Hyperfine structure in the configuration 4f 115d6s 2 of Er I

Hyperfine constants of low lying levels of the configuration 4f ¹¹5d6s ² in Er I have been measured for the only stable odd isotope,¹⁶⁷Er, using high resolution laseratomic-beam spectroscopy. Hyperfine parameters were evaluated from the experimental data using the effective tensor operator formalism. For this purpose eigenfunctions have been determined from an analysis of the fine structure energies of Er I as well as from ab initio multiconfiguration Dirac-Fock calculations. With the latter method also ab initio hyperfine constants for the levels investigated were evaluated. A comparison of calculated fine structure energies, Landég _J -factors and hyperfine constants with the experimental data allowed a test of the reliability of the fine structure and multiconfiguration Dirac-Fock wavefunctions. Effective nuclear electric quadrupole moments for¹⁶⁷Er have been determined from the experimental hyperfine constants using both calculated relativistic electronic radial integrals and hyperfine parameters for the 4f and 5d electrons in the configuration 4f ¹¹5d6s ² in Er I. From a comparison with the nuclear quadrupole moment measured in the mesic atom Sternheimer shielding factors are calculated. Configuration-interaction contributions to the radial integrals 〈r ^?3〉 _nl ⁰¹ of the 4f and 5d electrons have been determined.     

Hyperfine structure in the configurations4f 4 6s 2 and4f 4 5d 6s of Nd I

The high resolution laser-atomic-beam technique was used to investigate the hyperfine structure in Nd I 4f ⁴6s ^{2 5} I,⁵ F,⁵ S and 4f ⁴5d6s ⁷ L,⁷ K,⁷ I,⁷ H. The metastable states were populated by an arc discharge burning in the atomic beam. The measured hyperfine constantsA andB of the levels of 4f ⁴6s ² and 4f ⁴5d6s allow a parametric analysis to be performed using the effective tensor operator formalism. The experimental radial integrals of the 4f and 5d electrons fit with those of the other lanthanides. The 4f radial integrals are in agreement with values of optimized Hartree-Fock-Slater calculations. The spectroscopic quadrupole moments of¹⁴³Nd and¹⁴⁵Nd are deduced from the 4f parameters:Q _I =?0.610(21) b and ?0.314(12) b, respectively. TheQ _I resulting from the 5d parameter are in satisfactory agreement with these values. The hyperfine anomaly due to thes electron in 4f ⁴5d 6s amounts to about 1%.     

Hyperfinestructure and isotope shift in the configuration 4f 7 6s8s of Eu I

The investigation of the isotope shift (IS) and hyperfine structure (hfs) is extended from Eu 4f ⁷ 6s7s to the complete configuration 4f ⁷ 6s8s, by means of the transitions 432.3, 456.5, 463.0 and 493.8 nm to 4f ⁷ 6s6p. A thorough experimental and theoretical analysis — including two further lines 492.8 and 498.7 nm from 4f ⁷ 5d ² — is carried out which e.g. confirms former fine structure calculations of one of us (J.F.W.) concerning some reclassifications. The discussion of the IS of the four levels (4f ⁷)6s8s with the sharing rule manifests again the need for inclusion of crossed-second-order effects. For the parameters we evaluated:g ₃(4f, 6s)=?1, 2(2) mK andd=79, 3(1.0) mK. The ratiog ₃/G ₃=?5, 9(1.0)·10^?6 is again in full agreement with those found by us in other Eu configurations. The single electron hfs splitting constantsa _4f ¹⁰ =?2, 3(4) mK,a _6s ¹⁰ =389(4) mK anda _8s ¹⁰ =49 (4) mK were also evaluated and compared to those found in 4f ⁷ 6s7s.     

On the hyperfine structure in the configurations 4f n 6s 2, 4f n 5d6s, 4f n 6s6p,and 4f n−15d6s 2 of the lanthanides

A survey of hyperfine analyses in the low-lying configurations 4f ⁿ 6s ², 4f ⁿ 5d6s, 4f ⁿ 6s6p, and 4f ^n?1 5d6s ² of the lanthanides is given. Experimental hf radial integrals 〈r ^?3〉 _nl ^kj are indicated for the configurations under investigation. From a comparison of experimental and theoretical hf radial integrals configuration-interaction contributions Δ _nl ^kj to the hfs have been evaluated for the configurations for which corresponding integrals were available. With nuclear electric quadrupole moments from muonic x-ray investigations and radial integrals 〈r ^?3〉 _nl ⁰¹ and 〈r ^?3〉 _nl ⁰² from experimental hfs quadrupole shielding correctionsR _nl ⁰¹ have been obtained. The variation of hyperfine radial integrals, configuration-interaction contributions and quadrupole shielding corrections over the 4f shell in the configurations under study is discussed. Trends of these quantities in different configurations are compared.     

