Theoretical Study of Relativistic Retardation Effects： the Abnormal Fine Structure of OⅡ

Using multi-configuration Dirac-Fock and relativistic configuration interaction methods with high-order corrections, we report our precise calculation results of the fine-structure energy levels of the ground-state configuration of OⅡ（1s^22s^22p^3）. Our calculated fine-structure splittings of ^2D3/2,5/2 and ^2p1/2,3/2 are abnormal We elucidate that the transverse （Breit） interaction, i.e. relativistic retardation effect, plays an important role for the abnormal fine-structure splittings. Our calculation results are in good agreement with experimental measurements.     

Double-Exponentially Decayed Photoionization in CREI Effect： Numerical Experiment on 3D H2^＋

On the platform of the 3D H2^＋ system, we perform a numerical simulation of its photoionization rate under excitation of weak to intense laser intensities with varying pulse durations and wavelengths. A novel method is proposed for calculating the photoionization rate： a double exponential decay of ionization probability is best suited for fitting this rate. Confirmation of the well-documented charge-resonance-enhanced ionization （CREI） effect at medium laser intensity and finding of ionization saturation at high light intensity corroborate the robustness of the suggested double-exponential decay process. Surveying the spatial and temporal variations of electron wavefunctions uncovers a mechanism for the double-exponentially decayed photoionization probability as onset of electron ionization along extra degree of freedom. Henceforth, the new method makes clear the origins of peak features in photoionization rate versus internuclear separation. It is believed that this multi-exponentially decayed ionization mechanism is applicable to systems with more degrees of motion.     

New Types of the Lie Symmetries and Conserved Quantities for a Relativistic Hamiltonian System

For a relativistic Hamiltonian system,two new types of the Lie symmetries and conservation laws are given under infinitesimal transformaitons of groups.On the basis of the theory of invariance of the relativistic Hamiltonian equations under infinitesimal transformations and introducing infinitesimal transformations for time t,generalized coordinates qs and generalized monenta ps,we obtain the determinging equations,the structure equations and the conserved quantities of the Lie symmetries.Introducing infinitesimal transformation for generalized coordinates qs and generalized momenta ps,we construct the Lie symmetrical transformations of the system,which only depend on the canonical variables.A set of conserved quantities are directly obtained from the Lie symmetries of the syste.An example is given to illustrante the application of the results.     

Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Relativistic Birkhoffian Systems

For a relativistic Birkhoffian system, the Lie symmetrical perturbation and adiabatic invariants of generalized Bojman type are studied under general infinitesimal transformations. On the basis of the invariance of relativistic Birkhotfian equations under general infinitesimal transformations,Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The exact invariants in the form of generalized Hojman conserved quantities led by the Lie symmetries of relativistic Birkhoffian system without perturbations are given. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for relativistic Birkhoffian system with the action of small disturbance is investigated, and a new type of adiabatic invariants of the system is obtained. In the end of the paper, an example is given to illustrate the application of the results.     

Effects of Configuration Interaction on Dielectronic Recombination of Cu-Like Gold Ion through 3d+ e →4l''l'''' Capture Process

Effects of configuration interaction on dielectronic recombination of Cu-fike gold ions through the 3d ＋ e→4l′4l″ capture process are studied in the models of isolated configurations approximation, configuration mixing within 3d^94s4l′4″, and configuration mixing within 3d^94l4l′4l″ （l≥ 0）, employing a relativistic distorted-wave approximation. Nonresonant raditive stabilizing transitions and decays to autoionizing levels followed by radiative cascades, as well as resonant stabilizing transitions from the resonant levels, are taken into account. The additional mixing with 3d^94l4l′4l″ （0 〈 l 〈 l′ 〈l″≤ 3） shifts slightly the peaks of cross section towards low energy. The rate coefficient at low temperature is dramatically changed. The rate coefficient at temperature above 100 eV is enhanced by a factor between 26% and 13%.     

Absence of Charge-Resonance-Enhanced Ionization in Attosecond Pulse Photoionization： Numerical Result on One-Dimensional H2^＋

We present a numerical result of photoionization rate for the one-dimensional molecular hydrogen ion model exposed to intense light of 1 × 10^16-2×10^16 W/cm^2, 55-as pulse duration, and 800nm wavelength. In contrast to the previous calculation result of charge-resonance-enhanced ionization for lower intensity and much longer pulse, our result exhibits an ionization saturation. The numerical results are interpreted in the field-dressed potential picture as over-the-barrier liberation of electrons. This extremely short pulsewidth and relatively high field phenomenon requests experimental demonstration.     

Relativistic correction of （v/c）2 to the collective Thomson scattering for high-temperature high-density plasma

Collective Thomson scattering is theoretically investigated with the inclusion of the relativistic correction of (v/c)². The correction is rather small for the plasma parameters inferred from the spectra of the thermal electron plasma waves in the plasma. Since the full formula of the corrected result is rather complicated, a simplified one is derived for practical use, which is shown to be in good agreement with the un-simplified one.     

