Finestructure, hyperfine structure and isotope shift of 4f 6s7s in Er I

The isotope shift (IS) and hyperfine structure (hfs) of nine levels (31720 to 38921 cm^-1) assigned to the configuration 4 f ¹² 6 s 7 s in neutral erbium have been determined experimentally using Doppler-reduced saturation absorption spectroscopy in a gas discharge. We performed a fine structure analysis in the SL-coupling scheme of the single configuration 4 f ¹² 6 s 7 s, confirming and extending the classification of even parity Er I levels. We discriminated the different hfs contributions of the 4f¹² core and the (6 s +7 s) outer electrons of the shell in a non-relativistic JJ-coupling approach and in the relativistic effective tensor operator formalism in SL-coupling. The relativistic one-electron parameters of the hfs for ¹⁶⁷Er were fitted to the experimental data by a least squares fit procedure: [0pt] a ⁰¹ _4f =-147(3) MHz, [0pt] a ¹⁰ _6s + a ¹⁰ _7s =-1840(30) MHz, [0pt] b ⁰² _4f =6560(80) MHz. The level dependencies of the isotope shift were evaluated based on crossed second order (CSO) effects. We obtained the following results for the CSO parameters for the isotope pairs ^170-168Er: d _6s7s =-740(30) MHz, z _4f = 0(5) MHz, ( g _3,6s ( f , 6 s )+ g _{3, 7s} ( f , 7 s ))= -24(15) MHz and for ^170-166Er: d _6s7s =-1500(50) MHz, z _4f =0(10) MHz, ( g _3,6s ( f ,6 s )+ g _3,7s ( f +7 s ))=-50(29) MHz. The resulting parameters for the hfs are compared with those known for other configurations of the Er atom and ion. Received 16 May 1999 and Received in final form 31 January 2000     

Recent hyperfine structure investigations in the configurations 4f 136s 2, 4f 136s6p,and 4f 125d6s 2 of Tm I

By use of optical hyperfine structure investigations in the Tm I spectrum theA- values of 20 levels of the configurations 4f ¹³ 6s 6p and 4f ¹² 5d 6s ² and theA-value of 4f ¹³ 6s ^{2 2} F _5/2 were determined very accurately. These data and tenA-factors from former experiments are used for theoretical calculations. 30A-factors have been interpolated from intermediate coupling wave functions using 9 effective mono-electronic parameters. The r.m.s. deviation between experimental and theoreticalA- values amounts to 0.5 10^?3 cm^?1 and represents 3/100 of the average value of the measuredA-factors.     

Analysis of the isotope shifts and hyperfine structure in the 3 988 Å (6s6p 1 P 1↔6s 2 1 S 0) YbI line

High-resolution laser spectroscopy using a pulsed dye-laser acting on a collimated atomic beam has been used to determine the isotope shifts in the 3 988 Å YbI line. The following results have been obtained:Δσ(176, 174)=?509(4)MHz,Δσ (174, 173)=?291(10) MHz,Δσ(174, 172)=?530(4) MHz,Δσ(172, 171)=?414(5) MHz andΔσ(172, 170)= ?665(10) MHz. The sign of the magnetic dipole interaction constant in the¹ P ₁ state for¹⁷¹Yb is found to be negative,a(¹ P ₁, 171)=?213.4(3.0) MHz. The electric quadrupole interaction constant for¹⁷³Yb in the¹ P ₁ state is found to beb(¹ P ₁, 173)=605(20) MHz.     

Level crossing investigation of the hyperfine splitting in thez 6 P 7/2-level of EuI

By means of a level crossing experiment the hyperfine structure constants of thez ⁶ P _7/2-level of Eu have been determined. The results areA=-6.51(6) MHz andB= 131.2(1.0) MHz in the isotope¹⁵¹Eu andA=-2.84(3) MHz andB=327.5(1.5) MHz in the isotope¹⁵³Eu. Experimental data on the hyperfine splitting are available now for 11 of the 12 levels of the configuration 4f ⁷ (⁸S)6s 6p of EuI. These data are compared with the theoretical interpretation given by Bordarieret al. [1] which was based on only 7A-factors andB-factors. It is shown that the agreement between theory and experiment can be improved by taking into account configuration interactions.     

