Optical isotope shifts in neodymium

Isotope shifts have been measured in Nd II from which the shifts between pure configurations 4f ⁴ 6s and 4f ⁴ 5d can be determined. The specific mass shift for such a “transition” was estimated to be + 3 mK for a change of two neutrons. By comparison with electronic X-ray isotope shifts the following values were obtained for the change in the nuclear charge distributionδ〈r ²〉 [fm²]: (142, 144) 0.277; (144, 146) 0.257; (146, 148) 0.286; (148, 150) 0.381; (142, 143) 0.130; (144, 145) 0.111. Field shifts in several optical transitions have been compared with values of ¦ψ(0)¦² obtained from Hartree-Fock wave functions; agreement is good. Other specific mass shifts have been estimated 4f ⁴ 6s? 4f ⁴ 6p, ?1 mK; 4f ⁴ 6s? 4f ³ 5d ², ?30 mK. These values are in good agreement with calculated values of ?1.1 and ?30.6 mK.     

Isotope shift in osmium I: Experiment and theory

The isotope shift in the arc spectrum of osmium was studied in 10 lines for the highly enriched isotopes¹⁸⁸Os and¹⁹²Os and in 2 lines for natural¹⁹⁰Os by means of a photoelectric recording Fabry-Perot spectrometer with digital data processing. The observed shifts were analyzed by means of the parametric method. The field shift of 5d ⁷6s ⁵ F is 53.4 (9.6) mK larger than that of³ F, thus showing the influence of crossed-second-order effects produced by the interaction of the electrostatic operator and the field shift operator. Spin dependent effects were also able to be evaluated. The corresponding parameterz _s for the configuration 5d ⁷6s was found to be 2.5 (2) mK. The experimental data are compared with results from non-relativistic Hartree-Fock calculations. Except for a scaling factorS ^*(Z)=1.489 the calculated electron densities describe the measured isotope shifts of this work and of other authors.     

Isotope shift in molybdenum

The isotope shift in molybdenum has been studied in 16 lines of the arc and 6 lines of the spark spectrum for all stable isotopes by means of a photoelectric recording Fabry-Perot spectrometer with digital data processing. Mass shift and field shift were separated by two independent methods and were compared with the results of Hartree-Fock calculations. In the field shift large crossed-second-order effects ind ⁵ s ⁷ S and⁵ S were observed, which could be explained quantitatively by theory. The changes in mean square nuclear charge radii were evaluated from three 5s-5p transitions between different multiplets. The relativeδ〈r ² 〉 values are: [92, 94] 1; [94, 96] 0.854(3); [96, 98] 0.665(4); [98, 100] 1.003(5); [95, 97] 0.703(5);. [94, 95] 0.270(4); [96, 97] 0.119(5). The absolute values can be obtained withδ〈r ² 〉 ^{92, 94}=0.226(19)fm².     

Oscillator strengths for 3dn4s → 3dn4p transitions in the iron series

The observed oscillator strengths for the 3dⁿ4s → 3dⁿ4p transitions in the iron series show anomalous behaviour for Cr and Mn : the former is exceedingly small whereas the latter is unusually large.Theoretical Hartree-Fock gf-values are reported and a considerable discrepancy with experimental values is noted for Cr. The effect of the interaction of 3dⁿ4p with 3d^n?14s4p is studied using a fixed core, multi-configuration Hartree-Fock approximation. This interaction does not improve significantly the agreement with observed values.     

On classical rotational rainbow structures for initially rotating molecules

The specific mass shift (SMS) dominates the isotope shift for a light atom like Na. It arises from a correlation between the electronic momenta and is very sensitive to pair correlation effects in the wavefunction. We here extend earlier work on the SMS of Li and K and evaluate the second-order pair correlation contributions for the 3s, 3p and 3d levels of Na. For the resonance line, 3s→3p, the inclusion of the lowest-order correlation effects changes the theoretical result from 16% to about 80% of the experimental value. We also demonstrate that for scalar operators, like the SMS and also the field shift, diagrams involving only single excitations are included in a restricted Hartree-Fock calculation if the valence electron is included in the potential. The analogy is illustrated by numerical results both for the specific mass shifts and the field shifts for Na and K.     

Oscillator strengths for selected 3dn4s−3dn4p transitions of the iron-group elements

Absolute transition probabilities are calculated for selected 3dⁿ4s?3dⁿ4p transitions of the iron-group elements; configuration interaction effevts are taken into account. Comparisons with Hartree-Fock and multi-configuration Hartree-Fock results and with experimental data show that the scaled Thomas-Fermi method for calculation radial wave functions is useful procedure.     