The hyperfine structure in the configuration 4f 135d6s6p in ytterbium

Using Doppler-reduced laser induced fluorescence spectroscopy in an atomic beam, the hyperfine structure of 22 levels of the configuration 4f ¹³5d6s6p in neutral ytterbium has been investigated for the two odd isotopes ¹⁷¹ Yb and ¹⁷¹ Yb. The experimental results have been used in a study of the hyperfine structure in regard to a determination of the one-electron parameters for the magnetic dipole and the electric quadrupole hyperfine coupling of the isotope ¹⁷³ Yb in part II of this work.     

Hyperfine structure in the configuration 4f 136s7s of Tm I

Doppler-free saturation absorption spectroscopy was applied on an atomic thulium vapour in a see-through hollow cathode for the determination of precise values for the magnetic dipole hyperfine structure constantsA of 6 levels of the configuration 4f ¹³ 6s7s. A parametric analysis of the hyperfine structure has been performed, using wave-functions from a fine structure calculation, which leads to one-electron hyperfine structure parametersa _4f ⁰¹ =?500(6) MHz,a _6s ¹⁰ =?5058(47) MHz, anda _7s ¹⁰ =?1012 MHz.     

Calculation of electron densities for EuI 4f 7(8 S)6s7s

Using the non-relativistic Hartree-Fock computer code of Froese Fischer, calculations have been performed for all terms of the configuration 4f ⁷(⁸ S)6s7s of EuI. The results are compared with recent isotope shift and hyperfine structure measurements. The calculated electron charge densities reproduce, up to a scaling factor, the experimental field shifts.     

Hyperfine structure constants and isotope shift of the levels of the configuration 4f 6 5d 6s 2 in Eu I

The hyperfine structure (hfs) and the isotope shift (IS) of transitions between metastable levels of the configuration 4f ⁷ 5d 6s and levels of the configuration 4f ⁶ 5d 6s ² of¹⁵¹Eu and¹⁵³Eu were studied by means of the high resolution laser-atomic-beam technique. New data for the hfs in¹⁵¹Eu and¹⁵³Eu were obtained as well as new and more accurate for the IS between¹⁵¹Eu and¹⁵³Eu. The measured hfs constantsA andB of the 4f ⁶ 5d 6s ² configuration allow to perform a parametric analysis using the Sandars and Beck theory. The value of the Sternheimer correction is also disscused.     

Crossed-second-order-effects of the isotope shift and hyperfine-structure parameters in the Eu I configuration 4f 7 6s6d

In the Eu I configuration 4f ⁷ 6s6d the isotope shift (IS) and hyperfine-structure (hfs) of the termse ⁶ D ande ¹⁰ D were determined from fourteen transitions (4f ⁷ 6s6d-4f ⁷ 6s6p) with computer supported interference spectroscopy. From the IS of altogether nine levels of 4f ⁷ 6s6d the crossed-second-order-parameterg ₃(4f,6s)=?0.90(6)mK was evaluated. The ratiog ₃/G ₃=?4.4(3)·10^?6 (G ₃: Slater Integral of the fine structure) is of the same size as that from five other independent investigations and one theoretical value. The single electron hfs splitting constantsa _4f ¹⁰ =?1.9(3)mK,a _6s ¹⁰ =391(3)mK, anda _6d ¹² =0.9(3)mK were also evaluated and are compared with those of other Eu 4f ⁷ 6snl configurations.     

Hyperfine structure and core polarization in Nd I 4f 4f 4 5d6s

The high resolution laser-atomic-beam technique was used to investigate the hyperfine structure in Nd I 4f ⁴ 5d6s ⁷ L, ⁷ K, ⁷ I, ⁷ H, ⁷ G, ⁵ L, ⁵ K, and ⁵ I for both of the stable odd isotopes. The metastable states were populated by an arc discharge burning in the atomic beam, and 31 transitions to higher odd levels have been studied. Knowledge of the hyperfine constants of 34 levels of 4f ⁴ 5d6s allowed a comprehensive parametric analysis to be performed, using the effective tensor operator formalism. Compared to earlier analyses, a significant reduction of errors has been achieved for all the parameters. The contact parameter a _4f ¹⁰ has been fitted freely, thus providing an experimental value for the core-polarization effects. They are about six times larger than the relativistic effects.     