Laser-atomic-beam spectroscopy of 4f 75d6s−4f 75d6p transitions in Eu I

The hyperfine structure and the isotope shift of transitions between metastable levels of the configuration 4f ⁷5d6s and levels of the configuration 4f ⁷5d6p of¹⁵¹Eu and¹⁵³Eu were studied by means of the high resolution laser-atomic-beam technique. The metastable states were populated by an arc discharge burning in the atomic beam. The measured hyperfine constantsA andB of the 4f ⁷5d6s configuration allow to perform a parametric analysis using the effective tensor operator formalism. For the first time the nuclear quadrupole moments are deduced from the quadrupole interaction parameters of the 5d electron in Eu I. The values uncorrected for the Sternheimer effect are¹⁵¹ Q(5d)=1.53(5)b and¹⁵³ Q(5d)=3.92(12)b. A comparison with the quadrupole moments derived from the 6p electron and the intrinsic quadrupole moment of¹⁵³Eu gives information about Sternheimer's correction factors. The value found for the hyperfine anomaly due tos electrons in the 4f ⁷5d6s configuration agrees very well with previous results in other Eu configurations. The change in the mean-square nuclear charge radius is derived from the isotope shift measurements and compared with the results obtained from other optical transitions in Eu. The mean value isgd〈r ²〉^{151, 153} =0.577(25) fm².     

Tensor polarizabilities of levels of the configurations 4f 13 6s6p and 4f 12 5d6s 2 in thulium I

The level-crossing technique with parallel electric and magnetic fields was used to measure the tensor polarizabilities of six levels of the configuration 4f ¹³ 6s6p + 4f ¹² 5d6s ² in the Tm I-spectrum. Using intermediate coupling wave functions given by Camus and the experimental values of the tensor polarizabilities, the radial integrals for electric dipole transitions from levels of the configuration 4f ¹³6s6p + 4f ¹²5d6s ² to levels of the configuration 4f ¹³ 5d6s + 4f ¹² 6s ²6p have been determined. The results areI(4f ¹³6s6p,4f ¹³5d6s)=1.98(45)ea ₀ andI(4f ¹²5d6s ²,4f ¹²6s ²6p) = 0.88(25)ea ₀. A comparison between the experimental and the calculated values of the tensor polarizabilities shows an excellent agreement, provided that these radial integrals and the radial integrals for the electric dipole transitions to the ground state configuration 4f ¹³6s ² as determined by Wallenstein from lifetime measurements are used in the calculation, instead of radial integrals computed by Camus with Hartree-Fock wave functions.     

Analysis of the 4p 64d 7-(4p 64d 64f + 4p 54d 8) transitions in the Sn VIII spectrum

The spectrum of the 4p ⁶4d ⁷-(4p ⁶4d ⁶4f + 4p ⁵4d ⁸) transitions in Sn VIII occurring in the wavelength range 140–170 Å and excited in a vacuum spark plasma was investigated. For the first time, 113 spectral lines of these transitions were classified and the energies of 38 levels of the 4d ⁶4f and 4p ⁵4d ⁸ configurations were experimentally determined. The semiempirical energy parameters determined by least-squares fitting of the experimental energies of Sn VIII are in good agreement with the parameters of the corresponding configurations obtained previously in the analysis of the Sn VI and Sn VII spectra.     

Tensor polarizabilities and lifetimes of levels of the configurations 4f 66s6p and 4f 55d6s2 in samarium I

Stark splittings of 7 levels of the configurations 4f ⁶6s6p and 4f ⁵5d6s² in Sm I were measured by quantum beat spectroscopy in pure electric fields, allowing the determination of tensor polarizabilities. Additionally, the lifetimes of 11 levels of these configurations were determined from time-resolved registration of the exponential decay. From these values the radial integrals I(6p,6s), I(6p,5d), and I(5d,4f) were derived by a parametric analysis. Theoretical values of tensor polarizabilities and lifetimes which were calculated using these radial integrals show good agreement with experimental data of various authors.     

