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.     

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).     

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.     

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.     

Hyperfeinstrukturuntersuchungen mit einem sphärischen Fabry-Perot-Interferometer mit internem Absorptionsatomstrahl im Tm I- und Eu I-Spektrum

A spherical Fabry-Perot spectrometer with an absorbing atomic beam passing the interior of the interferometer is described. By use of the internal beam it is possible to reduce the amount of material needed for the atomic beam source to a few milligrams per hour. The set-up is especially suitable for hyperfine structure and isotope shift investigations. For the photoelectric recording of the signal the geometrical distance between the spherical mirrors was changed using the piezoelectric effect. In order to reduce the influence of the intensity distribution of the light sourceI ₀(λ) the ratio [I ₀(λ)-I(λ)]/I ₀(λ) was measured, whereI ₀(λ)=I ₀(λ) exp (—V·k(λ)·d) is the observed intensity with absorbing atoms between the mirrors, andV the increase of the absorption signal due to the multiple reflections of the light through the atomic beam (V≈75). For an accurate and easy evaluation of the data this ratio was measured by a digital voltmeter and punched into paper tape. The small line width of the absorption profile obtained in the experiments with Tm and Eu enabled us to measure hyperfine distances of the order of 5 · 10^?3 cm^?1 to 20 · 10^?3 cm^?1 with an error not exceeding 0.1 · 10^?3 cm^?1 in some cases. From the measurements theA-factors for five levels of the configurations 4f ¹³6s 6p and 4f ¹²5d 6s ² in Tm I and theA- andB-factors of the stable Eu isotopes of the 4f ⁷ 6s 6p y ⁸ P _5/2level in Eu I were determined.     

Energy Shift of the 4f 136s 1 Excited States of Yb2+ from Gas Phase to the CsCaBr3 Solid

ABSTRACT

Ab initio calculations on Yb²⁺-doped CsCaBr₃ show a large increase (20000 cm^?1) of the 4f ¹⁴ → 4f ¹³6s ¹ transitions from gas phase to CsCaBr₃, due to large embedding effects originated beyond the first bromide coordination shell. The 4f ¹³6s ¹ states of (YbBr₆)^4- in vacuo undergo a sudden energy and electron density change at short Br-Yb distances resulting in the formation of an Yb-trapped exciton, which evolves to full ionization, making Yb(II) unstable in hexabromide coordination in gas phase. Embedding in CsCaBr₃ localizes the 6s electron inside the Br₆ cage, which increases the 6s-Br₆ repulsion and increases the energy of the 4f ¹³6s ¹ states.     

Rumpfpolarisation des 4d 9 5s 22 D-Zustandes von Ag I

The hyperfine structure of the transition Ag I, 4d ⁹ 5s ²² D _3/2-4d ¹⁰5p ² P _1/2, λ=19,372 Å has been investigated by means of a photoelectrically recording Fabry-Pérot interferometer using separated isotopes. Evaluating the hfs-pattern by a digital analysis the following values for the magnetic dipole interaction constants have been obtained: $$A_{3/2}^{(109)} (d^9 5s^2 ) = - 12.11(6)mK; A_{1/2}^{(109)} (d^{10} 5p) = - 6.72(10)mK.$$ Using the knownA-factor of the other level of the configurationd ⁹ s ² and the values of the Ms anomalies of the levelsd ⁹ s ²² D _5/2 andd ¹⁰ s ² S _1/2 together with our result, the influence of the core polarization on theA-factors of the configurationd ⁹ s ² is discussed. Assuming that the used relativistic correction factors are correct, the influence of the core polarization cannot be due only to the unpaireds-electrons of the core, but must be described by the three-parameter hfs-Hamiltonian given by Harvey. Consequences for calculating the quadrupole moments from hfs data are mentioned.     

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.     

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.     

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.     

