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.     

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.     

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.     

Radiative constants in the spectra of ions of the erbium isoelectronic sequence

The probabilities of the 4f ¹³6p→4f ¹³5d lectric dipole transitions and the lifetimes of levels of the 4f ¹³6p and 4f ¹³5d configurations are calculated for spectra of ions Yb III, Lu IV, Hf V, and Ta VI of the erbium isoelectronic sequence. The wave functions of the intermediate coupling scheme, necessary for calculating the relative line strengths, are obtained semiempirically from experimentally measured energy intervals between fine-structure levels. To pass to the absolute values, the radial integrals of transitions, evaluated with the Hartree-Fock functions, are used.     

Radiative lifetimes and tensor polarizabilities of 1s4f 1 F and 1s5f 1 F level of He I

He atoms have been excited by Ne⁺ ion impact and the depolarization of the fluorescence lines at 668 nm and 492 nm by magnetic and electric fields has been studied. The Ne⁺ ion energy could be chosen such that pure cascade level crossing signals were observed. From the widths of magnetic depolarization signals the radiative lifetimes τ(1s4f ¹ F)=74(2) ns and τ(1s5f ¹ F)=133(5) ns have been determined. By investigating the electric field splitting of the magnetic depolarization signals the tensor polarizabilities ¦α _ten(1s4f ¹ F)¦=0.58(1) kHz/(V/cm)² and ¦α _ten(1s5f ¹ F)¦=4.2(1) kHz/(V/cm)² have been deduced. From the latter value a mean frequencyv(1s5g?1s5f)=14.4 GHz of the transitions between the levels of the 1s5f configuration and those of the 1s5g configuration has been derived.α _ten(1s4f ¹ F) depends sensitively on the singlet-triplet mixing in the 1s4f configuration and thus a mixing coefficient could be deduced for this configuration.     

Hyperfine structure investigations in the configuration 4f 125d6s 2 of Tm I by laser-atomic-beam spectroscopy

High resolution laser-atomic-beam spectroscopy has been applied to study the hyperfine structure of transitions starting from metastable states of the configuration 4f¹²5d6s² of Tm I. Precise values for the hyperfine constants of 8 levels belonging to the configuration 4f¹²5d6s² and 9 levels belonging to excited odd levels have been determined.     

Stark effect investigations of the 4f 14 6s 6p 3 P 1 and1 P 1 levels of ytterbium

The tensor polarizabilities of the 4f ¹⁴ 6s 6p ³ P ₁ level were investigated for all stable Ytterbium isotopes by the method of optical double resonance. The tensor polarizabilities were deduced from the rf-resonance signals in parallel electric and magnetic fields. The value obtained for the even Yb isotopes is in good agreement with the results derived from the measurements on the odd isotopes. The mean value isα _ten(³ P ₁)0=5.99(34)kHz/(kV/cm)². The tensor polarizability of the 4f ¹⁴ 6s 6p ¹ P ₁ level of¹⁷¹Yb was measured by means of the level crossing technique with parallel electric and magnetic fields. The experimental result isα _ten(¹ P ₁)=?14.3(1.4)kHz/(kV/cm)². This is compared with the prediction of the LS coupling approximation using the experimental data of the³ P ₁ level. Only poor agreement is obtained which is due to the configuration mixing in the¹P₁ level.     

The hyperfine structure of they 8 p-multiplet of 4f 7(8 S) 6s 6p in EuI

The hyperfine splitting constants of the 4f ⁷ 6s 6p y ⁸ P _7/2 level of Eul were determined using the level crossing method. These values and those for the hyperfine splittings of the other 4f ⁷ 6s 6p levels are compared to theoretical values calculated with eigenfunctions of Smith and Collins. For the quadrupole coupling constants a better agreement between theory and experiment is obtained if different 〈r ^?3〉 _p -parameters are assumed for 4f(⁸ S) 6s 6p(³ P) and for 4f ⁷(⁸ S) 6s 6p(¹ P).     

