Isotope shifts in odd and even energy levels of the neutral and singly ionised gadolinium atom

Isotope shift studies in the gadolinium spectra have been extended in the region 4140–4535 Å. Isotope shift Δσ(156–160) have been measured in 315 lines of the neutral and singly ionised galolinium atom using a recording Fabry—Perot Spectrometer and gadolinium samples enriched in ¹⁵⁶Gd and ¹⁶⁰Gd isotopes. Some of the Gd I lines studied involve transitions from newly identified high odd levels of 4f⁸6s 6p, 4f⁷5d 6s 7s and 4f⁷5d³ configurations to low even levels of 4f⁸6s² and 4f⁷6s²6p configurations. Electronic configurations of the energy levels have been discussed on the basis of observed isotope shifts. In some cases assigned configurations have been revised and probable configurations have been suggested.     

Electronic configurations and isotope shifts of the energy levels of the neutral dysprosium atom

Electronic configurations of the energy levels of the neutral dysprosium atom have been suggested on the basis of isotope shift studies carried out in the first spectrum of dysprosium using highly enriched isotopes excited in liquid-air-cooled hollow cathode lamps and a photoelectric recording Fabry-Perot spectrometer. Isotope shift Δ T(164-160) have been evaluated for 85 even and 82 odd energy levels. The configurations 4f⁹d6s6p, 4f⁹6p6s² and 4f¹⁰6s6d along with two new configurations 4f⁹5d²6p and 4f¹⁰6p² have been assigned to even levels whereas the configurations 4f⁹5d²6s, 4f¹⁰6s6p and 4f¹⁰5d6p have been assigned to some odd energy levels of the neutral dysprosium atom.     

Isotope shift studies in the spectra of Gadolinium in UV region and term shifts of high even levels of Gd I

Isotope shift Δσ(¹⁵⁶Gd?¹⁶⁰Gd) is reported in 70 spectral lines of neutral gadolinium atom (Gd I) in the 3290- 3920 Å region providing isotope shift data in UV lines of Gd I spectrum for the first time. The measurements were carried out on a photoelectric recording Fabry-Perot Spectrometer using highly enriched isotopic samples of gadolinium. Term isotope shifts ΔT(¹⁵⁶Gd?¹⁶⁰Gd) have been evaluated for 48 high lying even parity energy levels of Gd I using this data; new ΔT values have been obtained for 24 levels. Electronic configurations 4f⁷5d6s6p, 4ff⁷5df²6p and 4f⁸5d6s assigned earlier to these even levels have been either confirmed or configuration mixing pointed out in some of these levels. Probable assignment of 4f⁸5d6s configuration to 8 even levels between 32 930 and 35 500 cm^-1 have been confirmed.     

Spectre d'absorption de Dy I dans la région 2478–4100 Å

The absorption spectrum of the dysprosium has been observed with the use of a King-Tomkins induction furnace and a REOSC-UVGR spectrograph. The wavelengths of 1418 observed lines between 4100 and 2478 Å have been measured. With the known levels of the ground configurations 4f¹⁰6s² and 4f⁹5d6s² it was then possible to identify 81 new high levels of Dy I. The absorbed line intensities exhibited a non-thermal distribution among the population of the lowest f¹⁰s² and f⁹ds² levels.     

Reevaluation of term isotope shifts of low even levels of 4f86s2 configuration and high odd-parity levels of neutral gadolinium atoms

Isotope shift ΔT(¹⁵⁶Gd–¹⁶⁰Gd) of the even-parity energy levels of 4f⁸6s² and 4f⁷6s²6p configurations of neutral gadolinium atoms (Gd I) have been reevaluated using the level isotope shift (ΔT) of two odd-parity levels reported recently. Earlier the isotope shifts of these even-parity energy levels were evaluated using empirical relation. Our extensive isotope shift data has been used for the reevaluation of ΔT values of these low even-parity energy levels which have been utilised for revision of the ΔT values of high-lying odd-parity energy levels of Gd I.     

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.     