Density Dependence of the Detailed Spectral Line Effects on the Opacity of Astrophysical Abundant Elements： oxygen

A full relativistic detailed-level-accounting approach has been developed independently to deal with the detailed spectral line effects on the opacity of the third most abundant element in stars: oxygen. The atomic energy levels and the oscillator strengths of the radiative transitions between the energy levels are obtained by carrying out the full relativistic one-configuration Dirac-Fock calculations. The photoionization cross sections are obtained via an average atom scheme with a consideration for the splitting of the ionization threshold due to the ionization stages and the term-couplings. As an example, the spectra resolved opacities and the mean opacities of oxygen are calculated to show the importance of the detailed spectral line profiles with the density of the matter.     

A Remark on General Solution for Motion of Relativistic Strings in Minkowski Space R^（1＋n）

This note concerns the motion of relativistic strings in the Minkowski space R^（1＋n）. We rederive the general solution formula in closed form for the equation for the motion of relativistic string. Our method is different completely from others.     

Theoretical Investigation of Decay Process in a Doubly Excited 2s^2 ^1S0 State of He-Like Ions

In the framework of multi-configuration Dirac-Fock theory, a detailed calculation is performed for the decay rates and the energies of the doubly excited 2s^2 ^1So state of He-like ions, of which atomic number Z ranges from 6 to 92. The 2s^2 ^1So - ls ^2S1/2 Auger decay is predominant at low Z regime, whereas the 2s^2 ^1So - 1s2p ^1,3P1 two-electron one-photon transitions become quite important in moderate and high Z regimes. For heavy ions with Z ≥ 72, the contribution of 2s^2 ^1So - 1s2s ^3S1 M1 transition is significant. The Breit interaction considerably enhances the 2s^2 ^1So - 1s ^2S1/2 Auger rate at high Z regime.     

Photoionization cross sections of Fe XXI

Total and partial photoionization cross sections for (Fe XXI+hν→Fe XXII+e) are presented for the ground and excited bound states with n?10 and l?9. Fe XXI is prevalent in high-temperature astrophysical plasmas as well as in photoionized plasmas excited by hard X-rays. Results are reported for the first time for the high-energy photoionization with core excitations to n=2,3 states. Details of photoionization, especially the high-energy features that often dominate considerably over the low energy ones, are illustrated. These prominent features will affect the photoionization and the recombination rates in high-temperature plasmas. Calculations are carried out in the close coupling (CC) approximation using the R-matrix method. A large CC wavefunction expansion for Fe XXII which includes the ground and 28 excited core states from n=2 and 3 complexes and spans over a wide energy range is used. A total of 835 discrete bound states of Fe XXI in the singlet, triplet, and quintet symmetries are obtained. Total photoionization cross sections, σ_PI(nLS), for ionization into all 29 states are presented for all 835 final bound states and partial photoionization cross sections, σ_PI(g,nLS), for ionization into the ground ²P⁰ state of the core are presented for 685 states. While the n=2 core excitations are at relatively lower energy range (within 15 Ry from the ionization threshold), the n=3 excitations lie at considerably higher energy, 73 Ry and above, yet introduce resonant features and enhancements more prominent than those of n=2 states. Larger numbers of resonances are formed due to Rydberg series of autoionizing states converging on to the 29 core states. However, most noticeable structures are formed in the excited state cross sections by the photoexcitation-of-core (PEC) resonances in the photon energy range of 73-82 Ry. All these high-energy features are absent in the currently available results. The present results should enable more accurate modeling of the emission spectrum of highly excited plasma from the optical to far-ultraviolet region.     

Relativistic Multichannel Treatment of Ionic Rydberg States of Lanthanum

Ionic Rydberg energy levels of lanthanum are calculated from first principles by relativistic multichannel theory within the framework of multichannel quantum defect theory. The present calculated results are in better agreement with the experimental measurements than the previous calculations [J. Phys. B 34 （2001）369] due to the consideration of dynamical polarizations. Moreover, in the experimental spectra achieved by a five-laser resonance excitation via the intermediate state 5d6d^3 F2, a series of weak ionic Rydberg states and some of perturbing states are found and assigned in this work.     

Photoionization of 1s Electron and Corresponding Shake-Up Process in Ground and Excited Lithium Atoms

The cross sections of the ls electron photoionization and corresponding shake-up processes for Li atoms in the ground state 1s^22s and excited states 1s^22p, 1s^23s, 1s^23p and 1s^23d are calculated using the multi-configuration Dirac-Fock method. The latest experimental photoelectron spectrum at hv= 100 eV [Cubaynes D et al. Phys. Rev. Lett. 99 （2007） 213004] has been reproduced by the present theoretical investigation excellently. The relative intensity of the shake-up satellites shows that the effects of correlation and relaxation become more important for the higher excited states of the lithium atom, which are explained very well by the spatial overlap of the initial and final state wavefunctions. In addition, strong dependence of the cross section on the atomic orbitals of the valence electrons are found, especially near the threshold.     

