Hyperfine structure investigation on the (3d 4)3 G 4,5 levels of47Ti

Using two-step laser spectroscopy with the sideband technique the hyperfine structure (hfs) splittings of the levels (3d ⁴)³ G _4,5 in⁴⁷Ti have been measured. These are the first hfs measurements of the levels belonging to the 3d ^N+2 configuration of the system (3d+4s) ^N+2. The experimental results indicate a strong increase of the core polarization effect due to excitation of both 4s-electrons to the open 3d-shell.     

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%.     

Study of the hyperfine structure of Titanium atom by laser induced fluorescence on an atomic beam

Within the framework of systematic hyperfine structure (hfs) investigation of titanium atom the hfs splitting of 3d ³4s ³H_4,5,6 levels for two stable isotopes ⁴⁷Ti and ⁴⁹Ti have been measured by laser induced fluorescence. Experimental hfs constants A _exp and B _exp have been determined. The hfs measurements confirm an existence of a significant spin-dependent interaction effect on hfs structure of the level 3d ³ 4s ³H₄.     

Experimental and theoretical study of the hyperfine structure in the (5d+6s)96p configurations of Pt I

The hyperfine structure of the odd configurations 5d ⁹6p and 5d ⁸6s6p was studied with laser optogalvanic spectroscopy and high resolution interferometry in a platinum hollow cathode. A parametric hyperfine structure analysis for the configurations (5d+6s)⁹6p with 10 excited odd-parity levels was performed for¹⁹⁵Pt. We obtained one-electron hfs parameters,a _5d ⁰¹ =1160(320) MHz,a _6s ¹⁰ =35600(5300) MHz anda _6p ⁰¹ =1300(780) MHz for the configuration 5d ⁸6s6p. The corresponding $\left\langle {r^{ - 3} } \right\rangle _{nl}^{k_s k_l } $ values are compared with those known for other 5d-elements.     

Hyperfine structure in the configurations 4f 13 6s6p and 4f 125d6s 2 of TmI

The laser-atomic-beam spectroscopy has been used to make precise measurements of the hyperfine structure in transitions starting from metastable states of the configuration 4f ¹²5d6s ² in¹⁶⁹TmI. With the resulting experimental magnetic dipole hyperfine constantsA _J andA _J values from former investigations a parametric analysis of the hyperfine structure in the configurations 4f ¹³6s6p and 4f ¹²5d6s ² has been performed using wavefunctions from fine structure calculations. A comparison of theoretical and experimental hyperfine constants allowed a test of the reliability of the wave-functions used. The hyperfine parameters respectively hyperfine radial integrals determined from the analysis were compared with corresponding data from ab initio calculations for the ground configuration in TmI.     

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.     

Precise determination of the ground state hyperfine structure splitting of43Ca II

Within the framework of systematic hyperfine structure (hfs) investigation of titanium atom the hfs-splittings of 3d ³(² G)4s b ¹ G ₄ levels for two stable isotopes⁴⁷Ti and⁴⁹Ti have been studied. 5 hfs intervals for each isotope have been measured using ABMR-LIRF method (atomic beam magnetic resonance detected by laser induced resonance fluorescence) with an accuracy of about 300 Hz. TheJ-off-diagonal second order perturbation effects have been taken into account in the interpretation. Upper limit of the contributions from octupole and hexadecapole hyperfine structure interaction to hfs intervals of this level have been estimated to be about 400 Hz. However, for most of hfs intervals these contributions are almost within experimental error and in order to study such effects a more precise experimental method should be used.     

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.     

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 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.     

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.     

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.     

Laser and radiofrequency spectroscopy of the 5d 4 6s 6 D multiplet in Ta I

The hyperfine structure (hfs) of¹⁸¹Ta has been investigated using laser radio-frequency double resonance and high resolution laser spectroscopy on collimated atomic beams. The magnetic dipole and electric quadrupole hyperfine structure coupling constants of the 5d ^{4 6} s 6D _{3/2, 5/2, 7/2, 9/2} metastable states have been determined using radio-frequency spectroscopy. In the 5d ⁴ 6s ⁶ D _1/2 metastable state and the excited 5d ³ 6s 6p ⁴ D _3/2,⁶ D _{5/2, 9/2} as well as the unidentified 28 182.6 cm^–1 and 30 021.2 cm^–1 states, hfs constants have been obtained from high resolution laser spectroscopy. A radio-frequency converter has been developed in order to reach the frequency region 2.7–10 GHz.     

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%.     

On the hyperfine structure in the configuration 5f 3 6d7s 2 of neutral uranium

A Laser Induced Fluorescence experiment in an atomic beam has yielded experimental values of hyperfine structure (hfs) constants A and B for 28 low odd levels and 22 even levels, with an accuracy around 10^–5 cm^–1 for A and 10^–3 cm^–1 for B. A Condon Slater Racah parametric interpretation of the hfs data concerning 22 of these levels, on the basis of the configuration 5f ³ 6d 7s ², has provided values of monoelectronic parametersa _5f ⁰¹ ,a _5f ¹² ,a _6d ⁰¹ ,b _5f ⁰² ,b _6d ⁰² ,b _6d ¹³ . A least square fit calculation has been compared to the values deduced from Dirac-Fock monoelectronic radial integrals. The fit represents 18 A (16 B) values ranging from –0.42 to –2.96 mK (from –41 to 156 mK) with discrepancies less than 0.2 mK (8 mK).     

Sternheimer free determination of the51V nuclear quadrupole moment from hyperfine structure measurements

The hyperfine structure (hfs) of 18 metastable states of⁵¹V has been measured by laser induced fluorescence. 15 of these states have been measured additionally very precisely by the ABMR-LIRF method. Using results of earlier hfs measurements, the hfs of altogether 33 fine structure states is analyzed using a method of simultaneous parametrization of one- and two-body interactions in the atomic hfs of the model space 3d ^{3 +M} 4s ^{2 ?M} (M = 0, 1, 2). The hfs of these states is described by 16 parameters for the magnetic dipole interaction and 12 parameters for the electric quadrupole interaction. From these model space parameters corresponding configuration dependent parameters for the three configurations were determined. These parameters allow a prediction of the hfs constants of all states of the modelspace within an accuracy of 5 to 10%. The evaluation of the nuclear quadrupole moment of⁵¹V, free of Sternheimer corrections up to second order, yielded the value of -0.043(5) barn.     

Isotope shift and hyperfine structure of stable platinum isotopes

Isotope shift (IS) and hyperfine structure (hfs) measurements have been performed on seven lines of the platinum I spectrum with interference as well as laser fluorescence spectroscopy. In the latter case a frequency-doubled single-mode cw dye laser was applied. The IS of¹⁹⁰Pt with a natural abundance of only 0.01% was determined to beδν ^{190, 192}=?38.65(8) mK in theλ306.47 nm transition. The IS parameters and the effective hfs integrals in the configuration (5d+6s)¹⁰ were determined in intermediate coupling by a least squares fit of the IS and hfs data with eigenvectors obtained from the platinum fine structure (fs). The results are compared with theoretical values and yield improvedδ〈r ²〉 data.