A theoretical investigation of the singly excited two-electron atomic states 1s2s3S and 1s3s3S

The singly-excited two-electron states 1s2s ³S and ls3s ³S have been investigated by means of the variational perturbation theory procedure. The wave functions have been constructed as linear combinations of Hylleraas terms with hyperbolic factors in t, and the results obtained by carrying the computations through to 10th perturbation order and with 36(37)- 57(58)- and 85(86)-term basic sets, respectively, are reported. These results compare favourably with the corresponding best values from previous conventional variational calculations.     

Self-consistent calculation of 1s2s3S state of helium and heliumlike ions

In this paper we present a simple method within the coupled Hartree–Fock framework to calculate the 1s2s ³S state of helium and heliumlike ions. The results are in very good agreement with those obtained by the use of multiterm correlated wave functions. Some interesting observations associated with the wave function are presented.     

Relativistic calculation of autoionization widths of 1s2s2pjJ, 1s2s2 2S1/2, and 1s2pJ 2pj′J levels

The autoionization widths of levels 1s 2s 2p_jJ, 1s2s^{2 2}S_1/2, and 1s2p_j2p_j′ J have been calculated for ions with Z = 6–30. The calculation has been carried out in intermediate coupling. The decay amplitudes have been calculated in a relativistic approximation.     

Bound states of helium atom in dense plasmas

We have obtained the bound 1s^{2 1}S, 1s2s ^1,3S, and 1s2p ^1,3P states energies of helium atom in dense plasma environments in accurate variation calculations. A screened Coulomb potential to represent the Debye model is used for the interaction between the charged particles. A correlated wave function consisting of a generalized exponential expansion has been used to take care of the correlation effect. The 1s^{2 1}S, 1s2s ^1,3S, and 1s2p ^1,3P states energies along with the ionization potential, the energy splitting between the 1s2s ³S, and 1s2s ¹S states, transition energies between the ground state and low‐excited states of He estimated for various Debye lengths, are reported. The results show high degree of accuracy even under strong plasma conditions. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

The spin-allowed and spin-forbidden 5s 2 1 S 0-5s5p 1 P 1,3 P 1 transitions in strontium isoelectronic sequence

Relativistic multiconfiguration Dirac-Fock (MCDF) transition energies and oscillator strengths are determined for both the spin-allowed 5s ^{2 1} S ₀-5s5p ¹ P ₁ and the spin-forbidden 5s ^{2 1} S ₀-5s5p ³ P ₁ transitions in the strontium isoelectronic sequence. The modest relativistic configuration mixing to represent intravalence correlation is combined with a polarization model to account for valence-core electron correlations. The multiconfiguration Dirac-Fock calculations are performed in an average level scheme; however for neutral strontium and singly ionized yttrium a thorough comparison of the average and the optimal level schemes is presented. The average level scheme, though less accurate for the neutral end of the sequence, avoids the convergence problems encountered for highly ionized systems, where the 5s 5p ³ P ₁,¹ P ₁ states are raised owing to the collapse of the 4d _{3/2, 5/2} spin-orbitals in the isoelectronic sequence and, thus, allows us to extend our study to multiple charged ions (throughW ³⁶⁺). Since for such systems there is practically no difference between the results of the average and the optimal level versions of MCDF calculations, we believe that our average level predictions of ionization energies and oscillator strengths for states with total angular numberJ=0 andJ=1 are of comparable quality to those that could be obtained with an optimal level scheme.This study was supported by the Pedagogical Academy of Kraków Statutory Activity Grant No BS-29/91     

The electronic structure of the excited states for B,C+, and C arising from the configuration 1s2 2s 2pn—the effect of removal of the “equivalence” restriction

In order to test the effect of a removal of an “equivalence” restriction, some excited states of B, C⁺ and C arising from the configuration 1s²2s2pⁿ (n = 2, 3) are calculated by the use of a one-diffuse-electron model with the optimal spin coupling (DO), in which the freedom of the spin coupling is fully used. The configuration employed is 1s²2s2p^n–12p′ (n = 2, 3). The DO method gives a good agreement with the term energies especially for boron (⁴P → ²P) and carbon (⁵S° → ³S°). A diffuse 3p natural orbital with a large occupation number is found for boron ²P and carbon ³S° by DO . This result is confirmed by configuration interaction calculations. Using the same configuration as above, we also examine a one-diffuse-electron model with a fixed spin coupling for boron. This method almost reproduces the results of restricted Hartree–Fock and the effect of a removal of an “equivalence” restriction is not found. The importance of utilizing the freedom of the spin coupling in a one-diffuse-electron model is strongly indicated in this article.     

