Saddle-point Complex-rotation Method Research Articles

Auger width and branching ratios for berylliumlike2s22p23Pand2s2p35Sresonances

The energies and the widths of berylliumlike ${2s}^{2}{2p}^{2}{}^{3}P$ and ${2s2p}^{3}{}^{5}S$ resonances for Z from 3 to 10 are calculated using the saddle-point complex-rotation method. The Auger decay branching ratios of these states are explained using the spin-alignment-dependent theory.

Photoionization of Be-like neon (Ne VII) from the low-lying states: Energies, widths, branching ratios, and oscillator strengths of the1s−2presonances

Seventeen-state close-coupling calculations are performed on the photoionization near the 1 s-2 p resonance region from the terms belonging to the configurations 1s 2 2s 2 ,1 s 2 2s2p, and 1s 2 2p 2 , of Be-like neon ions, Ne VII. The calculations include the total and partial photoionization cross sections and the contributions of the main ionization channels to the partial cross sections. The resonance energies, widths, and branching ratios of the 1s-2 p core-excited states are determined from these cross sections. The resonance oscillator strengths of the corresponding 1s-2 p transitions from Ne VII low-lying states are also obtained by integrating the photoionization cross sections. Our theoretical resonance energies, widths, and branching ratios are compared with existing experiments on the Auger spectra and other theoretical results. The calculated resonance energies are in rather good agreement with the latest experiment on the Auger spectra. For the autoionization width, good agreement is also found with recent theoretical results wherever available obtained using a saddle-point complex-rotation method.

Auger width and branching ratios for berylliumlike1s2s2np1Poand1s2p31Poresonances and photoionization of beryllium from1s22s21S

The photoionization cross section (PICS) of Be from the ground state is studied with the saddle-point complex-rotation method for photon energies from 25 to 122 eV. A full-core plus correlation wave function is used for the ground state. For the resonances in the continuum, the energy and width for the singly core-excited Be-like ${1s2s}^{2}2p{}^{1}{P}^{o},$ ${1s2p}^{3}{}^{1}{P}^{o},$ and ${1s2s}^{2}3p{}^{1}{P}^{o}$ are calculated to high precision. The PICS are studied with a single open-channel approximation as well as fully coupled open channels. The Auger decay branching ratios of these states are studied to check the spin-alignment theory recently proposed by Chung. These results are compared with the existing theoretical and experimental data in the literature. For beryllium, our energy and width of ${1s2s}^{2}2p$ are 115.513 eV and 36.6 meV and those of ${1s2s}^{2}3p$ are 121.420 eV and 50.4 meV, which agree with the experiment of Caldwell et al., [Phys. Rev. A 51, 542 (1990)].

The Doubly Excited (3pnL)1,3L Resonances in H- Below the n = 3 H Threshold

We study the (3pnL)1,3L resonances of H- below the n = 3 hydrogen threshold. We report the resonant energies and widths of four 1Pe resonances, five 3Pe resonances, three 1D° resonances and two 3D° resonances. The classification by the set of quantum numbers, N(K, T)An, is made. No (3pnL)1,3(L ≥ 3) resonances are found. The present resonant energies and widths were calculated by the saddle-point complex rotation method with B-spline functions. We included the relativistic and QED corrections as first-order perturbation, and considered the coupling effects between the singlet and triplet states to examine the possibility of the resonances of H- (3pnL)1,3L dipole series. We found that the series will be terminated after the third resonance for 1Pe symmetry, the fourth resonance for 3Pe symmetry, the third resonance for 1D° symmetry and the second resonance for 3D° symmetry.

Auger branching ratios for berylliumlike1s2s2p21S,1P,1Dresonances and photoionization of beryllium from1s22s2p1Po

The photoionization cross section of Be from ${1s}^{2}{2s2p}^{1}{P}^{o}$ is studied with the saddle-point complex-rotation method for photon energies from 23 to 117 eV. A full-core plus correlation wave function is used for the initial states. In the continuum, the energy and width for the singly core-excited Be-like ${1s2s2p}^{2}{}^{1}S,{}^{1}P,$ and ${}^{1}D$ states are calculated to high precision for systems with $Z=4--10.$ The Auger decay branching ratios of these states are studied to check the spin alignment theory recently proposed by Chung. These results are compared with the available experimental data in the literature.