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.     

Radiative Lifetimes of the Energy Levels of Palladium-like Ions Pr XIV and Nd XV

Radiative lifetimes for the 4d⁹4f, 4d⁹5p, 4d⁹5d, and 4d⁹6s levels in the spectra of palladium-like ions Pr XIV and Nd XV are calculated in the electric-dipole approximation by the intermediate coupling semiempirical method with the use of experimental energy levels available in the literature. The radial integrals of transitions necessary for calculating absolute values of transition probabilities are obtained in the length form with Hartree–Fock functions.     

Radiative lifetimes of the levels in the Ba III spectrum

The radiative lifetimes of the 5p ⁵ (6s+5d), 5p ⁵ (6p+4f), and 5p ⁵5f levels in the spectrum of the Ba III ion are calculated. The wave functions of the intermediate coupling are found from the experimental energy levels by the method of least squares. The radial transition integrals are calculated by the Hartree-Fock method.     

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.     

The Stark effect in the 6snf Rydberg series of barium

The Stark effect has been studied in the odd-parity 6snf^1,3F₃ Rydberg series of barium with high-resolution laser-atomic-beam spectroscopy. Scalar and tensor polarizabilities have been measured of 6snf¹F₃ levels with n=11–30 and of 6snf³F₃ levels withn = 12 ? 40. The contributions of the adjacent even-parity Rydberg levels to these polarizabilities have been calculated as far as data are available. This results in important additional information on the only partly known 6sng^1,3G₄ series and confirms the perturbation of these series atn = 24 by a 5d7dJ= 4 level. A tentative three-channel quantum-defect-theory analysis of the^1,3G₄ series has been performed. It is shown that reported level energies of the 6snd^1,3D₂ series are systematically 0.14 cm^?1 too high.     

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.     

Second and fourth order stark shifts in the 6snd 1 D 2 barium rydberg series

Stark splittings of⁶ snd ¹ D ₂ Rydberg states were measured betweenn=10 and 24 by quantum beat spectroscopy at very low electric field strengths, allowing the determination of tensor polarizabilities and atn=14, 19, and 24 the determination of tensor hyperpolarizabilities. The irregular behaviour of the tensor polarizabilities was explained by Coulomb approximation calculations. The fourth order contributions to the Stark Hamiltonian were written as effective operators. Representation in spherical tensor form gives tensors of rank zero, two, and four. The associated scalar and tensor hyperpolarizabilities were derived. Using these formulae, theoretical values for the hyperpolarizabilities were calculated.     

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     

Determination of tensor polarizabilities in Yb and Sm by quantum beat spectroscopy

Tensor polarizabilities of the levels 4f¹⁴6s6p³P₁ in Yb and (4f⁶6s6p+4f⁵5d6s²)⁷D₁,⁷F₁,⁷G₁ in Sm were deduced for the even isotopes from the modulation frequency of quantum beat signals.     

Lebensdauer und Hyperfeinstrukturaufspaltung der Terme 4d5s5p y2D3/2,5/2 und 4d5s5p y2F5/2,7/2 im Yttrium I Spektrum

With level crossing technique the states 4d5s5p y²D_3/2,5/2 and 4d5s5p y²F_5/2,7/2 in the Yttrium I spectrum were investigated and the magnetic hyperfine structure splitting A factors and the lifetimes determined. The experimental values are discussed and compared with theoretical results.     

Absolute oscillator strengths of 5f-5f transitions of U4+ in ThBr4 and in hydrobromic acid solutions

Absolute oscillator strengths of 5f² transitions of U⁴⁺ in ThBr₄ and in hydrobromic acid solutions are found to be about 10^-4 which is two orders of magnitude larger than those for 4f-4f transitions (lanthanide series) and one order of magnitude larger than 5f³ ones (U³⁺). Applicability of Judd's theory to 5f² transitions is discussed with particular attention to the roles played by reduced matrix elements of odd rank tensor U^λ and by the proximity of the 6d configuration.