Optical oscillator strengths for lithium

A simple two-parameter analytic potential adjusted so as to reproduce the experimental energy levels is used to generate wave functions for the ground and excited states of the lithium atom. Using these wave functions in conjunction with the Born approximation and the Russell–Saunders LS-coupling scheme, we calculate the optical oscillator strengths for various excitations from the 1s²2s(²S_1/2) ground state. The results are compared to experiment and other calculations.     

Optical oscillator strengths for isoelectronic ions of nitrogen

An analytic atomic active electron model potential adjusted to experimental single-particle energy levels is used to generate wave functions for the valence and excited states of O¹⁺, F²⁺, Ne³⁺, Na⁴⁺, and Mg⁵⁺. Using these wave functions in conjunction with the Born approximation and the LS-coupling scheme, we calculate optical oscillator strengths for excitations from the 1s²2s²2p³(⁴S_3/2) ground state. The results are compared to experimental data and other calculations. Systematic trends along the isoelectronic sequence are discussed.     

Fine structure of the 1s5f and 1s5g levels of He I

The fine structure of the 1s5f and 1s5g levels of He I was measured using microwave spectroscopy. The helium atoms were excited by ion impact, and the eleven allowed 1s5f ^2S+1 F _J –1s5g ^2S′+1 G _J , transitions near ν≈15 GHz were induced and detected by measuring the 1s4d–1s2p or 1s3d–1s2p spectral-line intensities of the impact radiation as a function of the microwave frequency. The measured transition frequencies are in accord with theoretical values and, except for one transition frequency, with earlier experimental data. The existing discrepancy between these earlier data and theory could be solved.     

Precision energies and hyperfine structures of the 5s5p 3 P 0,1,2 0 and 5s6s 3 S 1 levels in In II

Absolute frequencies of hyperfine components of the 230.6 nm (5s ^{2 1} S ₀?5s5p ³ P ₁ ⁰ ), 193.6 nm (5s5p ³ P ₀ ⁰ ?5s6s ³ S ₁), 197.7 nm (5s5p ³ P ₁ ⁰ ?5s6s ³ S ₁) and 207.9 nm (5s5p ³ P ₂ ⁰ ?5s6s ³ S ₁) transitions in In II emitted from a hollow-cathode source have been measured using a high-resolution, scanning échelle monochromator. The measured frequencies of these four transitions have been used to determine the energies and hyperfine interaction constants of the 5s5p ³ P ₀ ⁰ ,³ P ₁ ⁰ ,³ P ₂ ⁰ and 5s6s ³ S ₁ levels in In II. The hyperfine interaction constants for the dominant isotope¹¹⁵In are found to be: 5s5p ³ P ₁ ⁰ A=0.2322(2) cm^?1,B=?0.0159(9) cm^?1 5s5p ³ P ₂ ⁰ A=0.1699(4) cm^?1,B= 0.021 (6) cm^?1 5s6s ³ S ₁ A=0.4022(4) cm^?1,B= 0.002 (2) cm^?1. The absolute frequency of the very narrow, strongly forbidden In II 236.5 nm (5s ^{2 1} S ₀?5s5p ³ P ₀ ⁰ ) transition, which has been proposed as a candidate for a new optical frequency standard, is found to be 42275.986(7) cm^?1.     

Abundance ratios of mercury isotopes by 6s6p3P1-intermediate state excitation with resonance ionization mass spectrometry

The isotope-selective excitation of mercury via the 6s6p ³ P ₁ intermediate state excitation is studied with two-color resonance ionization mass spectrometry to determine abundance ratios of stable mercury isotopes. Lifetime, isotopic shifts, and hyperfine structure (HFS) splittings are measured. Atomic hyperfine interaction constants are determined. Line strengths of the ten components of the 6s ^{2 1}S₀→ 6s6p ³ P ₁ transition are used for isotope ratio determinations. Ion signal intensities of even-mass components directly give the isotopic abundance, in contrast to the odd-mass components, for which the sum of the HFS components results in an anomalously high response for the isotopic abundance. The laser bandwidth dependence of the excitation and population probabilities of magnetic HFS sublevels due to linear polarization of the radiation are discussed. These considerations yield reasonable values for the apparent odd-mass isotope abundance. Received: 13 November 1998 / Revised: 18 January 1999 / Accepted: 21 January 1999     

