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.     

Precision measurement of the energy of the 4d 9 5s 2 2 D 5/2 metastable level in Ag I

The energy of the 4d ⁹ 5s ^{2 2} D _5/2 metastable level in Ag I, which is the upper level of the very narrow 5s ² S _1/2 – 4d ⁹ 5s ^{2 2} D _5/2 two-photon transition at 661.2 nm, has been determined from precision measurements of the wavelengths of the 206.1 nm (5s ² S _1/2 – 6p ² P ₃ ^2/0 ) and 547.5 nm (4d ⁹ 5s ^{2 2} D _5/2 – 6p ² P ₃ ^2/0 ) lines emitted from a hollow-cathode discharge. The measured energy of the 4d ⁹ 5s ^{2 2} D _5/2 level, 30 242.286(7) cm^–1, is combined with the known hyperfine splittings and the estimated¹⁰⁷Ag-¹⁰⁹Ag isotope shift to obtain accurate absolute frequencies for the hyperfine components of the 661.2 nm transition. These results should help in the detection of the narrow 661.2 nm two-photon transition, which has been proposed as a new optical frequency standard.     

Ab initio calculations on NO2 and NO 2 − : Optimization of diffuse Gaussian exponents

Ab initio calculations of NO₂ and NO ₂ ⁻ , using a Dunning [4s3p] basis augmented by 1 component diffuses andp functions were carried out. The SCF energies of NO₂ and NO_2/− (ground states) as a function of O _s , O _p , N _s , and N _p diffuse function exponents are given and discussed. The curves show some unexpected features which make the optimization of the diffuse function exponents problematic. The SCF vertical electron detachment energy for NO ₂ ⁻ as a function of the diffuse O _s , O _p , N _s , and N _p exponents is then discussed. Except for the case of O _p , the detachment energy is essentially independent of the O _s , N _s , and N _p exponents. Finally, results of SCF and MCSCF/CI calculations of the electron affinity of NO₂ are given and compared with experiment. Work performed under the auspices of the Division of Basic Energy Sciences of the U.S. Department of Energy. By acceptance of this article, the publisher and/or recipient acknowledges the U.S. Government's right to retain a nonexclusive, royalty-free license in and to any copyright covering this paper.     

Diatomic interactions in momentum space. The 1sσg and 2pσ u states of H 2 + system

The method of momentum electron density for interatomic interactions has been applied to the two lowest σ states of the H ₂ ⁺ system. For attractive (1sσ_g) and repulsive (2pσ _u ) interactions, the behaviour of momentum density and its effect on the stabilization energy of the system are examined quantitatively. The concept of contraction and expansion of the momentum density is shown to form an important guiding principle in this approach. The origin of covalent bonding is discussed based on the energy partitioning proposed previously.     

Calculation of Ionization,Excitation and Electron Capture Cross Sections for Be4++H(2s, 2p) Collisions

A computational study of Be⁴⁺+H(2s, 2p) collisions has been carried out employing the Classical Trajectory Monte Carlo (CTMC) method for the impact energy range from 20 keV/u to 1000 keV/u. The integral n partial cross sections for H(n) excitation and Be³⁺(n) electron capture and, the total ionization and electron capture cross sections are calculated and compared to recent semiclassical results. A general good agreement is observed for the n partial and total electron capture and ionization cross sections. The comparative study of the three inelastic processes show no significant differences between both excited targets.     

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.     

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     

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.     

Tensor polarizabilities of the 4f 7(8 S)5d6s 2 9 D 2,3,4,5,6 levels in Gd I

The optical pumping method with rf detection and the nonlinear level crossing technique were used in parallel electric and magnetic fields to investigate the Stark splitting of all the fine structure levels of the ground multiplet 4f ⁷ (⁸ S) 5d6s ^{2 9} D in Gd I. The tensor polarizabilities were deduced from the level crossing and the rf signals. The variation of the tensor polarizabilities is well reproduced by the LS coupling approximation, except for the small value of the⁹ D ₅ level. A value of the tensor polarizability of the 5d electron is evaluated from the experimental results, ₂(5d)=2.00(6) kHz(kV/cm)². It is shown that the ratio between the electric quadrupole constant and the tensor polarizability is constant, except for the⁹ D ₅ ratio, which is caused by a breakdown of the central field model.     

