Energies and electron correlation effects in two-electron doubly excited (nl)2 states

Energies of singlet doubly excited states 2p^{2 1}D, 3d^{2 1}G, 4f^{2 1}I of He isoelectronic series are calculated in the framework of the variational method by using Hylleraas-type wave functions and a real Hamiltonian. The results obtained show quantitatively the importance of electron correlation effects in the doubly excited states and they are in good agreement with some experimental data and other theoretical results. Received 30 March 2000 and Received in final form 4 July 2000     

Triply excited three-electron systems--semiclassical model

We calculate rovibronic intrashell spectra of the triply highly excited atomic hydrogen dianion, helium anion and lithium atom, within a simple semiclassical model. Zero-order electronic energy levels and half-lives are calculated for a number of principal quantum numbers and approximate thresholds for the appearance of vibronic modes are estimated. Since no quantum-mechanical and experimental data are available for the highly excited levels (N > 5), where the semiclassical models apply, no comparison with other results are possible at present. The problem of comparing semiclassical and quantum-mechanical calculations for moderately large quantum numbers, which seem attainable by the present day experimental technique, has been discussed. Received: 16 September 1998 / Received in final form: 16 March 1999     

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     

Decay of metastable states in Nd II

The difficulty associated with an accurate determination of transition rates for forbidden lines in lowly ionized heavy elements is illustrated in the case of Nd II. We have investigated the radiative decay of the low-lying metastable levels in Nd⁺ including the two levels K_11/2 and I_13/2. In these two particular cases, using different theoretical approaches, we find that the decay is dominated by the M1 channels but that the E2 contributions are of the same order of magnitude. These levels have also been studied experimentally by lifetime measurements with the heavy ion storage ring CRYRING of Stockholm University. The difficulties encountered when performing such experiments are underlined and discussed.     

The excitation energies,ionization potentials and oscillator strengths of neutral and ionized species of Uub (Z = 112) and the homologue elements Zn,Cd and Hg

Multi-configuration Dirac-Fock method (MCDF) is employed to calculate excitation energies, ionization potentials and oscillator strengths for all neutral and up to 5 times ionized species of element Uub, as well as the homologue elements Zn, Cd and Hg. On the basis of not too extended MCDF calculations, we studied some peculiar properties of element Uub resulting from its stronger relativistic and electron correlation effects. Using an extrapolative scheme, improved ionization potentials of Uub were obtained with an uncertainty of less than 0.5 eV. Furthermore, we calculated the low-lying resonance excitation energies, absorption oscillator strengths and the first ionization potential for Hg and Uub using large scale MCDF calculations, which improved the uncertainty of the excitation energies to less than 0.25 eV for element Hg. We hope that such calculations yield good results for element Uub.     

QED and relativistic corrections in superheavy elements

In this paper we review the different relativistic and QED contributions to energies, ionic radii, transition probabilities and Landé g-factors in super-heavy elements, with the help of the MultiConfiguration Dirac-Fock method (MCDF). The effects of taking into account the Breit interaction to all orders by including it in the self-consistent field process are demonstrated. State of the art radiative corrections are included in the calculation and discussed. We also study the non-relativistic limit of MCDF calculation and find that the non-relativistic offset can be unexpectedly large.     

Properties of doubly excited states of H- and He associated with the manifolds from N = 6 up to N = 25