Säurekatalysierte Dienon-Phenol-Umlagerungen von 6-Propargyl-6-methyl-cyclohexa-2,4-dien-1-onen; ladungskontrollierte,aromatische [1s, 2s]- und [3s, 4s]-sigmatropische Reaktionen

The acid catalysed dienone-phenol rearrangement of methyl substituted o-propargyl-cyclohexadienones (scheme 3) was investigated. The rearrangements were carried out in acetic anhydride containing about 1⁰/₀₀ sulfuric acid. Under these conditions acetoxy benzenium ions are formed as intermediates. These then undergo charge-controlled [3s, 4s]- and [1s, 2s]-sigmatropic rearrangements. Thus, the [3s, 4s]-process leads to the formation of the corresponding allenyl-phenol acetates ( 19 , 21 , 23 , 25 , 28 , 30 ) whereas the [1s, 2s]-process yields propargyl-phenol acetates ( 20 , 22 , 24 , 26 , 29 ), respectively (cf. scheme 4).     

Application of the extended method of calculation for atoms and ions having the electronic configurations 1s22s22pN

The atoms and ions in the electronic configurations 1s²2s²2p^N (N = 2, 3, 4, 5, 6) are examined. N hydrogen-like radial orbitals for 2p electrons were used. The calculated energies of the 2p shell are compared with those of the ordinary method and with experimental results. The intermultiplet separation ratios are considered as well.     

Lifetimes of the 4s4p 3 P 1 and 4s3d 1 D 2 states of Ca I

The lifetimes of the 4s4p ³ P ₁ and 4s3d ¹ D ₂ metastable states of Ca have been studied using the time-of-flight technique. Two kinds of observations were performed. First, the exponential decay of the fluorescence, using a (continuous) dc discharge for excitation and then the velocity distribution of the radiating atoms, using a pulsed discharge, were measured. From the combined results of these measurements the lifetimes were derived. The lifetimes of the 4s4p ³ P ₁ and 4s3d ¹ D ₂ states of Ca are determined to be 0.57±0.03 ms and 1.5±0.4 ms, respectively.     

Effect of the exchange integral K2s2p on the 2p-orbitals of the 1P and 3P states of the beryllium isoelectronic sequence arising from the configuration (1s)2(2s)(2p)

The ¹P and ³P states arising from the configuration (1s)²(2s)(2p) of the Be isoelectronic sequence are investigated. In the single configuration approximation, the energies of the two states are expressed as E⁰ + K_2s2p and E⁰ - K_2s2p, respectively. K_2s2p is the exchange integral between the 2s and 2p electrons and E⁰ is the energy of a model in which K_2s2p is deleted. First we calculate the 2s- and 2p-orbitals in this model. Second, by taking account of K_2s2p in this model, effects of this term on the 2p-orbitals in the ^1,3P states are investigated. In this manner, an explanation is given for the following facts which are obtained from a minimal Slater-type orbital set; (1) for Be and B⁺, the 2p-orbital of the ¹P state is broader than that of the ³P state; (2) for C²⁺, the extension of the 2p-orbital in the two states is almost the same; (3) for O⁴⁺ and Ne⁶⁺, in contrast to Be and B⁺, the 2p-orbital of the ¹P state is tighter than that of the ³P state.     

Observation of the electric-field-inducedE1 transition between 5s4d 1 D 2 and 5s 2 1 S 0 levels in Sr I

The angular distribution of the electric-field-inducedE1 radiation is asymmetric with respect to the external electric field direction. Measurement of this asymmetry for the 5s4d ¹ D ₂ → 5s ^{2 1} S ₀ transition in strontium permits the experimental determination of the 5s5p ¹ P ₁ → 5s4d¹ D ₂ decay rate. The result is:A(¹ P ₁ →¹ D ₂)=(4.37±0.93±0.66) × 10³ s ^?1.     

Radial and angular correlations in doubly excited states: A time‐dependent perturbation approach

The time‐dependent variation perturbation theory (TDVPT) was applied to estimate separately the effect of radial and angular correlations in the doubly excited states of two‐electron systems. Test calculations were performed for the transitions 1s² : ¹S^e→2s² : ¹S^e for H⁻ and 1s² : ¹S^e→ns² : ¹S^e (n=2,…,5) for He, Li⁺, Be²⁺, and B³⁺. Transition energies to various doubly excited states were estimated using radially correlated basis sets as well as with basis sets which take care of both radial and angular correlations. Angular correlation is taken care of by incorporating higher angular momentum basis sets in the expansion of the perturbed wave functions. The excitation energy is lower in all the cases, indicating the correct behavior. Overall improvement of the results is observed when angular correlation is included. The effect of angular correlation, however, diminishes rapidly with increase of the nuclear charge. This has been demonstrated explicitly for the lowest doubly excited transitions in the highly stripped ions Al¹¹⁺, Si¹²⁺, P¹³⁺, S¹⁴⁺, and Cl¹⁵⁺. © 1999 John Wiley & Sons, Inc. Int J Quant Chem 76: 99–104, 2000     