Hyperfine structure measurements in the4 I 9/2 ground state of141Pr

Using the atomic beam magnetic resonance method, the five hyperfine structure separations in the 4f ³ 6s ^{2 4}I_9/2 ground state of ₅₉ ¹⁴¹ Pr have been measured. The results are:F F′ E _FF′ ^* /h (MHz) 7 6 6477.913423(17) 6 5 5556.359848 (6) 5 4 4633.023306 (2) 4 3 3708.201146 (5) 3 2 2782.190601(15) From these quantities, the multipole interaction constantsA _k,k=1, 2, 3, 4 between the nucleus and the electron shell have been calculated.A ₄ especially then served to give the following limit for the intrinsic hexadecapole moment: ¦Q ₄₀¦<0.4eb ². Furthermore, theg _J -factors of the⁴ I multiplet have been measured at magnetic fields of 300 Oe. The results are:g _J(⁴ I _9/2)=0.7310371(15)g _J(⁴ I _11/2)=0.9651476(20)g _J(⁴ I _13/2)=1.1063197(40)g _J(⁴ I _15/2)=1.197963 (30) Small corrections due to perturbations by neighbouring fine structure levels are included.     

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.     

Mode-crossing signals of high order on the 4d 95s 2 2 D 5/2 state of Cd II isotopes

In the linearly polarized radiation field of a 442 nm He-Cd laser containing a natural isotope mixture, saturation-induced mode-crossing signals of the 4d ⁹5s ^{2 2} _5/2 state of Cd II are observed due to the even as well as the odd isotopes. The signal width of about 10^?4 T yields high resolution. Thus the signal splitting respective to the magnetic quantum number can be resolved. Theg _J - andg _F -factors of the² D _5/2 state are determined as follows:g _J=1.1980±0.0036,g _F(F=2)=1.397±0.008,g _F(F=3)=1.002±0.009.     

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     

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.     

Hyperfine structure and nuclear magnetic moments of some neutron-deficient thallium isotopes

Using the atomic-beam magnetic resonance method, hyperfine structure (h.f.s.) measurements have been performed in the²P_1/2 electronic ground state of the neutron-deficient thallium isotopes^193–202Tl. In the doubly odd isotopes, the magnetic dipole hyperfine interaction constantsa were determined, while in the odd-A isotopes, direct measurements of the nuclearg-factors,g _I , were made. The electronicg-factor was measured in¹⁹⁸Tl. The magnetic dipole moments of the doubly odd isotopes have been evaluated by a direct comparison with known values in the stable isotope²⁰³Tl. The moments of the odd-A isotopes are in agreement with pervious measurements by optical spectroscopy. A discussion of the magnetic dipole moments in terms of different nuclear models is included. The moments of the 2^? nuclear ground states of the doubly odd isotopes may be interpreted as arising from a combination of the configurations 2^? (πs_1/2 vf_5/2) and 2^? (πs_1/2 vp_3/2).     

Hyperfine splitting constants in the optical transition \boldsymbol{{4{f}^{7}} {6{s}^{2}} \;{^{8}{\rm S}_{7/2}} \to {4{f}^{7}} {6{s}6{p}}\; {^{6}{\rm P}_{5/2}} \ {\rm of} \ {^{151-155}{\rm Eu}}} isotopes and hyperfine anomaly

Using the method of laser-induced fluorescence in an atomic beam we have measured the hyperfine splitting constants, A and B, of the ground and excited states of the optical transition 4f ⁷6s ^{2 8}S $_{1/2}\to 4f^{7}$ 6s6p ⁶P_5/2 (564.58 nm) for ^151???155Eu isotopes. For all isotopes, the magnetic dipole constants of the ⁶P_5/2 atomic level are determined to a precision better than 0.04%. The A and B constants for the ground state ⁸S_7/2 of the radioactive ^152,154,155Eu were obtained for the first time with a precision better than 0.5%. Our data along with previous ground state hyperfine structure measurements for the stable europium isotopes allow us to determine the hyperfine anomaly for mentioned Eu isotopes.