Electric-field effects on He ground-statephotoionization

A saddle-point complex-rotation method is used to study thephotoionization of helium in the presence of a dc electricfield. A four-angular-symmetry calculation (i.e. Lmax = 3)is carried out to study two locally isolated resonance groups,one consisting of He (2, 5c) 1Po, (2, 5b)1Se, (2, 6b) 1Po and (2, 6a)1Se states, and the other consisting of He(2, 6c) 1Po, (2, 6b) 1Se, (2, 7b)1Po and (2, 7a) 1Se states. Thevariations of the structure of cross section profiles andresonance strengths for the ML = 0 components of these tworesonance groups are examined in detail. A general Ntot-state sum rule for the total resonance strength Stot is shown, which suggests that the sum of the totalresonance strength of a locally isolated resonance group is notaffected by the presence of a weak static field. We have alsoperformed a five-symmetry (i.e. Lmax = 4) multichannelcalculation for the doubly excited spectra converging to the n = 3threshold of He+. Overlapping resonances are found andresolved.

Resonances of helium in a DCfield

A saddle-point complex-rotation method is used to study electric-fieldeffects on the doubly excited resonances of He. By using a 892-termwavefunction, a seven-angular-symmetry calculation (i.e. Lmax = 6) is performed for a comprehensive study around the He (2, 6a)1Po and (2, 6a) 1De resonance pair in the presence ofan external electric field. A general M-state sum rule is shown whichsuggests the sum of total energy or total width of M-state system isnot affected by the presence of a weak static field. The M-state sumrule is used to investigate the sharing of resonance energies and widthsfor the locally isolated resonance groups around the He (2, 6a) 1Po and (2, 6a) 1De resonance pair in the small-field region.

Energies and lifetimes of the core-excited states of the Li isoelectronic sequence

The energies, fine structures, widths, and radiative rates of core-excited states of a Li isoelectronic sequence $(Z=4\char21{}14)$ are calculated using the saddle point and saddle-point complex-rotation methods. A restricted variational method is used to extrapolate a better nonrelativistic energy. Relativistic effects are included using first-order perturbation theory. The charged effects of the Li isoelectronic sequence are discussed. These results are compared with experimental and theoretical data in the literature.

Calculations of 2Po resonances in Be II

The positions and the widths of 21 2Po resonances in Be II between 1 1S0 and 2 1P thresholds are calculated using a saddle-point complex-rotation method. Relativistic and mass polarization corrections to the autoionization energy are included. Below threshold (1s2s)3S our results agree well with other calculations and experiments. We make an identification of states above the (1s2s)3S threshold. For the region above 2 3S, our present results for Be II are contrasted with those for Li I (Wu L J and Chung K T 1997 J. Phys. B: At. Mol. Opt. Phys. 30 1173). We discuss the dependence of the widths on the atomic number.

Energies and widths of triply excited states of lithiumlike oxygen and neon

Seven low-lying triply exited states of lithium-like oxygen and neon are calculated with the multichannel saddle-point and saddle-point complex-rotation methods. The term energies are given for these excited states, along with level shifts and partial Auger widths from dominant decay channels. The mass polarization effect and relativistic corrections are included. The radiative transition rates are also calculated. These results are compared with other theoretical data in the literature.

2s22p2Potriply excited state ofHe−

The triply excited ${2s}^{2}2p{}^{2}{P}^{o}$ state of ${\mathrm{He}}^{\ensuremath{-}}$ is studied by using the saddle-point complex-rotation method. The energy and Auger width of this resonance are calculated. Relativistic corrections are evaluated with the first-order perturbation theory, and the mass-polarization effect is also included. The partial Auger widths are calculated for the individual open channels. The total width is obtained by coupling the important open channels and summing over the other channels. These results are compared with the theoretical and experimental data in the literature.

Energy and lifetime of core-excited Be + resonances

The energies, shifts, widths, and radiative rates of double excited Be+ resonances are calculated using the saddle point and saddle-point complex-rotation methods. A restricted variational method is used to extrapolate a better nonrelativistic energy. Relativistic effects are included using first-order perturbation theory. These results are used to make a better understanding of observed Be+ spectra.

Even-parity triply excited states of lithium

In this work, 14 even-parity ${2l2l}^{\ensuremath{'}}{\mathrm{nl}}^{\ensuremath{''}}$ $(n>~3)$ resonances of lithium are calculated by using the saddle-point complex-rotation method. Among the 14 resonances, four are ${}^{2}P$ resonances, four are ${}^{2}D$ resonances, and six are ${}^{2}S$ resonances. Relativistic corrections are evaluated with the first-order perturbation theory and the mass-polarization effect is also included. The Auger widths are studied. The partial Auger widths are calculated for the individual open channels and the total width is obtained by coupling the important open channels. These results are compared with recent theoretical and experimental data in the literature.