A high resolution study of the transitions 4f 76s 2→4f 76s6p in the Eu I-spectrum

Eight transitions in the Eu I-spectrum connecting the ground state with configuration 4f ⁷ 6s ² with states of the configuration 4f ⁷ 6s6p were studied with high resolution laseratomic-beam spectroscopy. CW dye lasers operating in the wavelength regions 435–470 nm and 560–630 nm were used for this study. New data for the hyperfine structure in¹⁵³Eu were obtained as well as new and more accurate values for the isotope shifts between¹⁵¹Eu and¹⁵³Eu. The existing data for the hyperfine structure in¹⁵¹Eu were reproduced with an exception for the levelz ⁶ P _7/2.     

Ab-initio calculations of pair-correlation effects on the hyperfine structure of the 4s 4p and 4s 3d configurations of Ca

The hyperfine structure of the 4s 4p and 4s 3d configurations of Ca has been evaluated using many-body perturbation theory. Single excitations and pair-correlation effects have been included by solving coupled one-particle and two-particle differential equations numerically. The correlation between the valence electrons has been treated selfconsistently by solving these equations iteratively for the valence pair. Core-polarisation effects have been evaluated by hyperfine-induced single-particle functions. From the calculated and experimental results of the two configurations,Q=?49(5) mb has been evaluated for the nuclear quadrupole moment of⁴³Ca.     

类镓等电子序列ZrX—RhXV离子的4s^24p—4s^24d,4s^24p—4s4p^2,4s^24 …

本文对类镓等电子序列ＧａＩ－ＸｅＸＸＩＶ离子４ｓ＾２４ｐ、４ｓ＾２４ｐ、４ｓ＾２４ｄ、４ｓ４ｐ＾２、４ｐ＾３和４ｓ＾２５ｓ组态组级结果和组态相互作用了理论分析，找出沿等电子序列的变化规律。     

Determination of isotope shift crossed-second-order-effects and hyperfine-structure parameters in the Eu I configuration 4f 7 6s7s

In the Eu I configuration 4f ⁷(⁸ S)6s7s the isotope shift (IS) and hyperfine-structure (hfs) of the levelse ⁸ S _7/2 andf ⁸ S _7/2 were determined from the transitions 684.5 nm, 733.7 nm and 821.0 nm to 4f ⁷6s6p. Together with experimental results of our previous measurements a theoretical analysis of the IS and hfs for the complete configuration 4f ⁷ 6s7s can now be carried out. From the IS of the four 6s7s-levels we evaluated the two crossed-second-order-parametersg ₃(4f,6s)= ?l.l(l)mK andg ₃(4f, 7s)= ?0.1(l)mK. The ratiog ₃/G ₃ is determined for various Eu configurations and found to be equal to 5.6(3)·10^?6 in complete agreement with a theoretical value following from Hartree-Fock calculations. The single electron hfs splitting constantsa ¹⁰(4f)= ?1.9 (3) mK,a ¹⁰(6s)=396(3)mK, anda ¹⁰(7s)=65(3)mK are also determined and compared with those of other Eu configurations.     

Experimentally determined transition probabilities of the systems 6p2→6p6d, 6p7s, 6p8s of neutral lead

Branching ratio measurements have been performed for all of the observed transitions from eight levels in neutral lead (6p²→6p6d, 6p²→ 6p7s, 6p²→6p8s) excited in a hollow cathode discharge in the 200–730 nm spectral range. From the relative emission intensity data, a set of absolute transition probabilities is derived for 28 lines, including lines for which transition probabilities have not been previously published. The absolute scales are obtained by averaging the measured lifetimes of the ³P⁰_1,2, ¹P_1⁰(6p7s), ³F^0_2,3, ³D^0_1,2(6p6d) levels.     

