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.     

Hyperfine structure constants of the CaII states 4s 2 S 1/2 and 4p 2 P 1/2, 3/2 and the nuclear quadrupole moment of43Ca

The hyperfine structure splittings of the 4s ² S _1/2 → 4p ² P _{1/2, 3/2} transitions in⁴³CaII have been measured by fast ion beam collinear laser spectroscopy. The resonant laser interaction was observed using non-optical detection based on optical ground state depopulation pumping, state selective neutralization and charge state separated particle counting. The extracted magnetic dipole hyperfine structure constants for⁴³CaA(² S _1/2)=?805(2) MHz,A(² P _1/2)=?145.5(1.0) MHz andA(² P _3/2)=?31.9(0.2) MHz are in excellent agreement with relativistic many body perturbation theory predictions available for this alkali-like ion. The combined results are used to evaluate the semi-empirical analysis method. From the electrical quadrupole hyperfine structure constantB(² P _3/2)=?6.7(1.4) MHz and the calculatedB/Q value for this one valence electron configuration, the nuclear quadrupole momentQ(⁴³Ca)=?0.043(9)b is derived. This result supports a previous evaluation based on the hyperfine structure of the two valence electron³ P configurations of CaI.     

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.     

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-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%.     

Quadrupole moments of radium isotopes from the 7p 2 P 3/2 hyperfine structure in Ra II

The hyperfine structure and isotope shift of^221–226Ra and^212,214Ra have been measured in the ionic (Ra II) transition 7s ² S _1/2–7p ² P _3/2 (λ=381.4 nm). The method of on-line collinear fast-beam laser spectroscopy has been applied using frequency-doubling of cw dye laser radiation in an external ring cavity. The magnetic hyperfine fields are compared with semi-empirical and ab initio calculations. The analysis of the quadrupole splitting by the same method yields the following, improved values of spectroscopic quadrupole moments:Q _s (²²¹Ra)=1.978(7)b,Q _s (²²³Ra)=1.254(3)b and the reanalyzed valuesQ _s (²⁰⁹Ra)=0.40(2)b,Q _s (²¹¹Ra)=0.48(2)b,Q _s (²²⁷Ra)=1.58(3)b,Q _s (²²⁹Ra)=3.09(4)b with an additional scaling uncertainty of ±5%. Furthermore, theJ-dependence of the isotope shift is analyzed in both Ra II transitions connecting the 7s ² S _1/2 ground state with the first excited doublet 7p ² P _1/2 and 7p ² P _3/2.     

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 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.     

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.     

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.     

Precision energies and hyperfine structures of the 5s5p 3 P 0,1,2 0 and 5s6s 3 S 1 levels in In II

Absolute frequencies of hyperfine components of the 230.6 nm (5s ^{2 1} S ₀?5s5p ³ P ₁ ⁰ ), 193.6 nm (5s5p ³ P ₀ ⁰ ?5s6s ³ S ₁), 197.7 nm (5s5p ³ P ₁ ⁰ ?5s6s ³ S ₁) and 207.9 nm (5s5p ³ P ₂ ⁰ ?5s6s ³ S ₁) transitions in In II emitted from a hollow-cathode source have been measured using a high-resolution, scanning échelle monochromator. The measured frequencies of these four transitions have been used to determine the energies and hyperfine interaction constants of the 5s5p ³ P ₀ ⁰ ,³ P ₁ ⁰ ,³ P ₂ ⁰ and 5s6s ³ S ₁ levels in In II. The hyperfine interaction constants for the dominant isotope¹¹⁵In are found to be: 5s5p ³ P ₁ ⁰ A=0.2322(2) cm^?1,B=?0.0159(9) cm^?1 5s5p ³ P ₂ ⁰ A=0.1699(4) cm^?1,B= 0.021 (6) cm^?1 5s6s ³ S ₁ A=0.4022(4) cm^?1,B= 0.002 (2) cm^?1. The absolute frequency of the very narrow, strongly forbidden In II 236.5 nm (5s ^{2 1} S ₀?5s5p ³ P ₀ ⁰ ) transition, which has been proposed as a candidate for a new optical frequency standard, is found to be 42275.986(7) cm^?1.     