Analysis of autoionizing Rydberg series Cu I 3d 9 4snl with the multichannel quantum defect theory

Using atomic beam technique, a combination of collisional and laser excitation, and photoion detection, autoionizing Cu I states in the region of the ionization limits Cu II 3d ⁹ 4s(^3,1 D) were investigated. In spite of the complicated structure of the signals due to the four different ionization limits³ D ₃,³ D ₂,³ D ₁ and¹ D ₂ and the large number of possible (LSJ)-states, which can be reached by this experimental technique, the majority of the signals could be attributed to definite Rydberg series 3d ⁹ 4s(³ D ₃,³ D ₂,³ D ₁,¹ D ₂)nl (LSJ). Perturbations were analyzed by the three- and four-channel quantum defect theory and by Hartree-Fock calculations. General formulas for the calculation of the photoionization cross section by the four-channel quantum defect theory in the case of two closed and two open channels are given.     

Coherence parameters for He+(2p) capture and H(2p) excitation in He2+-H(1s) collisions

Semiclassical coupled channel calculations have been carried out for the collision system He²⁺-H(1s) in the velocity range 0.15–3.0 a.u. (impact energies 0.5–225 keV/amu) in order to study capture probabilities and alignment and orientation parameters for the dominant He⁺(n=2) channels. A 14-state AO basis set calculation has been combined with an analytical treatment of the asymptotic collision region. For impact velocities about and abovev=0.6 a.u. a strong propensity for resonance capture into an oriented He⁺(2p) state with the same sense of rotation as the collisional rotation of the internuclear axis is predicted together with a very smooth behaviour of the alignment angle as function of impact parameter. Eikonal method calculations of differential capture cross sections predict that the left/right orientation asymmetry will prevail in differential scattering experiments. The resulting total cross sections for capture into specificnl-substates (n=2, 3) and the total light polarisation parameter for He⁺(2p) capture compare well with previous work. Finally we report H(2s,2p) excitation cross sections, probabilties and H(2p) alignment and orientation parameters, following the established propensity rule for orientation in H(2p) excitation.     

Tensor polarizability of cadmium atoms in the excited state (5s5p)3 P 1

The tensor polarizability of the (5s5p)³ P ₁ level of cadmium atoms in a vapour cell were measured using level crossing technique and opto-magnetic double resonance in parallel electric and magnetic fields. The value of the tensor polarizability obtained from the level crossings is: ₂=1.33±0.04 kHz/(kV/cm)² and from the double resonance is: ₂=1.27±0.06 kHz/(kV/cm)². These results were compared with previous theoretical and experimental data of other authors.This work was supported in part by the Committee for Scientific Research under grant No. 2 0226 91 01     

Systematic determination of the Slater-Condon parameters of atoms and ions with 1s 2 2s m 2p n configurations

Semiempirical values of the Slater parameters F ²(2p,2p) and G ¹(2s, 2p) have been determined for the atoms and ions with the electron configurations 1s ²2s ^m2p ⁿ from the experimental atomic energy levels. Particular attention has been paid to get the values of the parameters to be used for semiempirical calculations on molecular electronic structure. The calculation has also yielded E _av's, the average energies of configurations of these atoms. Evaluation of the semiempirical or effective value of F ⁰ from E of an appropriate electron-transfer reaction, based on the idea presented by Anno [15], is also referred to in the present paper. The semiempirical values of the Slater parameters as well as those of E's and E _av's show almost linear dependence upon atomic number Z through isoelectronic series. From the overall tendency of the correlation lines, it is pointed out that the assignment of atomic energy levels of Na⁵⁺ (1s ²2p ⁴) must be wrong.

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Zusammenfassung Semiempirische Werte der Slater-Parameter F ²(2p,2p) und G ¹(2s, 2p) wurden für die Atome und Ionen mit der Elektronenkonfiguration 1s ²2s ^m2p ⁿ aus den experimentellen atomaren Energietermen bestimmt. Insbesondere wurden die Parameter bestimmt, die für semiempirische Berechnungen der Elektronenstruktur von Molekülen benötigt werden. Die Berechnung ergibt weiterhin Werte von E _av, der Durchschnittsenergie der Konfigurationen der genannten Atome. Die vorliegende Arbeit geht auch auf die Bestimmung des semiempirischen bzw. effektiven Wertes von F ⁰ aus E einer geeigneten Elektronenübertragungsreaktion ein, die auf die Arbeit von Anno [15] zurückgeht. Die semiempirischen Werte der Slater-Parameter sowie der E und E _av zeigen annähernd lineare Abhängigkeit von der Atomnummer Z innerhalb isoelektronischer Reihen. Aus dem Gesamtverhalten der genannten Kurven wird geschlossen, da die Zuordnung der atomaren Energieterme von Na⁵⁺(1s ²2p ⁴) falsch sein dürfte.

