A relativistic CI study on OIII: wavefunctions,excitation energies and transition probabilities

The relativistic CI method is used to determine N-electron wavefunctions for the 1s ² 2s ² 2p ² (³ P ₀,³ P ₂,¹ D ₂), 1s ² 2p ^{4 3} P ₂ even levels, and the 1s ²2s2p ³ (³ D ₁,³ P ₁,³ S ₁,¹ P ₁), 1s ²2s ²2p3s (³ P ₁ and¹ P ₁), 1s ²2s ²2p3d (³ D ₁,³ P ₁,¹ P ₁)J=1 OIII levels. Excitation energies and emission probabilities between these levels are reported in the electric dipole approximation, both for the Coulomb and the Babushkin gauges.ns, p,np,nd- andnd (n17) numerical basis functions have been used for the construction of CSF's entering the CI expansion for the ASF's of these levels. Radiative matrix elements of the type calculated here within the framework of the relativistic CI method, may be used in laser assisted spectroscopic studies of atoms and ions.     

Hyperfine structure of the 33 P state of3He and isotope shift for the 23 S-33 P 0 transition

The hyperfine structure of the³He 1s 3p ³ P state and the³He-⁴He isotope shift is determined by high precision measurements of the 1s2s ³ S ₁-1s 3p ³ p ³ P _J transition frequencies near 389 nm. A direct frequency measurement is made without the need for wavelength calibration by tuning a single laser to the atomic frequency, and using a novel heterodyne method to observe beat frequencies with a stable reference laser. A fit to a theoretical model of hyperfine structure is used to determine the hyperfine shifts. Additional off-diagonal mixing effects are investigated to resolve a possible systematic discrepancy in the hyperfine intervals. The final isotope shift without hyperfine structure of 42184308±165 kHz is used to deduce an rms nuclear charge radius for³He of 1.956±0.042 fm. This is in good agreement with other values obtained from atomic isotope shift measurements, and a recent theoretical value of 1.958±0.006 fm. The present result helps to resolve substantial differences in the³He nuclear radius derived from electron-nuclear scattering measurements, and it provides a significant test of the nuclear three-body problem.     

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.     

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.     

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.     

Isotope Shifts of Nitrogen around 800 nm

The Doppler-limited absorption spectra of ¹⁴N and ¹⁵N atoms were measured around 800 nm using concentration modulation spectroscopy to study their isotope shifts. The nitrogen atoms were generated by discharging molecular nitrogen buffered with helium in a homemade discharge tube. The isotope shifts of four multiplets (3s⁴P_J→3p⁴D_J^o, 3s⁴P_J→3p⁴P_J^o, 3s²D_J→5s²P_J^o, and 3p²P_J^o→5s²D_J^o) were measured and their J-dependent specific mass shifts were observed and discussed.     

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     

Geometrically active atomic states and the formation of molecules in their normal shapes

We present a theory of molecular formation according to which the shape of polyhedral or coordination compounds is fixed to a very good approximation by the shape of a particular state (or states) of the central atom, which is activated by spin and spacial coupling of optimal strength between this state, called the geometrically active atomic state (GAAS) and the state of the ligands. For a molecule with a central atom, spacial coupling of optimal strength, means that the shape of the GAAS fixes the position of the ligands according to the maximum overlap principle of the Heitler–London, Slater, and Pauling theory of covalent bonding, whereby much of the energy lowering from the free atom limit is obtained by the maximization of the contribution of the exchange integrals. Hence, a direct causal relationship between the shape of the GAAS and the shape of the molecular state at equilibrium seems to exist. This relationship implies a picture of diabatic connection between the geometrically asymptotic region and the equilibrium region, which is driven by the coupled GAAS and provides the “why” of molecular shape. Since the latter is fixed by the shape of the GAAS (in cases of electronic complexity or of molecular instability it is possible that more than one GAAS contribute simultaneously), prediction of the shape of certain large systems can be made based on the a priori recognition of the corresponding GAAS. The concept of the shape of atomic states defined and computed quantum mechanically from the probability distribution ϱ(cos θ₁₂) of the angle θ₁₂ that the position vectors of two electrons form in the given atomic state. Specifically, it is deduced from the distribution's maxima which provide the most probable values of θ₁₂. As shown previously [Y. Komninos and C. A. Nicolaides, Phys. Rev. A 50 , 3782 (1994)], ϱ(cos θ₁₂) is obtainable directly from the state-specific expression for the Coulomb interaction, where the R^k integrals are replaced by Legendre polynomials P_k, multiplied by normalization constants and radial overlaps. The theory is demonstrated by explaining the shape of BeH₂, BH₂, CH₄, SiH₄, H₂O, H₂S, NH₃, PH₃, SF₆, and TiH₄ in terms of the shapes of the following GAAS. Be: 2s2p ³P⁰, B: 2s2p^{2 4}P, C: 2s2p^{3 5}S⁰, Si: 3s3p^{3 5}S⁰, O: 2s2p^{5 3}P⁰, S: 3s²3p³3d ³P⁰, N: 2s2p^{4 4}P, P: 3s3p³3d ⁴P⁰, S: 3s3p³3d^{2 7}F⁰, and Ti: 3d²4s4p ⁵G⁰. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 321–328, 1998     

