Saddle-point Complex-rotation Method Research Articles

Auger processes of the Rydberg series for Be-like oxygen ions

The relativistic energies and Auger transition rates for the Rydberg series 1s23lnl′ 1,3F° (n = 3–6) of Be-like oxygen ions are determined by the saddle-point variation and saddle-point complex-rotation methods. Relativistic corrections and mass polarization effects are considered to improve the computational accuracy of the energy. The Auger branching ratios of the 1s22s and 1s22p decay channels for these Rydberg series are calculated. The accurate Auger electron energies are compared with high-resolution electron spectroscopy. The results will provide useful data for the identification of spectral lines arising from the Be-like oxygen ions and experimental studies in future work.

Theoretical calculation of atomic spectrum for 1s23l4l′ states of beryllium-like ions

Using the saddle-point variation and saddle-point complex-rotation methods, energies, radiative, and Auger rates are calculated for the doubly-excited states 1s23l4l′ of beryllium-like ions. The total wave function is expanded by the restricted variation method to saturate the functional space and improve the nonrelativistic energy. Relativistic corrections and mass polarization effects are taken into account by the first-order perturbation theory. The partial Auger rates for these states are studied. The calculated Auger electron energies are compared with the experimental results which are observed in high resolution electron spectroscopy. The total radiative rates and the total Auger rates for these doubly-excited states 1s23l4l′ in the beryllium-like ions are also analyzed along with the increase of atomic number Z. Calculated results show that the total Auger rates are several orders of magnitude larger than the total radiative rates for these low-Z systems.

Decay processes of doubly-excited 1s23lnl′ 1, 3S resonances of Be-like ions

Energies, radiative and Auger decay rates for the doubly-excited states 1s23lnl′ 1, 3S (n=3–4) of Be-like ions are calculated by the saddle-point variation and saddle-point complex-rotation methods. The configuration structure of the doubly-excited series is checked by the relative contribution to the normalization of the angular-spin components. Relativistic corrections and mass polarization effects are taken into account by the first-order perturbation theory. The partial Auger decay rates and the Auger branching ratios for these states are studied. The calculated Auger electron energies are compared with the high resolution electron spectroscopy. The total fluorescence yield of these doubly-excited states 1s23lnl′ 1, 3S in the Be-like ions are also analyzed along with the increase of atomic number Z.

Radiative and Auger transitions of K-shell excited resonance states in boron-like sulfur ion

<sec>Non-relativistic energy values and wave functions of the K-shell excited resonance states 1s2s<sup>2</sup>2p<sup>2</sup>, 1s2s2p<sup>3</sup>, 1s2p<sup>4 2, 4</sup><i>L</i> (<i>L</i> = S, P, D) in boron-like sulfur ion are calculated in the frame of multi-configuration saddle-point variation method. The electron correlation effects are considered by the expansion of configuration wave function. The wave functions are constructed and optimized by the orbital-spin angular momentum partial waves selected based on the rule of configuration interaction. To saturate the wave functional space and to improve the non-relativistic energy, the restricted variational method is used to calculate the restricted variational energy. Then, the mass polarization effect and relativistic correction are calculated by the perturbation theory. The quantum electrodynamics (QED) effect and higher-order relativistic correction are considered by the screened hydrogenic formula. Furthermore, the energy shift originating from the interaction between closed channel and open channel is also calculated. Finally, the accurate relativistic energy levels for these resonance states are obtained by adding the non-relativistic energy and all corrections.</sec><sec>Using the optimized wave functions, the line strengths, oscillator strengths, radiative transition rates and transition wavelengths of electric-dipole transitions for the K-shell excited resonance states in boron-like sulfur ion are systematically calculated. In this work, the oscillator strengths and transition rates are given in the length, velocity, and acceleration gauges. The good agreement among the three gauges reflects that the calculated wave functions are reasonably accurate. The calculated radiative transition rates and transition wavelengths are compared with other theoretical data. Good agreement is obtained except the transition: 1s2s(<sup>3</sup>S)2p<sup>3</sup> <sup>2</sup>P<sup>o</sup>→1s2<sup>2</sup>s2p<sup>2 2</sup>D. The deviation between our theoretical result and the MCDF theoretical value is about 46%, which needs further verifying. The Auger rates, Auger branching ratios, and Auger electron energy values of the important decay channels of the K-shell excited states are calculated by the saddle-point complex-rotation method. The calculated Auger rates and Auger electron energy values are also in good agreement with the corresponding reference data. For some K-shell states, the related energy levels and Auger branching ratios are reported for the first time. The present calculations results will provide valuable theoretical data for the calibration of spectral lines and Auger electron spectra in the relevant experiments.</sec>

K-shell photoionization of Be-like nitrogen from the ground state: energies and Auger widths of the high-lying double-excited states for N IV

The K-shell photoionization cross section of Be-like nitrogen (N IV) from the ground state is studied with the R-matrix and distorted-wave method for photon energies from 5.7 to 41.2 Ry. The close-coupling expansion includes 34 target states of N V with the 13 configurations in the LS-coupling scheme. The resonance energies, quantum defect and widths of 18 series of autoionization are determined from QB method and agree with these by cross sections. Our theoretical resonance energies and widths are compared with the existing experiments on the Auger spectra and other theoretical results. The results show that the calculated resonance energies are in rather good agreement with the experiment on the Auger spectra. For the autoionization width of some resonance states, good agreement is also found with recent theoretical results wherever available obtained using a saddle-point complex-rotation method.

