Atomic Multiplets Research Articles

Spin Polarization of 3dPhotoemission at 3pThreshold in Ferromagnetic Ni Expected from Configuration Interaction Model

We discuss the spin polarization of resonant 3 d photoemission spectra at the Ni 3 p threshold for ferromagnetic Ni from the viewpoint of a many-body configuration interaction, on the basis of the Anderson impurity model including atomic multiplets. The calculated relative spin polarization (majority-spin minus minority-spin divided by their sum) at the 6-eV satellite is shown to exhibit a dip structure with a minimum of ∼20% and a maximum of ∼35% separated by 7∼8 eV near on-resonance as a function of incident photon energy, which is consistent with the results of recent experiment. Its structure is, contrary to previous discussions, shown to be caused not only by the Fano interference effect but also by the 3 p -3 d exchange and 3 p spin-orbit interaction in the intermediate state of the second-order resonant process. The spin polarization in the main peak and in the various positions of satellites is also discussed.

Configuration Interaction in Ni Metal and Ni Alloys and High-Energy Spectroscopy

We discuss the electronic state of Ni atoms in Ni metal and of Ni impurity in Cu and Au metals from the viewpoint of 3 d configuration interaction (CI) using the Anderson impurity model including atomic multiplets. On the basis of the discussion, we give an interpretation for the Ni 2 p -core X-ray photoemission spectrum (2 p XPS) in Ni metal and Ni impurity systems and 3 d photoemission spectra in Ni metal. The interpretation is, furthermore, shown to be consistent with the previous one for the 2 p →3 d circularly polarized X-ray absorption in ferromagnetic Ni using the CI approach.

The complete UV spectrum of SO2 by electron impact, 1, The vacuum ultraviolet Spectrum

We have measured the vacuum ultraviolet (VUV) emission cross sections of SO2 from 40 to 200 nm in the laboratory in a crossed beam experiment. The wavelength range comprised the extreme ultraviolet (EUV) spectrum, from 40 to 120 nm, and the far ultraviolet (FUV) spectrum, from 120 to 200 nm. The EUV and FUV emission spectra induced by electron impact consist of atomic multiplets of S I, II, and III and O I, II, and III. The studies included the measurement of excitation functions of the strongest multiplets from 0 to 1 keV impact energy and the identification of dissociation processes from the analysis of the threshold excitation function. The O I (98.9 nm) resonance multiplet (g3 P‐3D) is the strongest EUV feature from electron impact induced fluorescence of SO2 with a peak cross section of 7.82 ± 1.59 × 10‐19 cm2 at 125 eV electron impact energy. The O I (130.4 nm) multiplet (g3P‐3S) resonance transition is the strongest feature in the FUV, with a peak cross section of 1.98 ± 0.44 × 10‐18 cm2 at 90 eV. The strongest feature of S I in the VUV is the S I (147.9 nm) multiplet (g3 P‐3D) resonance transition, with a peak cross section of 1.52 ± 0.33 × 10‐18 cm2 at 90 eV. Dissociation‐excitation cross sections of SO2 are important contributors to the total inelastic cross section of SO2 gas interacting with electrons. These cross sections are used in neutral cloud theory models of the Io atmosphere. The laboratory spectrum at low energy (~22 eV) matches a recently obtained IUE FUV spectrum of Io. The comparison represents evidence of a thin or intermediate atmosphere of SO2 that is directly impacted by the plasma torus. The existence of an atmosphere on Io embedded in the corotating torus plasma is an important remote sensing target for the Hubble Space Telescope, Goddard High Resolution Spectrograph and Faint Object Spectrograph, and Galileo EUV and FUV spectrometers, among other present and planned VUV studies of the Jovian system.