Laser and radiofrequency spectroscopy of the 5d 4 6s 6 D multiplet in Ta I

The hyperfine structure (hfs) of¹⁸¹Ta has been investigated using laser radio-frequency double resonance and high resolution laser spectroscopy on collimated atomic beams. The magnetic dipole and electric quadrupole hyperfine structure coupling constants of the 5d ^{4 6} s 6D _{3/2, 5/2, 7/2, 9/2} metastable states have been determined using radio-frequency spectroscopy. In the 5d ⁴ 6s ⁶ D _1/2 metastable state and the excited 5d ³ 6s 6p ⁴ D _3/2,⁶ D _{5/2, 9/2} as well as the unidentified 28 182.6 cm^–1 and 30 021.2 cm^–1 states, hfs constants have been obtained from high resolution laser spectroscopy. A radio-frequency converter has been developed in order to reach the frequency region 2.7–10 GHz.     

Theoretical study of transitions involving three rydberg series in two-valence electron systems: MgI and its electronic sequence

Oscillator strengths for transitions involving levels of three spectral series, 3s^{2 1}S → 3snp¹P⁰, 3s3p ¹P⁰ → 3snd ¹D, and 3s3p ¹P⁰ → 3sns ¹S, have been computed and analyzed for several ions of the MgI isoelectronic sequence (MgI-TiXI). The quantum defect orbital (QDO) formalism has been used throughout, and the results are comparable to those of more complex theoretical procedures.     

XPS analysis (ESCA) of the surface composition of poly(styrene/2-hydroxyethyl methacrylate) microspheres produced by emulsifier-free emulsion polymerization

Polymer microspheres composed of various compositions of styrene and 2-hydroxyethyl methacrylate (HEMA) were produced by batch emulsifier-free emulsion polymerization. The HEMA content at the surface, [HEMA] _s , of the microspheres powdered by freeze-drying was determined by both quantitativeC ^1s /O ^1s analysis andC ^1s peak shape analysis of the x-ray photoelectron spectroscopic spectra. When the HEMA content in the microsphere, [HEMA] _p , was less than about 5 mole%, the [HEMA] _s values determined by the two different methods showed good agreement. At [HEMA]_p above 5 mole %, [HEMA]_s values determined by the first method were about 15 mole % greater than those determined by the second. They both showed a similar tendency with the [HEMA] _s being higher than the [HEMA] _p , e.g., when [HEMA] _p was 1 mole %, [HEMA] _s was 11 mole %. The intensity of the satellite peak due to the ^* transition of the benzene ring of the styrene component decreased with an increase in [HEMA] _p , to zero at 5 mole % of [HEMA] _p . These results indicate that the HEMA component is localized at the surface.Part CVIII of the series Studies on Suspension and Emulsion.     

