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.     

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).     

Measurement of hyperfine structures and isotope shifts in 4f5d6s and 4f6s6p of Sm I

We report the first observation of hyperfine structures (HFSs) and isotope shifts (ISs) of Sm I in the range of 540–560 nm using an atomic beam resonance–fluorescence technique. The least square fitting was used to determine hyperfine constants in 4f⁵5d6s² and 4f⁶6s6p of atomic samarium (Sm I). The isotope shifts of 18 transition lines were also determined and analyzed by the King plot.     

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.     

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.     

Stark effect of hyperfine levels of the configuration 4f 7 (8 S) 6s6p in the europium I spectrum

The quadratic Stark effect in the hyperfine structure of all levels of the configuration 4f ⁷(⁸ S)6s6p in europium I, which can be excited by electric dipole radiation from the ground state, has been investigated by laser-atomic-beam spectroscopy. From the measured shifts and splittings of the hyperfine components the scalar and tensor polarizabilities have been deduced. From the polarizabilities radial integrals for electric dipole radiation were determined by a parametric analysis. With these radial integrals theoretical values of the polarizabilities were calculated.     

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%.     

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.     

Configuration interaction effect on the hyperfine structure of the levels of the 6s6p 3 configuration in Bi II

The hyperfine structure splittings of the lines: 318.6980 nm, 328.2567 nm, 330.6264 nm, 332.7443 nm, 339.1810 nm, 340.9208 nm, 549.0347 nm, 589.8241 nm, 610.3918 nm were measured and the hyperfine structures of the levels belonging to the configuration 6s6p ³ in Bi II were determined. The influence on the hyperfine structure of the electrostatic configuration interaction between 6s6p ³ and 6s ²6pn'd configurations was discussed.     

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.     

Magnetic hyperfine structure in the 4p 3 and 4p 25s configurations of arsenic

The magnetic hyperfine structure factorA of the quasi-totality of the levels of the low 4p ³ and 4p ²5s configurations of As I has been measured by Fabry-Perot interferometry in the far UV range. A good agreement is observed between experimental results and theoretical evaluations, which allows us to confirm that the 4p ²5^s configuration only mixes very weakly (less than 1%) with 4s4p ⁴.     

Fine structure and hyperfine structure in the excited configuration 5p 26s of the antimony I spectrum

By optical interference and VUV spectroscopy the doublet system of SbI 5p ²6s was investigated, so that now the hyperfinestructure of all 8 levels of 5p ²6s (A- andB-splitting constants) are known. From the analysis we receive a spin-orbit parameter ζ_5p =3,538(57) cm^?1 and from the hyperfine-analysis single electron splitting constantsa _5p ⁰¹ =52.4(4.6),a _5p ¹⁰ =?1.6(7.3),a _5p ¹² =72.3(2.3),a _6s ¹⁰ =91.7(4.1),b _5p ⁰² =?49.6(1.1) andb _5p ¹¹ =30.4(3.2) (all values in mK). For all calculations in the fs- and hfs-analysis the 5p ²6s ² D _3/2 has to be excluded (see discussion). With the figures given above the quadrupole moment¹²¹ Q(5p ²6s)=?0.44(3) barn was obtained. It is in good agreement with the¹²¹ Q(5p ³). For the core-polarization by the 5p electron in the innerfieldns-shells (n=1, 2, 3, 4, 5) and the unpaired 6s electron a field of +500(300) kG was obtained.     

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 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.     

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.     

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.     

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.     

Theoretical and experimental analysis of the fine structure and hyperfine structure in the configurations 5p6s and 5p6p of the antimony II spectrum

From 17 transitions in the singly ionized Sb II spectrum the hyperfine structure (A andB splitting constants) of the complete excited configurations 5p6s and 5p6p were determined by means of optical interference spectroscopy. In addition, a theoretical analysis both of the fine structure and also of the hyperfine structure was carried out (in the case of 5p6p of the general typenpn′p for the first time in literature). For the 3 levels 5p6p ³ P ₁, 5p7p ³ D ₂ and 5p6p ¹ P ₁ a different classification was found and consistent values for the fine structure parameters, mixing coefficients and single electron hyperfine structure splitting parametersa _nl ^ik andb _nl ^ik were obtained. The three new determinations in Sb II of the quadrupole moment (in barn) of¹²¹Sb (Q(5p6s)=?0.55(5);Q(5p6p)=?0.57(5) from the 5p-electron andQ(5p6p)=?0.7(2) from the 6p-electron) are well agreeing with each other but differ to former values from SbI. The core polarization and isotope shift of the lines, however, are compatible with our former results in SbI.