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Résumé Détermination à partir des niveaux d'énergie atomiques expérimentaux des valeurs semi-empiriques des paramètres de Slater F ²(2p, 2p) et G ¹(2s, 2p) pour les atomes et les ions ayant les configurations 1s ²2s ^m2p ⁿ. On a fait particulièrement attention d'obtenir les valeurs des paramètres à utiliser pour des calculs moléculaires semi-empiriques. Le calcul a aussi fourni les énergies moyennes des configurations de ces atomes. On évoque aussi le calcul de la valeur semi-empirique ou effective de F ⁰ à partir du E d'une réaction appropriée de transfert électronique, selon une idée de Anno [15]. Les valeurs semiempiriques des paramètres de Slater, ainsi que celles des E et E _moy, montrent une dépendance presque linéaire au nombre atomique Z à travers les séries isoélectroniques. A partir des tendances générales des lignes de corrélation, on remarque que l'attribution des niveaux d'énergie atomiques de Na⁵⁺(1s ²2p ⁴) doit être fausse.

     

Radiative lifetime determination for the 3s4p-1P1 state of magnesium using pulsed level-crossing spectroscopy

The natural radiative lifetime of the 3s4p ¹ P ₁ level of neutral magnesium was measured by pulsed level-crossing spectroscopy at the short excitation wavelength of 202.6 nm. We obtained =13.4(5) ns for this state, strongly deviating from a previous beam-foil result, but in good agreement with a multi-configuration Hartree-Fock calculation. A discussion of the applicability of the pulsed Hanle effect method is given.     

Electron emission in collisions of slow rare gas ions with partially cesiated W (110)

We report the spectra of electrons emitted after slow collisions (50 eV) of rare gas ions (He⁺, Ne⁺, Ar⁺, and Xe⁺) with partially cesiated W(110) surfaces. The electron spectra are discussed in terms of the two interatomic Auger processes, Auger Capture and Auger Deexcitation and the intra-atomic Auger process, Autodetachment of Rg^–* (He^–* (1s 2s ^{2 2} S) in the case of He). Model calculations including these processes can qualitatively reproduce the measured spectra as well as experimental values for the electron emission coefficients, . This is demonstrated for collisions of He⁺ ions and thermal metastable He atoms with clean and partially cesiated W(110).     

Long-range interaction between 1s and 2s or 2p hydrogen atoms

Long-range interaction energy between two hydrogen atoms has been computed in the second order of the perturbation theory. All states of the system arising when one of the atoms is in the 1s and the other in the 2s or 2p state have been considered. The energy represented by a series expansion in inverse powers of the internuclear distance, R, has been computed up to the terms in R^?8. The results are believed to give reliable interaction energies for R > 15 a.u. Accurate interaction energy for two ground-state hydrogen atoms has also been obtained up to the terms in R^?10. Results for the B′ ¹∑ state are employed to discuss the experimental ground-state dissociation energy of H₂, D₂, and HD. For H₂ all values of the dissociation energy obtained from various experimental absorption limits, by using the computed potential energy curve to separate off the effect of rotation, are shown to be satisfactorily consistent. The resulting total energy of H₂ is, however, higher than the most accurate theoretical value.     

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.     

Scaled AMO calculations on the hydrogen molecule. III. The 1s2s 3∑ state

The potential energy curve for the 1s2s ³∑ state of the hydrogen molecule is calculated in a scaled version of the AMO approximation. Deviations from a simple potential curve occur. The agreement with experimental data is found to be better for the present state than for the 1sσ2pσ ¹∑ state studied in a previous paper.     

Perturbation treatment of the Hartree–Fock equations of 1s2p3s 4Pθ state of the lithium isoelectronic sequence

The first order Hartree–Fock equations of the 1s2p3s ⁴P⁰ state of the three-electron atomic systems have been solved exactly. These solutions are used to evaluate Hartree–Fock energy up to third order with high accuracy. The third order Hartree–Fock energies for Li to Ne⁷⁺ are compared with those derived from experiment and other theoretical calculations.     

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.