This paper discusses theory and results on ¹P⁰ doubly excited states (DES) in He and in H^- of very high excitation, up to the N = 25 manifold. Our calculations employed full configuration interaction (CI) with large hydrogenic basis sets and produced correlated wavefunctions for the four lowest roots at each hydrogenic manifold by excluding open channels and the small contribution of series belonging to lower thresholds. The suitability of the hydrogenic basis sets for such calculations is justified, apart from their practicality, by the fact that, by computing from them natural orbitals, the results were shown to be the same with those of earlier multiconfigurational Hartree-Fock (MCHF) calculations on low-lying DES. In total, 160 states were computed, most of them for the first time. Their energy spectrum should be of use to possible future photoabsorption experiments. For certain low-lying DES up to N = 13, for which previous reliable results are available, comparison of the calculated energies shows good agreement. The correlated wavefunctions contain systematically chosen single and double excitations from each hydrogenic manifold of interest. From their analysis, we determined the “goodness" of different quantum numbers and the geometry (average angles and radii) as a function of excitation. For the Sinano lu-Herrick ( K , T ) classification scheme, whose basis is a restricted CI with hydrogenic functions and which has thus far been tested only on low-lying DES, we established that, whereas T remains a good index as energy increases, K does not. Consequently, a more flexible than K quantum number is needed in order to account for most of the additional correlation. This number, represented by F = N - K - 1, where N and K are not good numbers anymore, produces consistently a much higher degree of purity than the ( K , T ) scheme does, especially as N increases and as the relative significance of various virtual excitations due to electron correlation increases. Among the four states of each manifold, in all cases in H^- and in most cases in He, the three are of the intrashell type and one is of the intershell type with ( F , T ) = (0, 0). The lowest intrashell states and the lowest intershell states exhibit a wide angle geometry tending to 180 ^° as N ↦∞. Received 10 September 2001 and Received in final form 12 November 2001     

Quadruply excited beryllium-like atoms – a semiclassical model

The semiclassical spectrum of quadruply highly excited four-electron atomic systems has been calculated for the plane model of equivalent electrons. The energy of the system consists of rotational and vibrational modes within the circular skeleton orbit approximation, as used in a previous calculation for the triply excited three-electron systems. The full dynamical analysis is carried out within the Hamiltonian theory, accounting for the inertial effects and the complete coupling between different degrees of freedom. Here we present numerical results for energy spectrum of the beryllium atom. The lifetimes of the semiclassical states are estimated via the corresponding Lyapunov exponents. The vibrational modes relative contribution to the energy levels rises with the degree of the Coulombic excitation.     

Excited states of Ne isoelectronic ions: SAC-CI study

Excited states of the s, p, and d symmetries up to principal quantum number n = 4 are studied for the first eight members of Ne isoelectronic sequence (Ne to Cl⁷⁺) by the SAC-CI (symmetry-adapted-cluster configuration-interaction) method. The valence STO basis sets of Clementi et al. and the optimized excited STO are used by the STO-6G expansion method. The calculated transition energies agree well with the experimental values wherever available. Received 26 July 2000 and Received in final form 14 September 2000     

Ab initio correlation approach to a ferric wheel-like molecular cluster

We present an ab initio study of electronic correlation effects in a molecular cluster derived from the hexanuclear ferric wheel [ LiFe₆(OCH₃)₁₂-(dbm)₆] PF₆. The electronic and magnetic properties of this cluster have been studied with all-electron Hartree-Fock, full-potential density functional calculations and multi-reference second-order perturbation theory. For different levels of correlation, a detailed study of the impact of the electronic correlation on the exchange parameter was feasible. As the main result, we found that the influence of the bridge oxygen atoms on the exchange parameter is less intense than the influence of the apical ligand groups, which is due to the geometry of the cluster. With respect to the cluster model approach, the experimental value of the exchange parameter was affirmed.     

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.     

A multi-reference exponential expansion for the electronic wave function

The expansion structure of a CI vector as combination of excitations from a model-space reference determinant is investigated. It is shown that between the linear and the exponential expansions there is a relation which is similar to the single-reference case, if the internal excitations are adsorbed into the reference vector. Moreover, expansions with respect to different determinants are related by a set of linear equations. By using these two properties, a State-Specific Coupled-Cluster formalism is proposed. Received 2 November 2000 / Received in final form 1st March 2002 Published online 28 June 2002     

Atomic Compton profiles within different exchange-only theories

The impulse Compton Profiles (CPs) J(q) and the expectation values for some inert gas atoms (He-Kr) are computed and compared within the Harbola-Sahni (HS), Hartree-Fock (HF) theories and a Self-Interaction-Corrected (SIC) density functional model. The Compton profiles for excited states of helium atom are also calculated. While the calculated CPs are found to generally agree, they differ slightly from one another for small values of the Compton parameter q and are in good agreement for large q values. The expectation values within the three theories are also found to be comparable. The HS formalism is seen to mimic HF reasonably well in the momentum space, establishing the logical consistency of the former. Received: 11 December 1998 / Received in final form: 20 April 1999     