Parametrization of two-body perturbation on atomic fine and hyperfine structure. The configuration (6p)3 in the bismuth atom

A method of simultaneous parametrization of one- and two-body interactions on atomic hyperfine structure of configurationl ^N is proposed and applied for the analysis of the configuration (6p)³ in the bismuth atom. For this purpose, the hyperfine structure splittings of the levels²D ₃ ^2/0 ,²D ₅ ^2/0 and²P ₁ ^2/0 were measured. The finally obtained values of HFS parameters are: for one-body parameters (in MHz):a _p ⁰¹ =2,537(9),a _p ¹² =5,182 (12),a′¹⁰=?2,019(10),b _p ⁰² =?3,198(53),b _p ¹¹ =2,816(54); for two-body parameters (in MHz):x _pp ^′/01 ,₂=284(3),x _pp ^′/12 ,₂=581(5),x _pf ^′/12 ,₂=170(70),x _pp ^′/02 ,₂=?359(36),x _pf ^′/02 ,₂=?33(100). The value of the quadrupole moment of the nucleus ₈₃ ²⁰⁹ Bi is also discussed.     

4f 135s 25p 6-4f 135s 25p 56s transitions in the W VIII spectrum and spectra of isoelectronic hafnium, tantalum, and rhenium ions

Spectra of hafnium, tantalum, tungsten, and rhenium in the range of 145?C350?, excited in a low-inductive vacuum spark, have been recorded on a grazing-incidence vacuum spectrograph using a grating with 3600 lines/mm and a radius of 3 m. The wavelengths and intensities of more than 3800 lines in the tungsten spectrum have been measured. Comparison with the Hartree-Fock calculations showed that most spectral lines should be due to transitions in the W VIII spectrum. Short-wavelength lines due to the 4f ¹³5s ²5p ⁶-4f ¹³5s ²5p ⁵6s transitions have been identified in the W VIII spectrum and the Re IX, Ta VII, and Hf VI isoelectronic spectra.     

Crystal structure magnetic properties and hyperfine interactions in RFe4Al8 (R = rare earth) systems

X-ray, magnetic susceptibility and ⁵⁷Fe, ¹⁵¹Eu, ¹⁵⁵Gd and ¹⁷⁰Yb Mössbauer studies were performed. Detailed analysis of X-ray intensities yields all ion locations and interatomic distances in the body centered tetragonal structure (space group I4/MMM). The unit cell contains two formula units. The rare earth, iron and aluminum occupy the 2(a), 8(f) and 8(i) and 8(j) crystallographic sites, respectively. The susceptibility and Mössbauer studies indicate the existence of two independent magnetic sublattices. The iron sublattice orders into an antiferromagnetic structure at about 120 K, whereas the rare earth sublattice orders (excluding those with La, Ce, Eu, Y and Lu) antiferromagnetically at about 20 K. The ⁵⁷Fe, ¹⁵¹Eu, ¹⁵⁵Gd and ¹⁷⁰Yb Mössbauer studies yield, in addition to the hyperfine interaction parameters, also the direction along which the moments are aligned. In EuFe₄Al₈ the Eu ion is in a mixed valent state.     

Ga原子4s~24p及4s~25s态的超精细结构常数

基于相对论多组态Dirac-Fock（MCDF）方法的GRASP2K程序,通过系统的考虑电子关联效应和相对论效应,详细计算了⁷¹Ga原子的基态4s²4p²P_1/2、亚稳态4s²4p²P_3/2及激发态4s⁵s²S_1/2的超精细结构常数.结果表明原子实的极化效应对超精细结构常数起到了重要作用.     

The thermal behaviour of the quadrupole hyperfine interaction in (NH4)2HfF6

A TDPAC investigation has been accomplished on (NH₄)₂ HfF₆ between 14 and 620 K. A phase transition was observed below 390 K. The low temperature phase is characterized by two non-equivalent sites for hafnium atoms in a 1∶1 ratio. The high temperature phase, on the other hand, is depicted by a unique quadrupole interaction. Above 400 K, the compound decomposes successively to NH₄ HfF₅, NH₄ Hf₂F₉ and HfF₄. An enthalpy of 76±4 kJ/mol could be determined for the (NH₄)₂ HfF₆→NH₄ HfF₅+NH₄F chemical reaction. The hyperfine interaction and thermal evolution of (NH₄)₂ HfF₆ was found to be quite similar to that of (NH₄)₂ ZrF₆.