Relativistic Configuration Interaction Treatment of Generalized Oscillator Strength for Krypton

A fully relativistic configuration interaction method is developed to investigate the transition energies and general oscillator strengths of the lower lying states of krypton, for both optically allowed and optically forbidden transitions. The calculated results are in agreement with the recent experimental measurements. The calculated transition energies for the 5s and 5s＇ transitions are 9.970 and 10. 717eV, which agree with the experimental data of 10.033 and 10.643 eV. The calculated oscillator strengths are 0.211 and 0. 170, comparable with the experimental results 0.214（±0.012） and 0.194 （±0.012）, respectively. The momentum transfer positions （K^2 in a.u.） of the minimum and maximum GOSs in the 4s^24p^6 → 4s^24p^5 （5s ＋ 5s＇） transitions are 1.105 and 2.225, comparable with the measurements results 1.24 and 2.97 [Phys. Rev. A 67 （2003） 062708].     

Importance of Relativistic Effects for Intermediate-Z Elements： Photoionization Process of Excited Na

Using a modified R-matrix code, the fine-structure-resolved partial photoionization cross sections of excited Na （Z = 11） are calculated within the Breit-Pauli approximation. Our calculated energy levels of Na＋ and Na are in good agreement with the experimental values within 1% and the branching ratios of the J-resolved partial cross sections are consistent with the recent measurements within the experimental uncertainties. The agreements are impossible to be obtained without adequately taking into account the relativistic effects and the electron correlations together. Therefore, even for the intermediate-Z elements （e.g. Na with Z = 11）, the relativistic effects （mainly the spin-orbit interactions） should not be neglected.     

Relativistic Energies and Auger Widths of High-Lying Doubly-Excited States 1s^23lnl′ ^1De in Be-Like O^4＋ Ions

The saddle-point variational method and restricted variational method are used to calculate energies of doublyexcited singlet states 1s^23lnl′ （n =3-.） ^1 De in Be-like O^4＋ 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.     

Theoretical Study of Interesting Fine-Structure Splittings for 23P0, 1, 2 States along Helium Isoelectronic Sequence

Using the multi-configuration Dirac Fock method including the Breit interactions and QED corrections, we calculate the fine-structure energy levels of the 2^3 Po, 1,2 states along the helium isoelectronic sequence with atomic number up to Z = 36, where LS-coupling is appropriate. Our calculation results agree with the experimental results within about 1%. We elucidate the mechanism of the interesting fine-structure splittings for the 2^3Po,1,2 states along the helium isoelectronic sequence, i.e. the competitions between the spin-orbit interactions and the Breit interactions which represent the relativistic retardation effect of electromagnetic interactions.     

Fine-Structure Splittings of Nitrogen Isoelectronic Sequence： Competitions among Spin-Orbit Interactions, Breit Interactions and Electron Correlations

Using the multi-configuration Dirac-Fock self-consistent field method and the relativistic configuration interaction method with quantum-electrodynamics corrections performed by the GRASP code, we calculate the fine-structure energy levels of the ground-state configuration （1s^22s^22p^3） of the nitrogen isoelectronic sequence, according to the L-S coupling scheme with atomic number Z up to 22. Based on the calculated results, we elucidate the mechanism of the orderings of fine-structure energy levels of 2^ D3/2,5/2 and 2^P1/2,3/2 respectively, i.e. for 2^D3/2,5/2 orderings, the competition between the spin-orbit interactions and the Breit interactions; for 2^P1/2,3/2 orderings, the electron correlations, especially the electron correlations owing to the 2p^5 configuration interactions.     