Isotope shifts in the energy levels of the singly ionized neodymium atom

Isotope shifts ΔT (142–144) have been evaluated for odd and even energy levels of the singly ionised neodymium atom from the measurements carried out in 168 spectral lines in the 3930–5820 Å region, employing a recording Fabry-Perot spectrometer and highly enriched isotopes excited in liquid-air cooled hollow cathodes. The electronic configurations 4f³5d6s, 4f³5d6p and 4f⁴6p could be assigned to some of the energy levels on the basis of the present study.     

Simulation of isotopic selectivities and isotope ratio enhancement factors for gadolinium and lanthanum using narrow band laser excitation

Isotopic selectivities and isotope ratio enhancement factors have been calculated for 4f⁵5d6s^{2 9}D ₅ ⁰ -4f⁷5d6s6p ⁹D₆ (585.622 nm) transition of gadolinium and for 5d6s^{2 2}D_3/2-5d6s6p ⁴F _3/2 ⁰ (753.9 nm) transition of lanthanum by simulating the spectra assuming natural isotopic abundance of the samples. The atomic line shapes are assumed to be Lorentzian. Isotopic selectivities and isotope ratio enhancement factors for single step excitations have been computed. The isotope ratio enhancement factors estimated by us are half the value obtained by Young. et al. This is because the isotope ratio enhancement obtained by them is for a two colour RIMS where as our computations for selectivities are for a single step excitation. Considering the statistical error in the experimental values, our estimated isotopic selectivities are in good agreement with the available experimental data.     

Lifetime measurements of some TmI odd parity levels

Eleven new lifetimes of odd parity excited energy levels in four configurations: 4f ¹² 5d 6s6p, 4f ¹² 6s² 6p, 4f ¹³ 5d6s and 4f ¹³ 6s7s of atomic thulium have been mesured with atomic-beam laser spectrocopy. Two pulsed dye lasers are used for stepwise excitation and the time-resolved fluorescence decay was used to determine lifetime values. The accuracy of the measurements is about 10%.     

The electronic structure of thorium monoxide: Ligand field assignment of states in the range 0–5 eV

Configuration interaction ligand field theory (CI LFT) calculations of the electronic energy levels of ThO were performed by treating the molecular electronic states as Th ^{2 +} free-ion levels perturbed by the ligand field of O²⁻. Twenty nine experimentally characterized ThO v = 0 energy levels, together with the energy difference between the v = 0 levels of the Y and W states were fitted using a CI LFT model that included Th ^{2 +} 7s ² , 6d7s, 6d², 7s7p, 6d7p, 5f7s, and 7p² configurations. Predictions from these calculations were used to provide tentative assignments for 171 out of 250 ThO band heads listed by Gatterer et al. [“Molecular Spectra of Metallic Oxides”, Specola Vaticana (1957)]. Term energies for 30 electronic states have been determined based on these assignments. Subsequently, the CI LFT model was refined by fitting to a set of 59 electronic term energies. The inclusion of CI effects together with integer valence, atomic-in-molecule, ionic bonding ideas reveals atomic energy level patterns that are multiply replicated in the molecular energy level patterns of six Th ^{2 +} O²⁻ atomic ion configurations (6d7s, 6d², 7s7p, 6d7p, 5f7s, and 7p²) revealing the underlying atomic ion structure that gives rise to the complex and seemingly erratic unassigned bands reported in the Vatican Atlas. © 2018 Wiley Periodicals, Inc.     

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.     

Isotope shifts and electronic configurations of some of the energy levels of the neutral gadolinium atom

Isotope shift ΔT (156–160) have been evaluated for 52 odd and 90 even energy levels of the neutral gadolinium atom from the measurements carried out on 166 lines of the first spectrum in the region 4535–4975 Å on a photoelectric recording Fabry-Perot Spectrometer and enriched samples of ¹⁵⁶Gd and ¹⁶⁰Gd. Earlier studies provide data for just two lines in this region. Assignment of electronic configurations to some of the energy levels have been either confirmed or revised; some unassigned levels have been assigned probable configurations. The present study provides, for the first time, isotope shift of the two levels of 4f⁷6s²7 s configuration of Gd I.     

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.     