Hyperfine structure in 5s 4d 3 D —5snf transitions of87Sr

The hyperfine spectra of the 5s4d ³ D ₁-5s20f, 5s4d ³ D ₂-5s23f, and 5s 4d ³ D ₃-5s32f transitions of⁸⁷Sr (I=9/2) have been measured by collinear fast beam laser spectroscopy. The structure in the upper configurations is highly perturbed by fine structure splitting that is of comparable size to the hyperfine interaction energy. These perturbations can be adequately treated with conventional matrix diagonalization methods, using the 5s-electron magnetic dipole interaction terma _5s and the unperturbed fine structure splittings as input parameters. Additionally, hyperfine constants for the lower 5s4d ³ D configurations, including theA- andB-factors and a separation of the individuals- andd-electron contributions to these factors, are derived.     

Hyperfine structure measurements of the metastable (3d 6 4s 2)3 H 4, 5, 6 states of57Fe: Configuration interaction in the hyperfine structure of the iron atom

We report the hyperfine structure (hfs) measurement of the metastable (3d ⁶ 4s ²)a ³ H _{4, 5, 6} states of⁵⁷Fe. The kHz-precision of these experimental results together with the hyperfine structure values of (3d ⁶ 4s ²)a ⁵ D _{1, 2, 3, 4}, (3d ⁷ 4s)a ⁵ F _{2, 3, 4, 5}, and (3d ⁷ 4s)a ³ F _{2, 3, 4}, which were measured earlier, allowed to determine a very detailed set of effective radial parameters describing the hfs of these states, using a new parametrization method. This method treats one- and two-body contributions to the hfs separately. In this way configuration interaction effects in the hfs of the⁵⁷Fe atom can be studied in detail and compared with configuration interaction effects in the fine structure of the same atom.     

Hyperfinestructure-investigations in the mangan I configurations 3d 5 4s 4p and 4s 5s

Nine transitions (ranging from 475 till 733 nm) between the excited configuration 3d ⁵ 4s 5s and 3d ⁵ 4s 4p of⁵⁵Mn were investigated with computer supported interference spectroscopy. Thus the hyperfine structure (hfs) of the four 4s 5s and the twelve 4s 4p levels is now completely known from experiment. The hfs results are discussed with the effective operator technique and for 4s 4p the accuracy of the one-electron parametersa ^ik could be improved:a _3d ¹⁰ =?6.28(24),a _4s ¹⁰ =154.0(1.4),a _4p ⁰¹ =9.3(8),a _4p ¹² =7.7(2.5) in mK. For the configuration 4s 5s — for which fine structure calculations are not yet available — the experimental hfs data prove a practically pureS-character. Besides the one-electron splitting parameters deduced:a _3d ¹⁰ =?6.5(5),a _4s ¹⁰ =182(3),a _5s ¹⁰ =24(3) in mK, permit to determine the degree of mixing between the twoe ⁶ S _5/2 andf ⁶ S _5/2 levels which amounts to about 3%.     

Stark and Zeeman spectroscopies of 4f 66s6p 7G1-6 levels in Sm I under external electric and magnetic fields

Systematic study of hyperfine structures, Zeeman and Stark effects in Sm I is performed for the lowest ⁷G_1-6 levels belonging to the configuration 4f ⁶6s6p by atomic-beam laser spectroscopy with fluorescence detection. The hyperfine coupling constants of ⁷G_2-6 levels are determined. From the Zeeman splittings for the 4f ⁶6s ^{2 7}F_2-6 ? 4f ⁶6s6p ⁷G_2-6 transitions, g-values are determined for the ⁷G_2.6 levels and the precision is improved by several orders of magnitude. From the Stark splittings for the ⁷F_0-3 ? ⁷G_1-3 transitions, tensor polarizabilities α ₂(J) are determined for the upper ⁷G_1-3 levels. Particularly for the ⁷G₁ level (15 650.55 cm^?1) which has close-lying opposite-parity level, the isotope dependence of α ₂(J) is clearly observed for the first time.     