Multiplet strengths of excited transitions of Ne sequence

Absolute multiplet strengths of transitions between 2p⁴3p-2p⁴3d terms of Ne⁺ sequence have been obtained by the nuclear charge expansion method within the Hartree-Fock approximation and with mixing of terms of different L-S geneology. Comparison is made with known results for NaIII.     

Tensor polarizabilities of levels of the configurations 4f 13 6s6p and 4f 12 5d6s 2 in thulium I

The level-crossing technique with parallel electric and magnetic fields was used to measure the tensor polarizabilities of six levels of the configuration 4f ¹³ 6s6p + 4f ¹² 5d6s ² in the Tm I-spectrum. Using intermediate coupling wave functions given by Camus and the experimental values of the tensor polarizabilities, the radial integrals for electric dipole transitions from levels of the configuration 4f ¹³6s6p + 4f ¹²5d6s ² to levels of the configuration 4f ¹³ 5d6s + 4f ¹² 6s ²6p have been determined. The results areI(4f ¹³6s6p,4f ¹³5d6s)=1.98(45)ea ₀ andI(4f ¹²5d6s ²,4f ¹²6s ²6p) = 0.88(25)ea ₀. A comparison between the experimental and the calculated values of the tensor polarizabilities shows an excellent agreement, provided that these radial integrals and the radial integrals for the electric dipole transitions to the ground state configuration 4f ¹³6s ² as determined by Wallenstein from lifetime measurements are used in the calculation, instead of radial integrals computed by Camus with Hartree-Fock wave functions.     

Semiempirical investigation of perturbations of the g factors of electronic-vibrational-rotational levels of hydrogen: III. The r 3Π g − and s 3Δ g − states of the H2 and D2 molecules

The g factors of rovibrational levels of the (4d)r ³Π _g ^? and (4d)s ³Δ _g ^? states of the H₂ and D₂ molecules have been obtained for the first time. These values were found within the nonadiabatic model taking into account the interaction of the 4dπ³Π_g and 4dδ³Δ_g states in the pure precession approximation using semiempirical values of the expansion coefficients of the wave function in an adiabatic basis, which was obtained for the first time for the states of the triplet 4d complex of terms of the hydrogen molecules, and the results of numerical calculation of the overlap integrals of the vibrational wave functions of these states. It is established that the interference effects of the interaction between the 4dπ³Π _g ^? and 4dδ³Δ _g ^? states lead to significant (up to 7 times for the r ³Π _g ^? state of the H₂ and D₂ molecules and 70 and 8 times for the s ³Δ _g ^? state of the H₂ and D₂ molecules, respectively) differences between the nonadiabatic values of the g factors and the corresponding adiabatic values. It is found that the perturbed values of the g factors are much closer to the values corresponding to the case of Hund’s d coupling of angular momenta than to the values corresponding to the b coupling. It is established that the perturbations of the g factors of rovibrational levels of the states of the 4d complex of terms are much greater (up to 2 times for the ³Π _g ^? states and 350 times for the ³Δ _g ^? states) than the perturbations of the same characteristics for the 3d complex of terms of the hydrogen molecule with the same vibrational and rotational quantum numbers.     

Hyperfine-structure and isotope-shift measurements in the 6s 5d↔6p 5d transitions of Ba I in the far-red spectral region

Measurements of the hyperfine structures in the 6p5d ¹ D ₂,³ D ₁ and³ F _{2, 3, 4} states of¹³⁵Ba and¹³⁷Ba, and isotope-shifts in several far-red transitions between the 6s 5d and 6p 5d configurations, as well as the transition 6s ^{2 1} S ₀→6s6p ³ P ₁ at 7,911 Å have been performed using high-resolution laser spectroscopy on a collimated atomic beam of natural barium. An analysis of the magnetic-dipole interaction in the 6p 5d configuration using effective one- and two-body hyperfine operators is presented. In particular the contact interaction was studied with respect to the correlation between the two valence electrons. Effects of strong configuration interaction were found. From a King-plot analysis of the isotope shift term- andJ-dependence of the field shift have been evaluated for the transitions between the 6s 5d and 6p 5d configurations. Relativistic Hartree-Fock (RHF) calculations have been performed of electron densities at the nucleus for six different configurations in Ba I and Ba II. The RHF calculations reproduce the experimental King-plot slopes quite well, while the absolute values, of the changes in electron density at the nucleus for the studied transitions, are found to be 9% lower than the results derived from a muonic experiment.     