ENERGIES, FINE STRUCTURES AND LIFETIMES OF THE 2s2s2p2P0 AND 2s2p2p2D HOLLOW LITHIUM-LIKE SYSTEMS

The energies , fine structures and lifetimes of the 2s2s2p2P0 and 2s2p2p2D triply excited states of the Li isoelectronic sequence are calculated using multichannel saddle-point and saddle-point complex-rotation methods. A restricted variational method is used to extrapolate a better nonrelativistic energy. The relativistic corrections are calculated with first-order perturbation theory. The shifts and widths are studied with one open channel at a time as well as fully coupled open channels. The radiative transition rates and the fine-structure splittings for the 2P0 and 2D states are also calculated. These results are compared with the existing theoretical and experimental data in the literature.

Photoionization of lithium below theLi+1s2s3Sthreshold

A saddle-point complex-rotation method is used to calculate the resonance energy, width, and photoionization cross section (PICS) of lithium below the ${\mathrm{Li}}^{+}$ $1s2s$${}^{3}S$ threshold. Fourteen ${}^{2}{P}^{o}$ resonances are studied. These results are compared with the most precise experimental data in the literature. Most of the Auger widths of these resonances are extremely narrow, which makes a direct theory-experiment PICS comparison difficult. However, if we convolute the predicted cross section with a Gaussian profile using the experimental resolution for full width at half maximum, the resulting profile agrees closely with the high-resolution photoion measurement.

Doubly excited resonant states in below the hydrogen threshold

We calculated the (n=2,3,4), (n=3,4,5), (n=3,4), (n=2,3,4) and autoionizing states in below the n = 2 hydrogen threshold by the saddle-point complex-rotation method. The close-channel part of wavefunctions are constructed by B-spline basis functions. The resonance energies and autoionization widths are determined. They are compared with other theoretical and experimental results to examine the feasibility of applying B-spline basis functions through the saddle-point complex-rotation method in resonance states.

Energy and lifetime of triply excited states of lithium-like beryllium and carbon

Seven triply excited states of lithium-like beryllium and carbon are calculated with the multichannel saddle-point and saddle-point complex-rotation methods. Relativistic effects are included using first-order perturbation theory. The widths are studied with one open channel at a time as well as fully coupled open channels. The predicted Auger branching ratio is compared with the observed spectra. The radiative transition rates are also calculated. These results are compared with the theoretical data in the literature.

High 2Po resonances of a triply excited lithium atom.

Eleven lithium resonances, eight below the ${\mathrm{Li}}^{+}$ 2s2s${\mathrm{}}^{1}$S threshold and three above the ${\mathrm{Li}}^{+}$ 2s2p${\mathrm{}}^{3}$${\mathit{P}}^{\mathit{o}}$ threshold, are studied with the saddle-point complex-rotation method. These are the triply excited $^{2}$${\mathit{P}}^{\mathit{o}}$ resonances above the 2s2s2p${\mathrm{}}^{2}$${\mathit{P}}^{\mathit{o}}$ and 2p2p2p${\mathrm{}}^{2}$${\mathit{P}}^{\mathit{o}}$ states. They are classified based on the energy, the relative contribution of the different angular-spin components to the normalization, and by inspecting the relativistic corrections. 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. These results are compared with the recent experimental data. \textcopyright{} 1996 The American Physical Society.

Energies and lifetimes of triply excited states of lithium.

Nine triply excited states of lithium are calculated with the saddle-point and saddle-point complex-rotation methods. Relativistic corrections are computed with first-order perturbation theory. The widths are studied with one open channel at a time as well as fully coupled open channels. Some coupled calculations include up to ten open channels. Radiative decays of the triply excited states are also computed. The predicted Auger branching ratios are in excellent agreement with experiment. An identification is found for a weak line in the observed Auger spectra. Our predicted 2s2s2p${\mathrm{}}^{2}$${\mathit{P}}^{\mathit{o}}$ width is substantially smaller than the experiment of Kiernan et al. [Phys. Rev. Lett. 72, 2359 (1994)] but it agrees much better with the recent experiment of Kiernan et al. [J. Phys. B 28, L161 (1995)].

2s2p2p 4P state of He-

The triply excited ${\mathrm{He}}^{\mathrm{\ensuremath{-}}}$ 2s2p2p $^{4}$P state is studied. The resonance position and width are calculated to high precision with a saddle-point complex-rotation method. The relativistic corrections and fine structures are also calculated. The absorption wavelength and oscillator strength from the ${\mathrm{He}}^{\mathrm{\ensuremath{-}}}$ 1s2s2p $^{4}$${\mathit{P}}^{\mathit{o}}$ state is computed to facilitate the observation of this resonance in synchrotron-radiation experiments.