Ligand field strengths and oxidation states from manganese L-edge spectroscopy

L,, X-ray absorption spectra have been recorded for Mn(II), Mn(III), and Mn(IV) samples with a variety of ligands. For high-spin Mn(I1) complexes, a systematic variation in spectra is observed as the ligand field is increased. A dramatically different spectrum is observed for Mn(CN)6, consistent with the presence of a low-spin complex. Progressing in oxidation state from Mn(1I) to Mn(II1) through Mn(IV) complexes, the primary peak position shifts first 1.5-2 eV and then 1-2 eV to higher energy, and the ratio of L, to L2 intensity decreases. The spectra have been quantitatively simulated with an atomic multiplet program with an octahedral crystal field superimposed. The high resolution, strong sensitivity to chemical environment and amenability to quantitative spectral shape analysis indicate that L-edges of the first transition series metals are a potentially useful probe for bioinorganic studies.

Zeeman spectroscopy and deperturbation of the low-lying states of NiH

High resolution laser spectroscopy of the NiH molecule in a magnetic field has revealed strong homogeneous and heterogeneous perturbations among all of the low-lying electronic states. Fully resolved Zeeman splitting patterns from transitions between NiH magnetic sublevels were recorded with the technique of Zeeman optical–optical double resonance (ZOODR) spectroscopy. Using only the zero-field rotational energy levels as input to an electronic structure model, we have calculated Zeeman splittings (g values) for 19 rotational levels, and the predicted splittings are in very good agreement with observed Zeeman spectra. A group of 10 NiH molecular electronic states is seen to form a supermultiplet of levels originating from the Ni+ (3d9)2D atomic multiplet. We describe an effective Hamiltonian matrix that contains explicit terms coupling low-lying states through spin–orbit, vibrational, and rotational interactions. Supermultiplet eigenvectors graphically illustrate the profound mixing hidden beneath the apparent regularity of term value plots for the low-lying states of NiH. The success of the supermultiplet model for this simplest case (a single hole in a highly contracted 3d subshell), namely the successful prediction of strongly J dependent g values, makes us confident that this model will be applicable to other transition metal monohydrides.

L2,3 x-ray-absorption edges of d0 compounds: K+, Ca2+, Sc3+, and Ti4+ in Oh (octahedral) symmetry.

The ${L}_{2}$,3 x-ray-absorption edges of 3${d}^{0}$ compounds are calculated with use of an atomic description of the 2${p}^{6}$3${d}^{0}$ to 2${p}^{5}$3${d}^{1}$ excitation, with the inclusion of the crystal field. For reasons of clarity, we confine ourselves to ${d}^{0}$ compounds in octahedral symmetry, but the same approach is applicable to all other ${d}^{N}$ compounds in any point-group symmetry. The experimental spectra of ${\mathrm{FeTiO}}_{3}$, ${\mathrm{Sc}}_{2}$${\mathrm{O}}_{3}$, ${\mathrm{ScF}}_{3}$, ${\mathrm{CaF}}_{2}$, and the potassium halides are well reproduced by the present calculations, including the previously misinterpreted small leading peaks. The splitting between the two main peaks in both the ${L}_{3}$ and ${L}_{2}$ edge are related, though not equal, to the crystal-field splitting. Comparison to experiment showed that the broadening of the main multiplet lines is different. This can be related to Coster-Kronig Auger processes for the ${L}_{2}$ edge and to a solid-state broadening which is a combination of vibrational (phononic) and dispersional broadenings. With the full treatment of the atomic multiplets, the atomic effects can be separated from solid-state effects, which offers a better description of the latter. This includes vibrational broadenings, the covalent screening of the intra-atomic Coulomb and exchange interactions, via the position of small leading peaks, and surface effects. The same general framework can be used to discuss crystal-field effects in both lower symmetries, with the possibility of polarization-dependent spectra (e.g., ${\mathrm{TiO}}_{2}$), and partly filled d bands.

Effects of hybridization on multiplet structures in 3d- and 4d-core photoemission spectra in light rare earth compounds

La or Ce 3d- and 4d-core photoemission spectra are discussed for La and Ce compounds on the basis of the impurity Anderson model taking into account the atomic multiplets due to electron-electron interaction. A consistent explanation of 3d and 4d XPS of La and Ce compounds is presented. We also give an interpretation of the multiplet structures in the spectra. By transforming the Hamiltonian, we show that conditions that promote the "quenching" of the multiplet structure in the solids are small electron-electron interaction, large hybridization between the localized orbit and the valence band, and small energy difference between different fn configurations in the final state.

