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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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).     

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     

Doppelresonanzuntersuchungen zum Stark-Effekt des 4s 4p 3 P 1-Terms im Ca I-Spektrum

The influence of an electric field on the Zeeman-splitting of the 4s 4p ³P₁-level was investigated using the double resonance method. From the r.f.-resonance signals the tensor polarizability of the 4s 4p ³ P ₁-level was deduced to be α_ten(³ P ₁)=3.2(8) kHz/(kV/cm)². This value is used for an estimate of the oscillator strength of the infrared transition between the multiplets 4s 4p ³ P and 4s3d ³ D. Taking into account measured oscillator strengths of electric dipole transitions from the³ P ₁-level to other low lying levels one obtainsf(4s 4p ³ P→4s 3d ³ D)=0.09.     

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.     

Untersuchungen zum Stark-Effekt metastabiler Terme im Ba I-Spektrum durch Nachweis von Hochfrequenzübergängen

By detection of r.f.-transitions between Zeeman-sublevels the Zeeman-splitting of the metastable 6s 5d-levels and of the 6s 6p³ P ₁-level of the even Ba-isotopes was investigated under the influence of an electric field in addition to a magnetic field. From the measurements the following tensor polarizabilities were deduced: α_ten(³D₃)=?29(5) kHz/(kV/cm)², α_ten(³ D ₂)=?13(3) kHz/(kV/cm)², α_ten(³D₁)=?10(2) kHz/(kV/cm)², α_ten(¹ D ₂)=?16(3) kHz/(kV/cm)². No effect due to electric fields up to 50 kV/cm was observed in the Zeeman-splitting of the 6s 6p ³ P ₁-level. Therefore the tensor polarizability of the 6s 6p³P₁-level must be much smaller than those of the 6s 5d-levels. The results will be discussed by considering the oscillator strengths both of the infrared transitions between the two multiplets 6s 5d ³ D and 6s 6p ³ P and of transitions to other low lying levels.     

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.     

Model-potential oscillator strengths for 4fn6s2–4fn6s6p transitions in Sm(I), Eu(I), Dy(I), Er(I) and Yb(I)

The 4fⁿ6s²?4fⁿ6s6p transitions are studied for neutral samarium, europium, dysprosium, erbium, and ytterbium. Four different couplings between the valence electrons and the 4fⁿ shell are considered, three are based on the LS and one on the J_IJ_II scheme. The radial integrals are computed with the model-potential method, which includes both exchange and core polarization. The results are compared with those obtained by employing the Coulomb approximation and the ab initio Hartree + Exchange (HX) approach, as well as with available experimental data. The core-polarization influence on oscillator strengths for these transitions is also investigated.     

Calculation of the Hyperfinestructure and gJ-Values of the 3d 4s 4p-Configuration of Scandium

Wave functions for the 3d 4s 4p, 3d² 4p and 4s² 4p configurations of ScI are calculated, taking into account departures from SL-coupling and configuration interaction and on fitting the radial integrals to the experimental fine structure energies. Using these wave functions g J -values are derived. The intermediate coupled hfs matrix elements of the 3d 4s 4p configuration are reduced to the unknown electron coupling constants a_s, a_p and a_d and calculated on estimating these constants from the spin-orbit coupling constants and fitting them to some experimental A-values. By this way the absolute phases of the experimental A((¹P)²D)- and A((¹P)²F)-values are obtained. Good agreement between calculated and most experimental data has been achieved.     

Hyperfine-structure and isotope-shift measurements in the 6s 5d↔6p 5d transitions of Ba I in the far-red spectral region