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%.     

Crossed-second-order effects in the isotope shift for170–166Er and168–166Er in the configuration 4f 12 6s 2

High resolution interference and intermodulated optogalvanic saturation spectroscopy has been applied for isotope shift (IS) studies in the ground-configuration 4f ¹² 6s ² of ErI. For the isotope pairs^170–166Er and^168–166Er the results confirm a strongJ- and term dependence of the IS caused through crossed-second-order (CSO) effects. We performed a parametric analysis to evaluate the CSO-parametersz _4f for the interpretation of theJ-dependence andT(³ H),T(³ F),T(¹ G) to describe the term dependence. The following parameter values (in MHz) were determined, for^170–166Er:z _4f =40.1(0.6),T(³ F)=?153(5),T(³ H)=?220(6), andT(¹ G)=?79(4); for^168–166Er:z _4f =20.1(0.7),T(³ F)=?77(6),T(³ H)=?111(7), andT(¹ G) =?43(5). The normalization of these parameters with the corresponding nuclear parameters λ for both isotope pairs leads to almost identical parameter values indicating a dominant influence of the field shift effect in second-order for thez _4f parameter and in third-order for the parametersT(³ F),T(³ H), andT(¹ G).     

Fine structure and transition probabilities of the 2p 5 nl bound excited states of Ne atom

We present a semi-empirical calculational procedure for thep ⁵ nl bound excited states of rare gas atoms based on the use of an LS-dependent orbital for an excitednl electron outside a frozen Hartree-Fockp ⁵ core. The spin-orbit interaction is accounted for approximately using a localized Hartree potential. The contribution from the long-range core polarization is estimated by using a parametrized potential. A model potential is also introduced to represent partially the short-range multi-electron interactions for thep ⁵ np levels. The energy levels are calculated by diagonalizing the Hamiltonian matrix following anLS →jl transformation. The calculated fine structure of the Nep ⁵ ns,p ⁵ np,p ⁵ nd, andp ⁵ nf ¦ (jl)KJ〉 levels are in close agreement with the observed level splittings. The transition probabilities are also in agreement with earlier theoretical and experimental results.     

Spectroscopic properties of the Ar 2 * (5p) excimer states

The transitions between Ar ₂ ^* (5p) and Ar ₂ ^* (4sΣ _u) have been investigated by absorption spectrometry. The fine structure of the Ar ₂ ^* (5p ³ Π _g) was attributed to a predominantly Hund’s case a coupling. A spin orbit coupling constant of A = (9.8±0.3) cm^-1 results. Absorption by the singlet system allows one to determine the triplet/singlet splitting between the Ar ₂ ^* (4s Σ _u) states to be (540 ± 100) cm^-1. The transition probabilities of the Ar ₂ ^* (5p) and Ar ₂ ^* (6p) levels were determined by saturation spectrometry yielding values between (0.2–2.5) · 10⁶ s^-1.     

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 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.     

Collision energy dependence of He and Ne capture by C 60 +

The hyperfine structure and the isotope shifts in the optical transition of HfI with λ=5903 Å have been investigated using high resolution laser spectroscopy. The magnetic dipole and electric quadrupole hyperfine splitting constants of the lower 5d ² 6s ² a ³ F ₃ and upper 5d ² 6s 6p z ⁵ G ₃ ⁰ levels have been determined for the two stable odd hafnium isotopes¹⁷⁷Hf and¹⁷⁹Hf.     

Observation of quadrupole hyperfine structure in the v6 RQ3 (6) transition of 12CH335Cl

Quadrupole hyperfine structure has been observed in the v₆^RQ₃(6) transition of ¹²CH₃³⁵Cl using a stable CO₂ laser oscillating on the 9.4 μm P(26) line. By heterodyning this laser with another which is locked to the 4.3 μm fluorescence dip of the 00⁰1-00⁰ CO₂ transition, an accurate measurement of the hyperfine splittings has been made. The observed spectrum agrees, within experimental error, to the theoretical values evaluated without the need for a vibrational correction to the quadrupole interaction in the excited vibrational state. The hyperfine component closest to the center of the CO₂ P(26) transition is determined to be 5.6 ± 0.1 MHz from the P(26) line center.