U impurities in Au

The properties of U impurities in Au have been studied by magnetic susceptibility, electrical resistivity, and electron spectroscopic measurements. The results indicate that U forms a well-defined local magnetic moment of 3.6μB, giving rise to a Kondo resistance anomaly at low temperature. This is in agreement with spectroscopic data, which show localized impurity states well removed from the Fermi level. Comparison to calculated atomic multiplets shows the need for inclusion of crystal or ligand field effects for the multiplets. The intra-5f Coulomb correlation energy is found to be 2.6 eV.

Multiplet Structures in 3dand 4dCore Photoemission Spectra for Ce Compounds

The Ce 3 d and 4 d core X-ray photoemission spectra (3 d and 4 d XPS) of Ce compounds are studied based on the impurity Anderson model considering atomic multiplets arising from electron-electron interaction. We make a consistent analysis of 3 d and 4 d XPS of trivalent Ce compounds CeF 3 , CeCl 3 and Ce 2 O 3 , which can only be made by considering the atomic multiplets. We also apply the approach to the interpretation of the spectra of mixed valent Ce systems Ce–Ni compounds and CeO 2 . We show that the analysis of the multiplet structure gives information about many-body electronic states of the system.

Photoemission study of the valence-band electronic structure in FexO, Fe3O4, and alpha -Fe2O3 single crystals.

Valence-band photoemission spectra have been measured from cleaved stoichiometric iron oxide single crystals using synchrotron radiation. The total photoelectron yield is observed to increase dramatically at photon energies above the Fe 3p\ensuremath{\rightarrow}3d excitation threshold, and the resonant onset correlates directly with the oxidation state of the Fe cations. Features in the total yield profiles are interpreted in terms of atomic multiplets. The phenomenon of resonant photoemission is used to distinguish the Fe 3d-derived valence states from the overlapping unhybridized O 2p states in each of the oxides. By use of cleaved single crystals, the subtle differences in the valence-band photoemission features associated with ferrous (${\mathrm{Fe}}^{2+}$) and ferric (${\mathrm{Fe}}^{3+}$) cations have been determined. The measured energy distribution of the photoemission final states in single crystal \ensuremath{\alpha}-${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$ are in good agreement with recent measurements and configuration-interaction cluster calculations by Fujimori et al., which take into account ligand-to-metal charge transfer. Constant-initial-state spectra measured across the 3p\ensuremath{\rightarrow}3d threshold in each oxide indicate that most of the photoemission intensity near the top of the valence band is derived from hybridized cation-3d--ligand-2p states, whereas the emission at higher binding energies results from primarily 3${d}^{n\mathrm{\ensuremath{-}}1}$ final states. On this basis, each of the iron oxides is classified as a charge-transfer rather than a Mott-Hubbard insulator.

Localization of Cu 3d levels in the high Tc superconductor YBa2Cu3O∼7 by Cu 2p X-ray photoelectron spectroscopy

The copper 2p12 and 2p32 x-ray photoelectron core level spectra (XPS) of the single phase high temperature (Tc=91K) superconductor YBa2Cu3O∼7 have been measured. Evidence for the strong localization of valence Cu 3d electrons is indicated by the Coulomb interaction Ucd∼9 eV between the 2p32 core hole and the localized 3d valence electron. A Coulomb interaction Udd of the order of 6 eV between 3d valence electrons has been estimated. No evidence of the 2p3d8 underline indicates the hole) final state due to the Cu3+ ions has been found. The broadening of atomic multiplets of the final state 2p3d9 going from CuO to YBa2Cu3O∼7 has been observed. These results are consistent with the formation of holes L in the oxygen derived band, i.e. of the 3d9L configuration, with additional oxygen x in YBa2Cu3O6.5+x, which should play a key role in the high-Tc superconductivity.

Error distributions for effective atomic operators

The levels of an atomic multiplet can be exactly fitted by a model Hamiltonian comprising a set of scalar products of tensor operators. When this set is incomplete, a least-squares fit leads to errors Delta i that do not exhibit a normal distribution. This analysis suggests that normal distributions cannot be expected when the levels of more complex atomic systems are being fitted.