Measurements of the hyperfine structures in the 6p5d ¹ D ₂,³ D ₁ and³ F _{2, 3, 4} states of¹³⁵Ba and¹³⁷Ba, and isotope-shifts in several far-red transitions between the 6s 5d and 6p 5d configurations, as well as the transition 6s ^{2 1} S ₀→6s6p ³ P ₁ at 7,911 Å have been performed using high-resolution laser spectroscopy on a collimated atomic beam of natural barium. An analysis of the magnetic-dipole interaction in the 6p 5d configuration using effective one- and two-body hyperfine operators is presented. In particular the contact interaction was studied with respect to the correlation between the two valence electrons. Effects of strong configuration interaction were found. From a King-plot analysis of the isotope shift term- andJ-dependence of the field shift have been evaluated for the transitions between the 6s 5d and 6p 5d configurations. Relativistic Hartree-Fock (RHF) calculations have been performed of electron densities at the nucleus for six different configurations in Ba I and Ba II. The RHF calculations reproduce the experimental King-plot slopes quite well, while the absolute values, of the changes in electron density at the nucleus for the studied transitions, are found to be 9% lower than the results derived from a muonic experiment.     

Spectroscopic investigations and configuration-interaction-assisted crystal field analysis of Pr in YPO4 single crystal

An optical study of a Y_0.99Pr_0.01PO₄ single crystal is presented. Measurements of optical absorption, excitation, and emission by selective excitation into ¹D₂, ³P₀ and ³P₁, at different temperatures between 20 and 295 K, are described. A detailed account of the line assignments is given for absorption in the 4300-23 000 cm⁻¹ spectral range, and for emission in the 6400-23 000 cm⁻¹ range. The lifetimes of the emitting levels are determined. Vibronic sidebands accompanying absorption, emission and excitation spectra are reported. The decay processes of the ³P₁, ³P₀ and ¹D₂ levels are discussed. The aim of this study is a test of the configuration-interaction-assisted crystal field analysis as well as the accurate experimental determination of the energy level scheme. It was reported previously that the introduction of configuration interaction between the ground 4f² configuration with the excited 4f6p configuration always resulted in a decrease (≈50-60%) in the standard deviations between the observed and calculated energy levels. In the present work the 4f5d configuration is included as well. The crystal field is analysed in the theoretical D_2d site symmetry with and without configuration interaction. The results with 4f², 4f²+4f5d, 4f²+4f6p and 4f²+4f5d+4f6p are given. The calculation on the basis of the 315 (4f²+4f5d+4f6p) levels gives the best overall standard deviation lowering it by 75% with regard to the calculation on the 91 4f² levels only.     

Doppelresonanzuntersuchung des Einflusses eines elektrischen Feldes auf die Zeeman-Aufspaltung des 5s 5p 3P1-Terms im SrI-Spektrum

Under the simultaneous action of external electric and magnetic fields the 5s 5p ³ P ₁-level of the even Sr-isotopes splits into three non-equidistant Zeeman-sublevels. In an atomic beam experiment the spacings between the sublevels were investigated by the double resonance method at a magnetic field strength of ca. 22 Oe and at electric field strengths up to ca. 17 kV/cm. From the r.f.-resonance signals the tensor polarizability of the 5s 5p ³ P ₁-level was deduced to be α_ten(³ P ₁)=6.1(8) kHz/(kV/cm)². This value may be used to get an estimate of the oscillator strength of the infrared transitions between the multiplets 5s 5p ³P and 5s 4d ³ D. Taking into account oscillator strengths of electric dipole transitions to other low lying levels one obtainsf(³ P→³ D)≈0.09.     

Isotope shift and hyperfine structure of the transition5d6s 2 2 D 3/2-5d6s6p 4 F 3/2 of Lu175 and Lu176

Using a tunable single mode dye laser the isotope shift of the 573.7 nm-line between the isotopes Lu¹⁷⁵ and Lu¹⁷⁶ has been determined to be IS(176?175, 573.7 nm)=?394(5) MHz yielding a change of mean square nuclear radii ofδ〈r ²〉=0.022(5) fm². In addition from our measurements the following values of the hyperfine splitting constantsA andB could be deduced Lu¹⁷⁶ 5d6s6p ⁴ F _3/2:A=?651.4(0.3) MHz,B=2,494(4) MHz 5d6s ^{2 2} D _3/2:A=138.0(0.3) MHz,B=2,131(3) MHz Lu¹⁷⁵ 5d6s6p ⁴ F _3/2:A=?924.7(0.5) MHz,B=1,767(4) MHz.