Single photoeffect on helium-like ions in the non-relativistic region

We present a generalization of the pioneering results obtained for single K-shell photoionization of H-like ions by M. Stobbe [M. Stobbe, Ann. Phys. 7 (1930) 661] to the case of the helium isoelectronic sequence. The total cross section of the process is calculated, taking into account the correlation corrections to first order of the perturbation theory with respect to the electron–electron interaction. Predictions are made for the entire non-relativistic energy domain. The phenomenon of dynamical suppression of correlation effects in the ionization cross section is discussed.     

Resonance Energies,Absorption Oscillator Strengths and Ionization Potentials for the Element Hassium （Z = 108）

On the basis of successfully predicting low-lying energy levels for the element fermium （Z = 100）, we calculate the resonance energies, absorption oscillator strengths and the first ionization potential of the element hassium （Z = 108） by taking important relativistic and improved electron correlation effects into account using the multiconfiguration Dirac Fock method. These calculations are carried out with the aim of assisting experimental investigations of hassium.     

Comment on: “Photoionization of helium-like ions in asymptotic non-relativistic region” [Phys. Lett. A 358 (2006) 211]

The results of Mikhailov et al. [A.I. Mikhailov, A.V. Nefiodov, G. Plunien, Phys. Lett. A 358 (2006) 211] on single and double ionization of He at high energy can be obtained quite simply by combining two previous results long well known in the literature. The results of Mikhailov et al. can also be understood in a larger context, using an asymptotic Fourier transform approach, which also allows a justification of various statements assumed but not demonstrated by Mikhailov et al.     

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. Received: 25 May 1998 / Revised: 28 July 1998 / Accepted: 25 August 1998     

Relativistic and correlation effects in the anisotropy of near-threshold Kr 3d and Xe 4d photoionization

Angular distributions of the spin–orbit split components and their branching ratios have been studied experimentally and theoretically for the 3d photoelectrons of Kr and 4d photoelectrons of Xe. The focus was on the electron dynamics near the ionization threshold of each spin–orbit split component and its behaviour as a function of Z   in passing from Kr to Xe. The experimental spectra were measured with high photon and electron energy resolutions with photon energies at about 3–12 eV above the 3d_3/2$3{\text{d}}_{3/2}$ and 3d_5/2$3{\text{d}}_{5/2}$ thresholds for Kr and at about 5–12 eV above the Xe 4d_3/2$4{\text{d}}_{3/2}$ and 4d_5/2$4{\text{d}}_{5/2}$ thresholds. Experimental results for the angular distribution parameters have been compared with theoretical values obtained with relativistic Dirac–Fock method and results from independent particle approximation with a modified Hartree potential [A. Derevianko, W. Johnson, K. Cheng, Atom. Data Nucl. Data Tables 73 (1999) 153]. The branching ratios were compared with theoretical predictions from Dirac–Fock and relativistic random-phase approximation [K. Cheng, W. Johnson, Phys. Rev. A 28 (1983) 2820].     

Electron-ion recombination and photoionization of Fe XXI

Results for electron-ion recombination and photoionization of , with emphasis in high-temperature region, are presented from ab initio unified method. The unified method, based on close coupling (CC) approximation and R-matrix method, (i) subsumes both the radiative recombination (RR) and dielectronic recombination (DR), (ii) enables self-consistent sets of photoionization and recombination cross sections from using an identical wavefunction for both the processes, and (iii) provides state-specific recombination rates of a large number of bound states. A large CC wavefunction expansion, which includes the ground and 28 core excitations of n=2 and 3 complexes and span a wide energy range, has been used. Compared to Δn=2-2, Δn=2-3 core excitations are found to introduce strong resonant structures and enhance the background photoionization cross sections (σ_PI) in the high-energy region. These features along with prominent photoexcitation-of-core (PEC) resonances at n=3 core thresholds have increased the unified total recombination rate coefficients (α_R(T)) at temperatures , region of maximum abundance of the ion in collisional equilibrium, by a factor of 1.6 over previous calculations. State-specific recombination rate coefficients α_R(nLS), which include both the RR and DR, are presented for the first time for 685 bound states with n?10 and l?9. The unified total recombination rate with photoelectron energy α_R(E) is presented and the role of low-energy near-threshold fine structure resonances is illustrated. The present results should provide a reasonably complete self-consistent set of recombination rates and photoionization cross sections for astrophysical modelings of high-temperature plasmas from optical to far-ultraviolet wavelength regions.