Higher-order Stark effect on atomic multiplets

The term of the order of F4 for the fine splitting of an atomic multiplet in an electric field is determined by the tensor polarisability alpha T.

Collisional relaxation and transfer of coherence in excited atomic multiplets of the type(j1,j2;j)=(1,12;32 or 12)

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Multiplet-mixing collisions and nearly resonant light scattering

We study the effect of multiplet-mixing collisions on the strength and the polarization of fluorescence radiation emitted by an atomic multiplet at irradiation with non-saturating resonant or nearly resonant light. Explicit expressions are derived for the strengths and the polarizations in terms of generalized multipole-relaxation matrices, which in turn are expressed in terms of the exact quantum-mechanical collisional cross sections. Multiplet-mixing collisions redistribute the fluorescence over the various emission lines, thereby changing the anisotropy and the polarization of the fluorescence. Special attention is paid to the case of the principal series of alkali atoms.

Collisional depolarization and redistribution of radiation in near resonance with an atomic multiplet

We derive an expression for the spectral distribution and the polarization of the intensity of near-resonant radiation scattered from atoms in a perturber gas. The effects of the degeneracy of the levels and of the interference between different levels are accounted for. In the case of far-wing irradiation the scattered spectrum separates in a Rayleigh or a Raman peak, and a series of fluorescence peaks. We study the variation of the polarization and the strength of these various peaks as a function of the incident frequency and of the perturber density.

X-Ray Photoemission Study of the Bond Structure of KMF3 (M: Mn, Fe, Co, Ni, Cu, Zn) Crystals

The band structure of KMF 3 crystals (M: Mn, Fe, Co, Ni, Cu, Zn) are investigate by means of the X-ray photoemission spectroscopy (XPS) in the valence band region. The stationary bands found in XPS spectra which are almost independent of the kind of M ion are assigned to the F - 2 p valence band. The remaining structure shows a fairly good agreement with the levels of atomic multiplets of M ions having (3d) n -1 electron configurations (n is the number of d-electrons in the initial state of M ++ ions) both in position and in intensity, and is attributed to the localized 3d-electron states of M ion.

A rocket measurement of the extreme ultraviolet dayglow

Extreme ultraviolet spectra of the mid‐latitude dayglow in the wavelength range of 550 to 1250A have been obtained with a rocket borne grating spectrometer at a resolution of 20A. Spectra were obtained in the altitude range of 140 to 280 km. The spectra are dominated by emissions from atomic multiplets and no molecular bands have been identified with certainty. The strongest emissions other than H Lyman‐alpha are OI(989) and OII(834). Other prominent emissions include HeI(584), NII(916) and NII(1085). An unexpected feature near 612A has an intensity comparable to HeI(584).

Frequency dependence of the polarization of radiation emitted by polarized atoms

We study the possible sources of frequency-dependent polarization of the radiation emitted by polarized excited atoms immersed in a perturbing gas. For an isolated line we conclude that a frequency dependence may be due to correlation between Doppler and collisional broadening, to anisotropy in the translational states or in the internal states of the perturbers, or to an external field. For an atomic multiplet the effect of line coupling may cause transfer of radiation emitted by atoms in a certain excited state to lines attributed to other excited states. This would cause a frequency-dependent polarization. Further the simple proportionality of the intensity of a broadened multiplet line to the population of the corresponding upper state would be destroyed.

An analysis of energy differences in atomic multiplets in connection with the inequality formulation of Hund's rules

A detailed consideration is given of a recent reformulation of Hund's rules in terms of inequalities. The interpretation of Hund's rules is reconsidered assuming that each energy level is known exactly in the restricted Hartree-Fock approximation. Some general theorems and series expansions are derived for energy differences between atomic states. As is now well known, the state of lower energy in a multiplet has the higher expectation value for the electron-electron repulsion, especially in neutral systems. The behaviour of this repulsion is analysed in terms of the Fermi hole and the contraction of the wavefunction which one finds for the state of lowest energy. Numerical examples are given for the 1P and 3P states of the He isoelectronic series, the 1S, 1D and 3P states of the C and O series and the 2P, 2D and 4S states of the N series.