Effect of Electron Correlations and Breit Interactions on Ground-State Fine-Structures along the Nitrogen-Like Isoelectronic Sequence

The accurate atomic data of nitrogen and nitrogen-like ions have an importance role in fusion plasma studies and astrophysics studies. The precise calculation of fine-structures is required to obtain such atomic data. Along the whole nitrogen isoelectronic sequence, the contributions of the electron correlations, the Breit interactions and the quantum electrodynamics corrections oi1 the ground-state fine-structures are elucidated. When Z is low, the electron correlations are important, and the Breit interactions, which cannot be neglected cause interesting anomalous fine-structure splittings. When Z is high, the electron correlations are less important, and the Breit interactions are important in addition to spin-orbit interactions for precise calculations.     

Interesting Features of n2D Rydberg Series Fine-Structure Splittings along the Sodium-Like Isoelectronic Sequence

Using a simplified multi-configuration Dirac-Fock （SMCDF） scheme based on the multi-configuration Dirac-Fock （MCDF） theory, we study the systematic variations of the fine-structure splittings of n^2 D3/2,5/2 Rydberg series along the sodium-like isoelectronic sequence, i.e. the fine-structure orderings vary with increasing atomic number Z. The competition between the spin-orbit interactions and the exchange interactions due to relativistic effects of the nd orbital wavefunctions well explain such variations. Furthermore, the effect of Breit interactions which plays the secondary role is studied.     

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.     

Relativistic Distorted-Wave Collision Strengths of Ni-, Cu- and Zn-like Au Ions

Excitation energies and electron impact excitation strengths from the ground states of Ni-, Cu- and Zn-like Au ions are calculated. The collision strengths are computed by a 213-levels expansion for the Ni-like Au ion, 405- levels expansion for the Cu-like Au ion and 229-levels expansion for the Zn-like Au ion. Configuration interactions are taken into account for all levels included. The target state wavefunctions are calculated by using the Grasp92 code. The continuum orbits are computed in the distorted-wave approximation, in which the direct and exchange potentials among all the electrons are included. Excellent agreement is found when the results are compared with previous calculations and recent measurements.     

The effect of a 2s vacancy on two-electron-one-photon lines: Relativistic approach

Energies and rates for two-electron-one-photon transitions and their satellites have been calculated using multiconfiguration Dirac-Fock method for a number of atoms having nuclear charges within Z=12-20. In addition, the energies and transition rates of the Kα hypersatellite lines have been computed for these atoms. From these rates, the branching ratios between the Kα hypersatellite and two electron one photon lines are evaluated and compared with existing experimental and theoretical results.     

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.     

Relativistic Distorted-Wave Calculations of Electron Impact Excitation Cross Sections of Be-Like C2＋ Ions

A fully relativistic distorted-wave program is developed based on the Grasp92 and Ratip packages to calculate electron impact excitation （EIE） cross sections. As a first application of the program, the EIE cross sections of Be-like C^α＋ ions from the metastable 1s^22s2p^3 p to 1s^22p^2 ^3 p excitation and the inner-shell excitations are calculated systematically. Meanwhile, the correlation effects of target states are discussed. It is found that the correlation effects play an important role in the low energy EIE cross sections. An excellent agreement is found when the results are compared with previous calculations and recent measurements.     

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     

Radiative and interelectronic-interaction corrections to the hyperfine splitting in highly charged B-like ions

The ground-state hyperfine splitting values of high-Z boronlike ions are calculated. Calculation of the interelectronic-interaction contribution is based on a combination of the 1/Z perturbation theory and the large-scale configuration-interaction Dirac-Fock-Sturm method. The screened QED corrections are evaluated utilizing an effective screening potential approach. Total hyperfine splitting energies are presented for several B-like ions of particular interest: ⁴⁵Sc¹⁶⁺, ⁵⁷Fe²¹⁺, ²⁰⁷Pb⁷⁷⁺, and ²⁰⁹Bi⁷⁸⁺. For lead and bismuth the experimental values of the 1s hyperfine splitting are employed to improve significantly the theoretical results by reducing the uncertainty due to the nuclear effects.     