Energy levels, radiative transitions and Auger transitions of the core excited states for B-like ions

Energy levels, radiative transitions and Auger transitions of the core excited states from 1s2s22p2 and 1s2s2p3 2,4L (L=S,P,D) configurations for B-like systems including P10+, Ca15+, Mn20+, and Zn25+ ions are calculated using the saddle-point variation and saddle-point complex-rotation methods. The first-order perturbation theory is used to calculate relativistic and mass polarization corrections. Present energy levels, radiative transition rates and wavelengths, Auger rates and electron energies are compared with theoretical and experimental values in the literature. The total radiative rates and the total Auger rates for these resonances are also discussed with nuclear charge numbers.

Inner-shell excitation energy levels, and radiative and Auger transitions of B-like nitrogen

Inner-shell excitation energy levels, and radiative and Auger transitions of the 1s2s22p2, 1s2s22p3p, 1s2s2p3, 1s2p4, and 1s2p33p 2,4L (L = S, P, D) resonances for B-like nitrogen are calculated using the saddle-point variation and saddle-point complex-rotation methods. The first-order perturbation theory is used to calculate relativistic and mass polarization corrections. Present autoionization energy levels, radiative transition rates and wavelengths, Auger rates, and Auger electron energies for these resonances agree well with theoretical and experimental data available in the literature, and will provide valuable background data for astrophysics and plasma physics in future.

Energies, radiative and Auger transitions of the core-excited states for the boron atom

Energies, radiative and Auger transitions of the 1s vacancy resonances 1s2s22p2, 1s2s22p3p, 1s2s2p3, 1s2p4, and 1s2p33p, 4L (L=S, P, D) for the neutral boron atom are calculated using the saddle-point variation and saddle-point complex-rotation methods. Large-scale wave functions are used to obtain reliable results. Relativistic and mass polarization corrections are included by the first-order perturbation theory. The calculated term energies, x-ray wavelengths, and Auger electron energies for these core-excited states are compared with available theoretical and experimental results. Auger electron energies and branching ratios are used to identify high-resolution B Auger spectrum produced in 300keV B+ on CH4 collision experiment. It is found that the Auger decay of core-excited states of the boron atom gives significant contributions to Auger spectrum in the range of 165–210eV, and many previously unknown line identifications are presented.

Energies and the radiative and Auger transition rates of1s2p4resonances of B-like ions

Energy levels and the radiative and Auger transition rates of the 1$s$2${p}^{4}$ ${}^{2,4}L$ ($L=S$, $P$, $D$) resonances in the boron isoelectronic sequence are calculated using the saddle-point variation and saddle-point complex-rotation methods. Large-scale wave functions are used to saturate the functional space. Relativistic and mass polarization corrections are included by the first-order perturbation theory. The Auger branching ratios of the important decay channels for these core-excited states are calculated. The reliable transition wavelengths and Auger electron energies are used to identify available x-ray spectra and Auger electron spectra. Identifications of several unknown experimental lines from 1$s$2${p}^{4}$ resonances are reported. The total radiative rates and total Auger rates of these 1$s$2${p}^{4}$ resonances are also reported and discussed along with the increase of atomic number $Z$. It is found that the total Auger rates are several orders of magnitude greater than the total radiative rates in these low-$Z$ ions.

Energy levels, Auger branching ratios, and radiative rates of the core-excited states of B-like carbon

Energy levels, Auger branching ratios, and radiative rates of the core-excited states of B-like carbon are calculated by the saddle-point variation and saddle-point complex-rotation methods. Relativistic and mass polarization corrections are included using first-order perturbation theory. Calculated Auger channel energies and branching ratios are used to identify high-resolution Auger spectrum in the 300-keV C(+) → CH(4) collision experiment. It is found that Auger decay of these five-electron core-excited states gives significant contributions to Auger spectrum in the range of 238-280 eV.

Energies and Auger widths of the high-lying double-excited states for Be-like neon

Energies and Auger widths of high-lying doubly-excited states 1s23lnl′ (n = 3–6) for Be-like neon are calculated using a saddle-point variational method and saddle-point complex-rotation method. The relativistic corrections and mass polarization are obtained with first-order perturbation theory. The configuration structure of the high-lying doubly-excited series is checked by relativistic perturbation corrections. The oscillator strengths and radiative transition probabilities are also calculated. Our results of energies and Auger widths are compared with the available theoretical results in the literature. Auger channel energies are compared with those from high-resolution electron spectroscopy. Excellent agreement is obtained in each state.