Valence orbital ionization potentials of 1s 22s m2p n atoms and ions

The 2s and 2p valence orbital ionization potentials (VOIP) are determined systematically for atoms and ions with configurations 1s ²2s ^m2p ⁿ , using the Anno-Teruya values of the average energies of the configurations. All the cases with possible values of m and n, in conformity with the Pauli principle, are treated. The 2s or 2p VOIP of a particular ion with the configuration of this type is almost independent of the electron configuration. The VOIP's of an isoelectronic series are fitted to a quadratic equation in terms of atomic number Z: VOIP=A ₀+A ₁ Z+A ₂ Z ², by a least-squares method. There are remarkable regularities among A ₀'s, A ₁'s or A ₂'s, for different isoelectronic series, which may be explained by Slater's simple expression for the total energy of an atom (or ion) with the idea of screening effect due to inner electrons. Various screening constants have been determined from the analysis of such regularities.

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Zusammenfassung Unter Benutzung der Anno-Teruya-Werte für die durchschnittliche Energie der Konfigurationen werden systematisch für Atome und Ionen der Konfiguration 1^{s 2}2s ^m 2p ⁿ die 2s- und 2p-VOIP's bestimmt. Alle FÄlle mit den nach dem Pauli-Prinzip möglichen Werten für m und n werden behandelt. Das 2s- oder 2p-VOIP eines besonderen Ions ist beinahe unabhÄngig von der Elektronenkonfiguration. Nach der Methode der kleinsten quadratischen Abweichung werden die VOIP's einer isoelektronischen Serie mit Hilfe einer in Z (Z=Kernladungszahl) quadratischen Gleichung bestimmt: VOIP=A ₀ +A ₁ Z+A ₂ Z ². Die Koeffizienten A ₀,A₁ und A ₂ zeigen untereinander für verschiedene isoelektronische Serien bemerkenswerte RegelmÄ\igkeiten, die mit der einfachen Slaterformel für die Gesamtenergie eines Atoms oder Ions als Abschirmeffekte der inneren Elektronen erklÄrt werden können. Durch die Untersuchung dieser RegelmÄ\igkeiten konnten verschiedene Abschirmkonstanten bestimmt werden.

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Résumé Les potentiels d'ionisation des orbitales de valence (VOIP) 2s et 2p sont systématiquement déterminés pour les atomes et les ions de configuration 1s ²2s ^m2p ⁿ, en utilisant les valeurs de Anno-Teruya pour les énergies moyennes des configurations. Tous les cas possibles d'après le principe de Pauli sont traités. Le VOIP 2s ou 2p d'un ion donné avec une configuration de ce type est presque indépendant de la configuration électronique. Une relation quadratique en fonction du numéro atomique Z est ajustée pour les VOIP d'une série isoélectronique par la méthode des moindres carrés: VOIP=A ₀+A ₁ Z +A ₂ Z ². Des régularités remarquables se manifestent pour A ₀, A ₁, A ₂ dans différentes séries isoélectroniques; ceci peut Être expliqué à l'aide des expressions simples de Slater pour l'énergie totale d'un atome (ou d'un ion) avec l'idée d'un effet d'écran d aux électrons internes. Différentes constantes d'écran ont été déterminées par l'analyse de ces régularités.

     

Why do the second row transition metal atoms prefer 5s14dm+1 to 5s24dm?

Numerical Hartree-Fock (NHF) calculations have been performed for 332 ground and low-lying excited states of the fifth period atoms Rb through Xe, with our special interest in the states arising from the 5s ²4d ^m , 5s ¹4d ^m +1, and 5s ⁰ 4d ^m +2 configurations of the second row transition metal atoms. Among various properties, orbital energies and mean values ofr of the outermost orbitals of each symmetry are presented as well as total energies. It is discussed in some detail why the second row transition metal atoms have a tendency to prefers ¹ d ^m +1 as the ground configuration in contrast to the preferreds ² d ^m configuration in the first row transition metal atoms. Our systematic NHF computations reported in this and the previous papers conclude that the Hartree-Fock method correctly predicts the experimental ground state of the atoms He through Xe with the sole exception for Zr.