Autoionization resonances in atomic Ga,In, and Pb

Autoionization resonances of the type (n?1)d→np, wheren pertains to the outermost shell of Ga, In and Pb, were studied with the use of electron spectrometry in combination with synchrotron radiation. The relative strengths of the exit channels for the various resonance states were measured. In the case of Ga and In, a complete partitioning of the total absorption cross section into thes ^{2 1} S,sp ¹ P, andsp ³ P components (exit channels) was achieved, and in the case of Pb the decay of the resonance states into the major exit channels 6s ² 6p ² P _1/2, 6s ² 6p ² P _3/2, 6s 6p ^{2 4} P _1/2, 6s 6p ^{2 2} D _3/2 and 6s 6p ^{2 2} P _1/2 was determined. In Ga, strong coupling was observed for those states of the 4p ² manifold that have the same symmetries as the final ionic states, e.g. 4p ^{2 3} P→4s 4p ³ P and 4p ^{2 1} S→4s ^{2 1} S. In In, there is a similar, but weaker correlation, which also includes two-electron excitation channels. Comparison between Ga and In shows that thesp ³ P channel is much stronger in In (52% vs 40% in Ga) while thesp ¹ P channel is correspondingly weaker (28% vs 37%), with thes ^{2 1} S channel remaining practically unchanged (20 vs 23%). In Pb, the 6s ² 6P ² P _1/2 channel displays interference patterns due to a strong, competing direct transition, whereas the other channels do not, indicating population predominantly via the resonance states.     

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.     

Ionization potential of excited states of Be‐like sequence in the concept of iso‐spectrum‐level series

With the introduction of the concept of the iso‐spectrum‐level series, a linear relationship is found between the first differences of the ionization potential of excited states and nuclear charge Z along an iso‐spectrum‐level series, and the ionization potential of excited states of Be‐like sequence are studied systematically on the basis of the weakest bound electron potential model theory. The expression of nonrelativistic ionization potential is derived from the weakest bound electron potential model theory, and relativistic effects are included by using a fourth‐order polynomial in Z. As a demonstration, the ionization potentials of [He]2s2p ³P, [He]2s3s ¹S₀, [He]2s3p ¹P, [He]2s3d ¹D₂, and [He]2s4d ¹D₂ series for a range of Be‐like sequence from Z = 4–23 are calculated. The results are compared with the experimental data and the recent sophisticated ab initio results. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 344–350, 2003     

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     

Second-order isotope shifts in the ground configuration of Nd I

The isotope shift between all stable neodymium isotopes has been measured for 21 transitions in the Nd I spectrum by means of laser-atomic-beam absorption spectroscopy. A parametric analysis of the observed shifts in all the levels of the terms⁵ I,⁵ F, and⁵ S of the ground configuration 4f ⁴6s ² yields not only the magnetic parameterz _4f but, for the first time, also the effective electrostatic parametersa,b, andc. A more accurate value of the nuclear parameter ^148,150 (Nd)=0.369(20) fm² is obtained from the investigation of a 4f ³5d6s ²–4f ³5d6s6p transition. The comparison of non-relativistic Hartree-Fock calculations with the experimental data yields a scaling factorS _I ^* (Nd)=1.50(9) that agrees with the corresponding one from the hyperfine structure analysis.     

Theoretical study of Na(4p2P) + Na(3s2S) and Cd(5p3P0) + Na(3s2S) collisions and their role in the energy transfer between Cd.* and Na

We have computed the cross sections for the energy transfer process Cd(5p³P₀) + Na(3s²S) → Cd(5s¹S) + Na(4p²P) and for the state changing collision Na(4p²P) + Na(3s²S) → Na(3d²D) + Na(3s²S), based on theoretical interaction potentials for the NaCd and Na2 systems, respectively. Our calculations shed light on the interpretation of experiments with laser excited Na+Cd vapour mixtures [1]. It turns out that Cd(5p³P₀), in rapid equilibrium with the doorway state Cd(5p³P₁), efficiently transfers energy to Na, populating the 4p²P state. The collisions with ground state Na cause a very fast conversion of the 4p³P₁ to the 3d²D state, from which the strongest emission is observed.     

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.     

New approach to the effects of pressure dependence on sedimentation velocity experiments

A theory is developed for sedimentation velocity experiments when the sedimentation coefficient s_p depends on pressure P as s_p/s_o = (1 + γP)^?1, where γ is a constant. In contrast to the more usually analyzed from s_p/s_o = 1 ? γP, this model does not lead, in extreme cases, to a negative sedimentation rate. A theory is presented for homogeneous macromolecules sedimenting with no diffusion. It leads to estimations of s_o and γ from a knowledge of the point of maximum concentration gradient as a function of time. Results of these calculations are compared with accurate numerical solutions of the Lamm equation with diffusion included.