetic splitting constantsA is given. TheA constants of the levels 5d ⁸ 6s ^{2 3} P ₁ and¹ D ₂ were determined for the first time. From these data the electronic splitting constants a_{6 s}=l010(10) mK, a_{d 3/2}=57 (6) and a_{d 5/2}=27 (2) mK could be evaluated. The effect of core polarization is discussed and a fieldκ _cp=?5.6(1.0) a.u. per 5d-electron spin is found. Also the isotopic shift is determined and for the mean quadratic nuclear charge radius the valueΒδ <r ²>=0.095 (10) fm² is derived.     

Two-photon excitation and ionization of inner atomic shells

The spectrum of platinum is studied in the region from 250 to 1250 Å. The twenty-two 5d6s-5d6p spectral lines of the PtIX are assigned. All levels of the 5d6s configuration are found. The assignment of the previously known 5d6p levels is confirmed and their positions are refined. The 5d ², 5d6s, and 5d6p configurations are theoretically described by the method of orthogonal operators. These calculations are compared with the data obtained by a conventional method using the Cowan program.     

Lebensdauern und Oszillatorstärken im Sr I- und Ca I-Spektrum

Radiative lifetimes of some highly excited levels in Sr I were measured by zero-field level crossing technique. These levels have been populated using optical excitation starting from the metastable 4d 5s ¹ D ₂ or 5s5p ³ P _2,1,0 states. The high population of these metastable levels necessary for the experiments was obtained by a discharge in the pure Sr vapour burning in the atomic beam oven. The following lifetimes have been determined (in units of 10^?8 sec):τ(5s 6s³ S ₁)=1.09±0.11,τ(5s 5d ³D₁)=1.67±0.10,τ(5s4f¹ F ₃)=3.43±0.28,τ(4d5p ¹ D ₂)=2.19±0.16,τ(5p ^{2 3}P₁)=0.88±0.12,τ(5p ^{2 3} P ₂)=0.78 _?0.10 ^+0.26 . These results are compared with lifetimes derived from oscillator strengths given in the literature, and the reliability of different oscillator strengths tables is discussed. A corresponding discussion is given for radiative lifetimes of some levels in Ca I published previously. Good agreement with data derived from arc emission oscillator strengths has been found. Ca lifetimes are fairly well consistent with oscillator strengths calculated with semiempirical scaled Thomas-Fermi-wave functions.     

Study of the energy level structure for ions of the thallium isoelectronic sequence

The structure of the energy level diagram for 30 ions of the thallium isoelectronic sequence is studied on the basis of the relativistic Dirac-Fock self-consistent field method with the configuration interaction taken into account. It is discovered that the ground-state configuration and the lowest term change along the thallium isoelectronic sequence: At the beginning of the sequence, the ground-state configuration is 6s ²6p, and it becomes 6s ²6f beginning from the Cf¹⁷⁺ ion. On the basis of theoretical calculations, the ground-state ionization potentials are determined for each ion. The influence of interaction of the 6s6p ² configuration with the 6s ²6d configuration on the ² D _{3/2, 5/2} levels of the latter was also studied, and values of the fine-structure splitting of the 6s ²6p ² P ⁰ and 6s ²6d ² D levels were determined for the Tl-like ions considered.     

类镍等电子系列离子M1,M2,E2禁戒跃迁特性的理论研究

利用基于全相对论框架下的多组态Dirac-Fock理论方法发展起来的程序包GRASP92和新发展的处理辐射跃迁过程的程序REOS99，计算了类镍等电子系列离子(Z=45—95)的基组态3s²3p⁶3d¹⁰¹S₀以及低激发组态3s²3p⁶3d⁹4l,3s²3p⁵3d¹⁰4l和3s3p⁶3d¹⁰4l(l=s,p,d,f)的能级及其向基态的M1,M2,E2禁戒跃迁概率.通过分析高离化类镍离子在特定的原子序数范围内由于存在能级交叉而产生的强组态相互作用，解释了高离化类镍离子禁戒跃迁概率的反常变化现象，探讨了禁戒跃迁概率受强组态相互作用影响而变化的一般规律.     

Hyperfine structure in the Gd II spectrum and the nuclear electric quadrupole moment of157Gd

The hyperfine structure of¹⁵⁷Gd was investigated in 20 Gd II lines by means of a photoelectric recording Fabry-Perot interferometer with digital data processing. The hyperfine splitting factors,A andB, were obtained by computer fits to the observed line structures. Using a multiconfigurational set of wave functions in intermediate coupling derived by Wyart, mono-electronic hyperfine parameters were deduced by a parametric treatment. The nuclear electric quadrupole moment of¹⁵⁷Gd was evaluated from the quadrupole interaction of the 5d electron in 4f ⁷ 5d6s, the 5d electron in 4f ⁷ 5d6p, and the 6p electron in 4f ⁷ 5d6p. The three values obtained for the quadrupole moment agree very well. The final result, corrected for Sternheimer shielding, isQ(¹⁵⁷Gd) =1.34(7)·10^?24 cm².     