Lineshapes of the even mp1/2 5n(p′/f′) autoionizing resonances of Ar, Kr and Xe

The even parity mp_1/2 ⁵np^′ and mp_1/2 ⁵nf^′ autoionizing resonances of Ar, Kr, and Xe (m=3,4,5) were investigated experimentally and theoretically by one-photon excitation from lower-lying intermediate levels. In particular, high resolution measurements for the Ar(nf^′), Kr(12p^′,8f^′), and Xe(8p^′) resonances are reported; lineshape parameters for these resonances have been derived by a Fano-type analysis, thus yielding reduced resonance widths. The experimental spectra and the resonance parameters are compared with theoretical calculations which are based on the configuration interaction Pauli–Fock approach including core polarization. The measured and calculated lineshapes are in good agreement. In addition, theoretical predictions are presented for other resonances, which have not yet been observed experimentally, and some systematic trends are elucidated.     

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.     

Investigation of auto-ionizing states in xenon by resonantly enhanced multi-photon ionization

We have examined the autoionization spectrum of xenon by resonantly enhanced three-photon ionization (2 + 1 REMPI) involving intermediate states 5p ⁵6p[J = 0, 2]. The properties of the observed autoionization resonances change significantly with the choice of the intermediate state. For ionization via an intermediate state with predominantly 5p ⁵(²P_3/2) core character, a strong continuum with embedded window-type 5p ⁵(²P _1/2)nd'-autoionization resonances is observed. For intermediate states, predominantly with 5p ⁵(²P_1/2) core character, both 5p ⁵(²P _1/2)nd'- as well as 5p ⁵(²P _1/2)ns'-resonances are present in the spectrum as overlapping, nearly symmetric peaks on a rather weak continuum. Calculations confirm the significant dependence of the spectral lineshapes upon the excitation pathway to the autoionizing state. The ionization data are compared with spectra obtained by monitoring third-harmonic generation via autoionizing states without resonant excitation of intermediate states. These spectra also exhibit the signature of both the nd'- and ns'-resonances. Received 30 September 2002 Published online 28 January 2003 RID="a" ID="a"Permanent address: Rostov State University of Transport Communication, 344038, Rostov-on-Don, Russia. RID="b" ID="b"e-mail: halfmann@physik.uni-kl.de     

Coherent excitation of Rydberg atoms in an ultracold gas

We demonstrate two schemes for the coherent excitation of Rydberg atoms in an ultracold gas of rubidium atoms employing the three-level ladder system 5S_1/2-5P_3/2-n?_j. In the first approach rapid adiabatic passage with pulsed laser fields yields Rydberg excitation probabilities of 90% in the center of the laser focus. In a second experiment two-photon Rydberg excitation with continuous-wave fields is applied which results in Rabi oscillations between the ground and Rydberg state. The experiments represent a prerequisite for the control of interactions in ultracold Rydberg gases and the application of ultracold Rydberg gases for quantum information processing.     

Circular dichroism in radiative and nonradiative inelastic XUV scattering

Accepted: 6 March 1997     

Transition Energy and Oscillator Strength of 1s22p-12nd for Fe23 ion

Transition energies, wavelengths and dipole oscillator strengths of 1s^2 2p - 1s^2 nd （3 ≤ n ≤ 9） for Fe^23＋ ion nre calculated. The fine structure splittings of 1s^2nd （n ≤ 9） states for this ion are also evaluated. The higher-order relativistic contribution to the energy is estimated under a hydrogenic approximation. The quantum defect of Rydberg series 1s^2nd is determined according to the quantum defect theory. The energies of any highly excited states with （n ≥ 10） for this series can be reliably predicted using these quantum defects as input. The results in this paper excellently agree with the experimental data available in the literature. Combining the quantum defect theory with the discrete oscillator strengths, the discrete oscillator strengths for the transitions from same given initial state 1s^2 2p to highly excited 1s^2nd states （n ≥ 10） and the oscillator strength density corresponding to the bound-free transitions is obtained.