Stark effect,hyperfine structure and isotope shifts in highly excited states of BaI and CaI

The electric dipole polarizabilities of 9 even-parity barium states (6s8s ¹ S ₀,³ S ₁; 6s7d ¹ D ₂,³ D _1,2; 5d7s ¹ D ₂ and 6p ^{2 3} P _0,1,2) in the interval 33,800–35,800 cm^?1 have been measured with high resolution laser-atomic-beam spectroscopy. Simultaneously, values of isotope shifts and hyperfine coupling constants for theJ=1 states have been obtained. Comparison of the experimental polarizabilities with calculated values as well as inspection of the data on isotope shifts and hyperfine structure from the present and earlier work strongly suggests erroneous assignments of theJ=2 states, with an exception for the 5d 7s ¹ D ₂ state. The influence of an electric field on the 3d ^{2 3} P _0,1,2 states of calcium has also been studied. A marked departure from a quadratic Stark effect has been observed at relatively small field strengths. This can be attributed to the large polarizabilities of neighbouring Rydberg states. The low field data allow the determination of admixtures of Rydberg states into the 3d ^{2 3} P-states as small as 0.02%.     

Hyperfine structure and isotope shift of high-lying metastable states of rhenium

Fourteen transitions in ReI, starting from high-lying metastable states belonging to the configurations (5d+6s)⁷, have been studied by laser-induced fluorescence in a collimated atomic beam, and accurate values for the isotope shifts in these transitions as well as for the hyperfine structure constants of 13 metastable and 9 excited states have been obtained. In addition, high precision measurements of the hyperfine structure of the states 5d ⁵ 6s ^{2 4} D _7/2 and 5d ⁶ 6s ⁶ D _{1/2, 3/2, 5/2, 9/2} have been performed using the atomic beam magnetic resonance technique coupled with laser-induced state-selective detection of metastable atoms. The analysis of the hyperfine structure data yields experimental evidence for far configuration mixing effects on the off-diagonal spin-dipole matrix elements. The phenomenological interpretation of the isotope shifts shows the significance of off-diagonal field-shift effects.     

Electronic structure of the valence bands of H2-, Mg- and Pt-phthalocyanine derived from soft X-ray emission and photoelectron emission spectra

The soft X-ray emission and photoelectron emission spectra of H₂-, Mg- and Pt- phthalocyanine (PC) obtained using synchrotron radiation are reported and compared. In this way, an overall view of the pattern of valence bands is obtained and the electronic structure determined in terms of the component partial densities of states. In particular, from the valence p → 1s carbon and nitrogen K-emission spectra we determine for all three compounds the C and N 2p-like valence-band density of states with strong maxima located at binding energies of 8, 11 and 13.5 eV (carbon 2p) and 8 eV (nitrogen 2p) below the vacuum level. For PtPC the partial density of d-like valence states is determined from photoelectron emission difference-spectra and compared to previous XPS results. The sharp (1.2 eV FWHM) maximum of the Pt-derived partial density of states, observed at 6.9 eV binding energy, is assigned to the ⁴F term of a 5d⁸6s final-state configuration. A second, broader maximum at around 9.5 eV binding energy contains contributions from other terms of this 5d⁸ configuration, as well as from a 5d⁷ satellite (shake-up multiplet).     

Analysis of the spectrum of the Zn-like Kr VII ion: Highly excited 4<Emphasis Type="Italic">p</Emphasis>4<Emphasis Type="Italic">d</Emphasis> and 4<Emphasis Type="Italic">p</Emphasis>5<Emphasis Type="Italic">s</Emphasis> configurations

The spectrum of the Zn-like Kr VII ion, excited in a capillary discharge and recorded with a high resolution in the wavelength range of 300–1000 Å, was studied. Previously performed identification of the transitions from the levels of the 4s4f, 4s5s, 4s5p, and 4s5d configurations is confirmed and extended, and the energies of these levels are specified. The (4p ²+4s4d)?4p4d and (4p ²+4s5s)?4p5s transitions are identified for the first time, and the energies of all the levels of the 4p4d and 4p5s configurations are determined. The results of the analysis performed are confirmed by semiempirical calculations in terms of the Hartree-Fock method. These results are also shown to conform to the experimental data obtained for lighter ions of the Zn I isoelectronic sequence.     

