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.     

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.     

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.     

Stark effect study of the 4f66s2 7 F 1, 2, 3, 4, 5, 6 levels of samarium using nonlinear level crossing technique

The nonlinear level crossing technique with parallel electric and magnetic fields was used to investigate the Stark effect of six levels of the ground multiplet 4f⁶6s^{2 7} F in the Sm I-spectrum. The tensor polarizabilities were deduced from the level crossing signals. The variation of the tensor polarizabilities of the levels of the ground multiplet is well reproduced by the LS coupling approximation, which gives an average value of α₂(F)=?0.88(6) kHz/(kV/cm)² for the six measured levels. The experimental results confirm the validity of the central field approximation in the ground configuration of Sm.     

Hyperfine structure and Zeeman effect studies in the 6p7p-6p7s transitions in Bi II

The hfs and hfs Zeeman splitting of nine lines from the array 6p7p→6p7s as well as lines λ = 496.9 nm (6p8p ³D₂→6p7s ³P₂) and λ=581.8 nm (6p8s ³P₀→6p7p ³D₁) of Bi II have been analysed. The Zeeman effect studies were performed for transverse direction of observation and separated π; and σ components of lines. The electrodeless discharge tube containing metallic Bi was used as the light source. The spectral apparatus consisted of a sliver-coated Fabry-Perot etalon and a grating spectrograph combined with a diode array detector. In the analysis of the spectra we used the computer simulation technique. The magnetic-dipole (A) and the electric-quadruple (B) hfs constants as well as Lande-g_j factors for the level 6p8p ³D₂ and all levels of configurations 6p7s and 6p7p (with the exception of 6p7p ³S₁) were determined. Our results are compared with recent theory and other experiments.     

Hyperfinestructure constants of the Eu-I level 4f 7 6s 6p z 6 P 7/2

The hyperfinestructure constantsA andB of the levelz ⁶ P _7/2 of the Eu I configuration 4f ⁷ 6s6p and the IS (isotopic shift) of the line combining this level with the ground state were determined to be:¹⁵¹Eu:A=?6.109(30) MHzB=134.05(66) MHz¹⁵³Eu:A=?2.993(18) MHzB=321.04(46) MHz IS (¹⁵¹Eu?¹⁵³Eu)=?3616(1) MHz (λ=5765.20 Å) These values agree very well with those of other authors [1–6].     

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.     

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 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.     

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.     

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.     

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.     

Surface anchoring and the saturation behaviour of a NLC cell under external electric and magnetic fields

Based on the modified Rapini-Papoular formula for surface anchoring energy, the saturation behaviour of a weak anchoring nematic liquid crystal cell under electric and magnetic fields has been studied by the methods of analytical derivation and numerical calculation. The results show that the transition at saturation point may be second order, as many authors have predicted. However, it may also be first order. The condition for the first order transition is deduced; it is related to the anchoring parameters. The influence of anchoring on the saturation field strength is also discussed, both for second and for first orders; the results are shown by graphically.     

Tensor polarizabilities of the 4f 7(8 S)5d6s 2 9 D 2,3,4,5,6 levels in Gd I

The optical pumping method with rf detection and the nonlinear level crossing technique were used in parallel electric and magnetic fields to investigate the Stark splitting of all the fine structure levels of the ground multiplet 4f ⁷ (⁸ S) 5d6s ^{2 9} D in Gd I. The tensor polarizabilities were deduced from the level crossing and the rf signals. The variation of the tensor polarizabilities is well reproduced by the LS coupling approximation, except for the small value of the⁹ D ₅ level. A value of the tensor polarizability of the 5d electron is evaluated from the experimental results, ₂(5d)=2.00(6) kHz(kV/cm)². It is shown that the ratio between the electric quadrupole constant and the tensor polarizability is constant, except for the⁹ D ₅ ratio, which is caused by a breakdown of the central field model.     

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.     

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.     

Measured Stark widths and shifts of the neutral argon spectral lines in 4s–4p and 4s–4p′ transitions

We investigate the Stark widths (W) and the shift (d), of the seven neutral argon (Ar I) spectral lines from the 4s–4p and 4s–4p′ transitions. The line shapes are measured in a linear, low-pressure, optically thin pulsed arc discharge at about 16 000 K electron temperature (T) and about 7.0 × 10²² m^− 3 electron density (N). The new data separates the electron width (W_e) and ion width W_i from the total Stark width (W_t), as well the separation of electron total Stark shift (d_t) on electron (d_e) and ion (d_i) parts. There are no theoretical predictions for these lines. Comparison to theoretical predictions for other lines within the same multiplets finds that the experimental data exhibits stronger influence by the ion contribution to the measured Ar I line shape. We have also deduced the ion broadening parameters which describe the influence of the ion static (A) and the ion–dynamical (D and E) effect on the width and the shift of the line shape.Applying the line deconvolution procedure, the basic plasma parameters i.e. electron temperature (T) and electron density (N) are recovered. The plasma parameters (T and N) are measured using independent diagnostics techniques as well. Good agreement is found among two sets of the N and T plasma parameters obtained from deconvolution procedure and independent diagnostics techniques.     

J-dependence of the isotope shift in Gd I 4f 7 5d 2 6s(a 11 F)

TheJ-dependence of the isotope shift in the terma ¹¹ F of 4f ⁷ 5d ² 6s between six stable Gd isotopes was found to be represented by these parameter values (in MHz):z _5d (160?158)=19.4(1.8),z _5d (160?157)=37.2(1.0),z _5d (160?156)=42.4(1.7),z _5d (160?155)=49.1(2.0),z _5d (160?154)=59.0(2.0). The normalization with the corresponding changes in the mean-square nuclear charge-radiiδ〈r ²〉 yields values which are almost constant, mean value:z _5d /δ〈r ²〉=134(14) MHZ/fm². This indicates a second order IS interaction of the magnetic and the field shift operator.