Transition wavelengths and probabilities for spectral lines of Zr III

Wavelengths and oscillator strengths for all 4d4f↦4d² dipole-allowed fine-structure transitions in Zr III have been calculated within the Multi-Configuration Dirac-Fock method with QED corrections. These transitions are included in the spectrum of some chemically peculiar stars, like the B-type star χ Lupi observed by the Hubble space telescope. The results are compared to existing experimental and semi-empirical data.     

Electron capture into few-electron heavy ions: Independent particle model

We apply the density matrix theory to re-investigate the radiative electron capture into heavy ions with one valence electron. Attention has been paid particularly to the magnetic sublevel population of the residual ions, as described in terms of alignment parameters. Simple method, based on an independent particle model, which takes into account the Pauli principle, is proposed for evaluating the alignment of the excited ionic states. By making use of this method, detailed calculations are performed for electron capture into (initially) hydrogen-like and lithium-like europium, gold and uranium ions, and are compared with the results of the multiconfiguration Dirac-Fock approach.As seen from the calculations and from the comparison with available experimental results, the independent particle model provides a good estimate for the alignment parameters of few-electron heavy ions. Therefore, our simple model may help to understand the basic properties of the X-ray emission from heavy, few-electron ions without the need for invoking sophisticated MCDF calculations.     

The and transitions in the oxygen isoelectronic sequence

Multiconfiguration Dirac-Fock results are reported for the and transitions in the oxygen-like sequence for Z =9,...,18. Both transition energies and transition rates are included. Received: 29 June 1998 / Accepted: 1st July 1998     

Screening constant by unit nuclear charge calculations for (n s2)1Se, (np2)1De and (N s n p)1P○ excited states of He-like systems

Screening Constant by Unit Nuclear Charge (SCUNC) is a new analytical method suitable for the treatment of the properties of He-like systems. In this paper, the possibilities of the method are demonstrated for calculating in the framework of semi-empirical procedure, total energies, total electron-electron interaction energies and excitation energies for (ns²)¹S^e, (np²)¹D^e and (Nsnp)¹P° doubly excited states of He-like ions. The proposed semi-empirical scheme, leads to accurate results in good agreement as well as with available other theoretical results than experimental data.     

The theoretical calculation of transition probabilities for some excited p-d transitions in atomic nitrogen

The atomic transition probabilities are calculated for individual lines between some quartet terms of 3p↦4d and 3p↦5d transition arrays using weakest bound electron potential model theory (WBEPMT). In the determination of relevant parameters which are needed for calculation of transition probabilities, we employed numerical non-relativistic Hartree-Fock wave functions for expectation values of radius in both ground and excited states unlike to NCA method used on traditional WBEPMT procedure. We have obtained very good agreement between our results and the accepted values taken from NIST.     

Radiative lifetime and oscillator strength determinations in potassium ions (K V, K VI and K VII)

Oscillator strengths have been calculated for the transitions depopulating levels of the 3s²3p³, 3s3p⁴ configurations of K V, of the 3s²3p², 3s3p³ configurations of K VI and of the 3s²3p, 3s3p², 3p³ and 3s3p3d configurations of K VII. A multiconfiguration Dirac-Fock method, incorporating the relativistic two-body Breit interaction and quantum electrodynamics corrections due to self-energy and vacuum polarization, has been used for the calculations. The reliability of this approach has been tested by comparison with relativistic Hartree-Fock calculations and also with some experimental measurements performed by beam-foil spectroscopy at a beam energy of 1.7 MeV.     

On the finite-field transition dipole moment calculations by effective Hamiltonian methods

A simple finite-field scheme of calculations on electronic transition dipole moments in molecules by effective Hamiltonian methods is presented and discussed. The reliability of underlying approximations is analyzed by means of the quasidegenerate perturbation theory and corroborated by the results of pilot numerical applications. Received: 11 May 1998 / Revised and Accepted: 20 July 1998