Isotope shift and configuration mixing in dysprosium II

The isotope shift in the spark spectrum of dysprosium was studied by means of a photoelectric recording Fabry-Perot spectrometer with digital data output. For 29 lines the isotope shift of¹⁶²Dy and¹⁶⁴Dy was measured in order to check the mixing of the three configurations 4f ⁹5d6s, 4f ⁹5d ², and 4f ¹⁰6p calculated by Wyart. By means of the sharing rule the configuration mixing could be confirmed as a whole. In the ground state configuration the influence of relativistic effects was demonstrated and explained by theory. The order of magnitude of crossed-second-order effects contributing to the isotope shift of 4f ¹⁰6s⁶ I and⁴ I could be estimated. In three lines the isotope shift of all stable Dy isotopes was measured. Mass shift and field shift were separated by comparison with results obtained in the arc spectrum.     

Isotope shifts in Sm II and changes in mean-square nuclear charge radii of the stable even Sm isotopes

Isotope shifts have been measured in Sm II from which the shifts between pure configurations 4f ⁶ s and 4f ⁶5d can be determined. The specific mass shift for such a “transition” was estimated to be (?1±2)mK for a change of two neutrons. The values derived for the change in the nuclear charge distribution,δ〈r ²〉, are in good agreement with the results obtained from isotope shift measurements in Sm I (H. Brand et al.: J. Phys. B11, L99, 1978). The weighted mean values representing the best information onδ〈r ²〉 presently available are in fm²: [144, 148] 0.488(23); [148, 150] 0.285(14); [150, 152] 0.400(19); [152, 154] 0.217(11).     

Autoionizing and highly excited states in the spectrum of triply ionized tin Sn IV

Transitions from autoionizing states in the spectrum of Sn IV in the range 200–630 Å, occurring due to the excitation of electrons from the inner 4d ¹⁰ shell, are investigated with high resolution. The transitions from the 4d ⁹5p ², 4d ⁹5s6p, and 4d ⁹5snf (up to n = 9) configurations are identified and their autoionization widths are measured. Transitions from the highly excited 4d ¹⁰ ns (n = 8–10), 4d ¹⁰6p, and 4d ¹⁰7d configurations are also revealed and the ionization potential of Sn IV is refined. The data obtained are compared with the results of calculations by the Hartree-Fock and semiempirical methods.     

Multielectron effects in photoemission from quasi-atomic copper in Cu-phthalocyanine

Photoelectron energy distribution curves for Cu in Cu-Phthalocyanine have been investigated around the Cu 3p threshold at hv = 75 eV. A sharp 3d-electron satellite with two peaks with initial energies of 5.5 and 8.5 eV below the center of the Cu 3d main peak was found which exhibits a strong resonant enhancement at threshold. These results are explained as a two-electron shake-up multiplet with a 3p⁶3d⁸4s² + e^? final state configuration. The results are compared with metallic Cu, and the different chemical, relaxation (screening) and configuration shifts are discussed.     

Laser-atomic-beam spectroscopy in Sm: Isotope shifts and changes in mean-square nuclear charge radii

A systematic investigation of the isotope shifts of all natural Samarium isotopes was performed in 15 lines of the Sm I spectrum using the laser-atomic-beam technique. The observed lines correspond to transitions between the ground configuration 4f ⁶6s ² and the upper configurations 4f ⁶6s6p and 4f ⁵5d6s ². In one line a contribution of hyperfine-structure second-order effects to the isotope shift of the odd isotopes could be demonstrated. The measured isotope shifts have been separated in all lines into field shift and mass shift contributions assuming the specific mass shift to be zero in pures ²-sp transitions. From the field shift of the pures ²-sp transitions the changes in mean-square nuclear charge radii, δ<r ²>, have been evaluated for all natural Sm isotopes (in fm²): [144, 148] 0.517(27); [148, 150] 0.303(16); [150, 152] 0.423(22); [152, 154] 0.230(12); [147, 148] 0.152(8); [148, 149] 0.092(5). There is good consistency with recent muonic x-ray measurements of the changes in the Barrett nuclear charge radii,δR _k , of the even Sm isotopes.     

New neutron deficient isotopes with mass numbersA=136 and 145

High resolution laser-atomic-beam spectroscopy was applied to study crossed-second-order effects in the isotope shift of the terms 4f⁷5d6s a¹⁰D and a⁸D for¹⁵¹Eu-¹⁵³Eu. The term dependent effects lead to a difference in the isotope shift of the terms a¹⁰D and a⁸D of 415(20) MHz. The J dependent effects are interpreted through the use of one parameter z_5d for each term; z_5d(a¹⁰D)=41(7)MHz, z_5d(a⁸D)=50(26)MHz.