DIELECTRONIC RECOMBINATION OF Co-LIKE Ag AND Ta IONS

Ab initio calculations of the rate coefficients for dielectronic recombination (DR) of Co-like Ag and Ta ions are performed based on Cowan's quasi-relativistic multi-configuration Hartree－Fock code. Co-like (3s ²3p⁶3d¹⁰)^-1 configurations and Ni-like (3s²3p⁶3d¹⁰)^-24l4l' autoionization configurations are included in the present calculation. Because of the extensive distribution of autoionization state energy levels, the DR rate coefficients cannot be reproduced or interpolated by a simple analytical formula, such as the Burgess－Merts formula, or the Hagelstein approximation. We propose to use multi-set Hagelstein parameters, which is convenient in practice and can reproduce well the ab initio calculated DR rate coefficients.     

Integral electronic excitation cross sections of hydrogen atom levels

Bombined results on the integral electron impact excitation cross sections of the 1s → 2s, 2p, 3s, 3p, and 3d transitions in the hydrogen atom obtained on the basis of the global approximation of all available data are presented. The parameters of a four-parameter approximation of the dependence of the excitation cross sections on the electron energy are calculated. Although the values of the cross sections reported in different papers differ by several times, the relative variance obtained by us for the 1s → 2s and 2p transitions is about 25%, while that for the 1s → 3s, 3p, and 3d transitions amounts to 30–40%, which corresponds to the real accuracy for these transitions reported to date. The data obtained on the basis of the global approximation seem to be more reliable than the data of any separate study.     

Fine-structure energy levels, oscillator strengths and lifetimes in Co XV

Excitation energies from ground state for 97 fine-structure levels as well as oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the fine-structure levels of the terms belonging to the (1s ²2s ²2p ⁶)3s ²3p, 3s ³ p ², 3s ²3d, 3p ³, 3s3p3d, 3p ²3d, 3s3d ², 3s ²4s, 3s ²4p, 3s ²4d, 3s ²4f, and 3s3p4s configurations of Co XV are calculated, using extensive configuration-interaction (CI) wave functions, obtained with the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are included through the Breit-Pauli approximation via spin-orbit, spin-other-orbit, spin-spin, Darwin and mass correction terms. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made. Our calculated excitation energies, including their ordering, are in excellent agreement with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology (NIST) wherever available. The mixing among several fine-structure levels is found to be very strong, with most of the strongly mixed levels belonging to the (1s ²2s ²2p ⁶)3p ²3d and 3s3d ² configurations. The strong mixing among several fine-structure levels makes it very difficult to identify them uniquely. Perhaps, that may be the reason for the lack of both experimental and theoretical results for these levels. We believe that our extensive calculated values can guide experimentalists in identifying the fine-structure levels in their future work. From our radiative decay rates we have also calculated radiative lifetimes of some fine-structure levels. In this calculation we also predict new data for several fine-structure levels where no other theoretical and/or experimental results are available.     

Recent hyperfine structure investigations in the configurations 4f 136s 2, 4f 136s6p,and 4f 125d6s 2 of Tm I

By use of optical hyperfine structure investigations in the Tm I spectrum theA- values of 20 levels of the configurations 4f ¹³ 6s 6p and 4f ¹² 5d 6s ² and theA-value of 4f ¹³ 6s ^{2 2} F _5/2 were determined very accurately. These data and tenA-factors from former experiments are used for theoretical calculations. 30A-factors have been interpolated from intermediate coupling wave functions using 9 effective mono-electronic parameters. The r.m.s. deviation between experimental and theoreticalA- values amounts to 0.5 10^?3 cm^?1 and represents 3/100 of the average value of the measuredA-factors.     

Lifetimes of some highly excited levels in the Pb-I spectrum measured by the hanle method

Natural lifetimes of some highly excited levels in the Pb-I spectrum have been measured by the zero field level crossing (Hanle) method. The levels were reached by optical excitation from the metastable 6p ^{2 3} P ₂ and 6p ^{2 3} P ₁ states, were a considerable population had been created by means of adc discharge in a Pb atomic beam. An atomic beam source producing atoms in metastable states is described. For the lifetimes τ of the investigated levels we find:τ(6p(1/2)6d ³ D ₁)=3.74(28) ns,τ(6p(1/2)6d ³ F ₂)=25.8(1.3) ns,τ(6p(1/2)6d ³ D ₂)=4.17_(?31) ^(?49) ns,τ(6p(1/2)6d ³ F ₃)=6.08(26) ns,τ(6p(3/2)7s)³ P ₂=5.85(27) ns. These results are compared with lifetimes derived from oscillator strengths given in the literature.