Isotope shift studies and electronic configuration assignments to the energy levels of neutral erbium

Isotope shifts ΔT (170-166) have been evaluated for 54 even and 94 odd energy levels covering almost all the known configurations of the neutral erbium. These ΔT values have been derived from the isotope shift measurements carried out in 159 lines in the region 3900–4605 A using a Fabry-Perot spectrometer and liquid-air-cooled hollow cathode source with highly enriched ¹⁷⁰Er and ¹⁶⁶Er isotopic samples. Electronic configurations assigned to energy levels of Er I by earlier workers have been mostly confirmed and in few cases revisions have been suggested on the basis of observed ΔT values. Probable configurations have been also suggested for unassigned levels of Er I, and a large number of even levels could be assigned to 4f¹¹ 5d 6s 6p configuration.     

New levels and calculations in the Nd I spectrum

The energies of all the levels of Nd I 4f ⁴ 6s ^{2 5} F and of⁵ S ₂ as well as of 4f ⁴ 5d 6s ⁷ H ₂ have been determined by means of laser-induced fluorescence in a hollow cathode. Their interpretation was carried out with the use of hyperfine structure data and a new parametric calculation of (4f ⁴ 6s ² + 4f ⁴ 5d 6s). Furthermore, the energies andJ values of 5 new odd levels were found.     

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.     

Magnetic field-induced ΔF=±2,3,4 transitions in the Eu I-spectrum

The occurrence of ΔF=±2, ±3, and ±4 transitions in the hyperfine structure of the Eu I lineλ 629.1 nm (4f ⁷6s ² a ⁸ S _7/2?4f ⁷6s6p z ⁸ P _5/2) was investigated with the application of high-resolution laser-atomic-beam spectroscopy. It was possible to show that the appearance of such transitions depends on the magnitude of an external magnetic field. Calculations of the hyperfine Zeeman splittings of the excited and the ground state were performed. This allowed the identification of the forbidden transitions.     

Quasirelativistic energy-consistent 5f-in-core pseudopotentials for divalent and tetravalent actinide elements

Quasirelativistic energy-consistent 5f-in-core pseudopotentials modeling divalent (5f ⁿ⁺¹ occupation with n = 5–13 for Pu–No) respectively tetravalent (5f ^n-1 occupation with n = 1–9 for Th–Cf) actinides together with corresponding core-polarization potentials have been generated. Energy-optimized (6s5p4d) and (7s6p5d) valence basis sets as well as 2f1g correlation functions have been derived and contracted to polarized double, triple, and quadruple zeta quality. Corresponding smaller (4s4p) and (5s5p) respectively (4s4p3d) and (5s5p4d) basis sets suitable for calculations on actinide(II) respectively actinide(IV) ions in crystalline solids form subsets of these basis sets designed for calculations on molecules. Results of Hartree–Fock test calculations for actinide di- and tetrafluorides show a satisfactory agreement with calculations using 5f-in-valence pseudopotentials. Electronic Supplementary Material The online version of this article doi: contains supplementary material, which is available to authorized users.     

Term isotope shift of high lying odd and even energy levels of Nd II

The isotope shifts of the odd and even parity energy levels of singly-ionised neodymium (Nd II) have been evaluated using the measurements carried out in more than 300 spectral lines of Nd II in the region 3290–5820 Å. Term shift, ΔT (¹⁴⁴Nd-¹⁵⁰Nd), is being reported for 23 low even and 15 high lying even parity levels of Nd II. ΔT for a level of 4f ³6s6p configuration and 8 even levels between 36892 and 43212 cm^-1 are being reported for the first time. ΔT values of 151 high lying odd parity levels are being reported and compared with some of the available earlier reported values. ΔT values of 47 odd parity levels are being reported for the first time, most of which are based on our isotope shift studies in UV region. The electronic configuration assignments to energy levels of Nd II by earlier workers are discussed on the basis of present ΔT values. Electronic configurations to some of the unclassified high lying odd levels have been suggested; the levels with ΔT (144–150) between 300mK and 380mK are assigned to 4f ³5d6s configuration whereas a level with ΔT value of 60mK to 4f46p configuration.