On the tensor polarizabilities in the 4f N 6s 2 ground levels of the neutral rare-earth atoms

A systematic study of the Stark splitting of the 4f ^N 6s ² ground levels in the lanthanides was performed by the nonlinear level-crossing technique and the optical pumping method with rf detection in parallel electric and magnetic fields. The tensor polarizabilities of the hyperfine structure levels in¹⁴¹Pr I,¹⁵⁹Tb I,¹⁶⁵Ho I,¹⁶⁹Tm I and of the fine structure levels in¹⁴²Nd I,¹⁶⁴Dy I, and¹⁶⁶Er I were deduced from the level-crossing and rf signals. Values of the tensor polarizability of the 4f electron were evaluated from the experimental results. On average these values decrease with the increasing number of 4f electrons from the value of¹⁴¹Pr (4f ³ 6s ²) α₂(4f)=1.16(12) kHz/(kV/cm)² to the value of¹⁶⁹Tm (4f ¹³6s ²) α₂(4f)=0.68(4) kHz/(kV/cm)². This decrease is caused by the lanthanides contraction.     

Hyperfine structure and isotope shift of some even parity levels in the YbI spectrum

Using laser induced fluorescence spectroscopy the hyperfine structure of the even parity levels 4f ¹⁴6s6d ³ D ₁, 4f ¹⁴ 6s8s ³ S ₁ and 4f ¹³ 5d6s6p (7/2, 5/2)J=1,2,3 as well as of the odd parity level 4f ¹⁴ 6s6p ³ P ₂ in neutral ytterbium has been investigated. The isotope shift of the transitions 4f ¹⁴6s6p ³ P ₀ → 4f ¹⁴ 6s6p ³ D ₁ and 4f ¹⁴ 6s6p ³ P ₂ → 4f ¹⁴ 6s8s ³ S ₁, 4f ¹³ 5d6s6p (7/2, 5/2)J=1,2,3 could be measured with high accuracy. The results for the 4f ¹⁴ 6s6p ³ D ₁ level show a considerable influence of second order effects of the hyperfine interaction. The isotope shifts of the 4f ¹⁴ 6s8s ³ S ₁ and 4f ¹³ 5d6s6p (7/2, 5/2)J=1 levels indicate a possible configuration mixing for these levels.     

Test of advanced hyperfine structure theory by precision radio-frequency and laser spectroscopy in molybdenum

The hyperfine structure splittings of 32 even parity states and of 26 odd partity states of molybdenum have been measured by atomic beam magnetic resonance and by laser induced fluorescence. The analysis of the hyperfine structure data of the even parity configurations (4d+5s)⁶ yields experimental evidence for second order hyperfine interactions. In addition, theg _J factors of 19 fine structure levels have been determined in order to test the quality of intermediate coupling wave functions for the (4d+5s)⁶ configurations.     

Fine structure of the 1s5f and 1s5g levels of He I

The fine structure of the 1s5f and 1s5g levels of He I was measured using microwave spectroscopy. The helium atoms were excited by ion impact, and the eleven allowed 1s5f ^2S+1 F _J –1s5g ^2S′+1 G _J , transitions near ν≈15 GHz were induced and detected by measuring the 1s4d–1s2p or 1s3d–1s2p spectral-line intensities of the impact radiation as a function of the microwave frequency. The measured transition frequencies are in accord with theoretical values and, except for one transition frequency, with earlier experimental data. The existing discrepancy between these earlier data and theory could be solved.     

Radiative lifetimes of levels of the configuration 4f 7 (8 S) 6s 6p in Eu I

Radiative lifetimes of the 4f ⁷ (⁸ S) 6s 6p z ¹⁰ P _{7/2, 9/2},z ⁸ P _{5/2, 7/2, 9/2} andz ⁶ P _{7/2, 5/2} levels of Eu I were measured by the time resolved recording of the exponential decay of the fluorescence. Three of them were measured for the first time, the others agree with previous determinations. From the values of the lifetimes absolute oscillator strengths are deduced, taking into account the branching ratios for the transitions to the 4f ⁷ 6s ² and 4f ⁷ 5d 6s levels. From these absolutef values the radial integralI(6s ², 6s 6p) was derived by a parametric analysis. Theoretical values of oscillator strengths which were calculated using this radial integral show good agreement with the experimental data.