Relativistic Energies and Auger Widths of High-Lying Doubly-Excited States 1s23lnl′ 1De in Be-Like O4+ Ions

The saddle-point variational method and restricted variational method are used to calculate energies of doubly-excited singlet states 1s23lnl′ (n = 3–5) 1De in Be-like O4+ ions, including the mass polarization and relativistic corrections. The saddle-point complex-rotation method is used to compute the Auger widths and Auger transition rates. These results are compared with other theoretical and experimental data in the literature.

Energies, fine structures, and Auger widths of the high-lying triply excited states of 2S(m) and 2D(m) (m=2—7) for the “hollow atom” lithium

The relativistic energies and fine structures of the high-lying triply excited states 2l2l′nl″ 2S(m) and 2D(m) (m=2—7) for the “hollow atom” lithium are studied using the saddle-point variational method and the saddle-point complex-rotation method, including the mass polarization and relativistic corrections. The partial Auger widths and the total widths are also calculated. By the discussion of relativistic effect, we recalibrated the configurations of 2S(7) , 2D(6) and 2D(7).

Energies and Auger widths of the high-lying triply excited states for Li-like beryllium

The energies, fine-structure splittings, Auger channel energies, and the Auger widths of the high-lying triply excited 2l2l{sup '}nl{sup ''} (n>=2) states of {sup 2}S, {sup 2}D, and {sup 2}P{sup o} resonances for Be{sup +} are studied using the saddle-point variational method and saddle-point complex-rotation method. The relativistic corrections and mass polarization are included using the first-order perturbation theory. Restricted variational method is carried out to extrapolate better energies. The partial Auger widths are calculated for the individual open channels and the total Auger widths are obtained by coupling the important open channels and summing over the other channels. The configuration mixings of the triply excited resonances are described and differences in the literature on the designation of the intershell states are pointed out. These results are compared with other theoretical and experimental data in the literature.

The 1Po resonant states of LiII between the N = 2 and 3 thresholds

We studied the lowest five doubly excited 1Po resonant states of Li+ between the N = 2 and 3 thresholds by the saddle-point complex rotation method with B-spline functions. The doubly excited states are grouped in Rydberg series labeled by the quantum numbers K, T, A. Our results of energies and widths are in good agreement with other theoretical and experimental results.

Energies, fine structure, hyperfine structure and Auger widths of the core-excited states for the Li isoelectronic sequence

The relativistic energies, fine structures, hyperfine structures, Auger rates and widths of the core-excited states for the Li isoelectronic sequence (Z = 10–20) are studied using the saddle-point variational method and the saddle-point complex-rotation method. The oscillator strengths, radiative rates, wavelengths and lifetimes are also reported. Properties such as fine-structure splitting, radiative and Auger rate regularly change along the Li isoelectronic sequence are discussed. The results are compared with other theoretical and experimental data in the literature.

The 1,3Po Resonant states of LiII and BIV below the n = 2 threshold

We studied doubly excited 1,3Po resonant Li+ and B3+ below the n = 2 threshold by the saddle-point complex rotation method with B-spline functions. We calculated the ten lowest 1Po and ten lowest 3Po resonant states of Li+and B3+, respectively. The doubly excited states are grouped in Rydberg series labeled by the quantum numbers K, T, A. Our results of energies and widths are in good agreement with other theoretical and experimental results.

Energies, Auger widths and branching ratios of the doubly core-excited 2s2p3 resonances for Be-like oxygen

The energies, Auger widths and Auger decay branching ratios of the doubly core-excited 2s2p3 5,3S°, 3,1P° and 3,1D° resonances for Be-like oxygen are calculated using a saddle-point complex-rotation method. The relativistic corrections and mass polarization are included using the first-order perturbation theory. The partial Auger widths are obtained for the individual channels and the total Auger widths are obtained by coupling the important open channels and summing over the other channels. The Auger transition energies of these resonances are calculated and compared with the available experimental and other theoretical results in the literature.

Energies, Auger width and branching ratios of the core-excited triplet 1s2p3 3Po and 3Do resonances for a beryllium-like system

The relativistic energies, Auger width and Auger decay branching ratios of the core-excited 1s2p3 3Po and 3Do states for the beryllium isoelectronic sequence (Z = 4–10) are studied using the saddle-point variational method and the saddle-point complex-rotation method. The total Auger width is obtained by coupling the important open channels and summing over the other channels. The oscillator strengths and transition rates are also calculated. Our results are compared with the available experimental and other theoretical results in the literature.

Energies and Auger widths of the triply excited states of He -

Some triply excited states of He- ion are studied using the saddle-point complex-rotation method. The energies and Auger widths of these resonances are calculated with the relativistic corrections and mass polarization taken into account. The total Auger width is obtained by coupling the important open channels and summing over the other channels. These results are in good agreement with other theoretical and experimental data in the literature.