Symmetry Of Final States Research Articles

Double Photoionization of Atomic Carbon

Double photoionization events provide a direct evaluation of electron correlation. The recent focus on few-electron targets continues to reveal the consequences of electron correlation for targets that possess several electrons. We consider the double photoionization of the 2p2 valence electrons of atomic carbon and focus on the first energetically accessible final-state symmetries that originate from coupling the active electrons in 3P configurations, which are doubly ionized by a single photon. Comparison of this process in carbon with neon provides an analogous case for the resulting final-state symmetries within the framework where the ejected electrons are influenced by the remaining bound electrons in a frozen-core approximation. Choosing this symmetry allows for comparison with previous theoretical results for total and energy sharing cross-sections of carbon. Fully differential cross-sections for both carbon and neon are also compared.

Two-photon double photoionization of atomic Mg by ultrashort pulses: Variation of angular distributions with pulse length

We investigate the two-photon double ionization of atomic magnesium induced by ultrashort pulses. Though the initial and final state symmetries are comparable to the same process in helium, in stark contrast the range of photon energies for which nonsequential ionization is the only open pathway is narrow (less than 1 eV) in magnesium. Thus several sequential ionization pathways feature heavily in these processes. Nonetheless, it is found that for pulse durations between 0.25 and 2.0 fs, the joint angular dependence of the ejected electrons can depend sensitively on pulse length, varying between the strictly back-to-back ejection characteristic of nonsequential ionization to other distributions. The significance of excited-state correlating configurations in representing the initial state of magnesium is discussed in the light of their consequences for the resulting angular distributions at photon energies where sequential ionization can access intermediate states that lie nearby in energy, particularly for longer pulses.

Double photoionization of atomic carbon and neon

SynopsisWe consider the double photoionization of the 2p2 valence electrons of atomic carbon, which provides for distinct final-state symmetries depending on the three possible angular momentum couplings (3P, 1 D, and 1S) of the initially-bound p2 electrons that are ejected into the continuum by a single photon. Comparison of this process with neon provides an analogous case for the resulting final states within the treatment of the double photoionization proceeding with the ejected electrons influenced by the remaining bound electrons.

Fully Differential Single-Photon Double Ionization of Neon and Argon

Triply differential cross sections are calculated for one-photon double ionization of neon and argon at various photon energies and electron energy sharings by using a frozen-core treatment to represent the remaining electrons of the residual ion. Angular distributions agree well with all existing experimental data, showing that in spite of its simplicity the method can treat the double ionization of complex targets reliably. A comparison of the cross sections for helium, neon, and argon into the same final state symmetry at the same relative excess energies reveals a distinctive signature of the role of electron correlation in each target.

N 1s photoelectron angular distributions from fixed-in-space NO2 molecules: Stereodynamics and symmetry considerations

Angular distributions of N 1s photoelectrons from fixed-in-space NO(2) molecules have been measured over the energy region of shape resonance and above. A multiple-coincidence velocity-map imaging technique for observation of molecular frame photoelectron angular distributions (MF-PADs) has been extended to nonlinear molecular targets. Density functional theory calculations have also been conducted to elucidate the photoionization dynamics and shape resonance in the N 1s photoionization of NO(2). Results show that the N 1s MF-PADs exhibit strong shape variation as a function of both photoelectron kinetic energy and symmetries of final states, whereas asymmetry parameters of laboratory frame PADs show a local minimum around the shape resonance region and increase monotonically as the photon energy increases. Over the shape resonance, the spatial shape of the photoelectron wave function with b(2)-symmetry closely resembles that of 5b(2)(∗) unoccupied molecular orbital of NO(2), although the MF-PAD pattern for b(2)-symmetry does not correspond directly to the 5b(2)(∗) orbital shape. At higher kinetic energy of 90 eV, MF-PADs become less structured, but still show a significant dependence on the symmetry of final states.

Final-state symmetry ofNa 1score-shell excitons in NaCl and NaF

We report measurements of the $\text{Na}\text{ }1s$ contribution to the nonresonant inelastic x-ray scattering (NRIXS) from NaCl and NaF. Prior x-ray absorption studies have observed two pre-edge excitons in both materials. The momentum-transfer dependence ($q$ dependence) of the measured NRIXS cross section and of real-space full multiple scattering and Bethe-Salpeter calculations determine that the higher-energy core excitons are $s$ type for each material. The lower-energy core excitons contribute at most weakly to the NRIXS signal and we propose that these may be surface core excitons, as have been observed in several other alkali halides. The analysis of the orbital angular momentum of these features leads to a discussion of the limited sensitivity of NRIXS measurements to $d$-type final states when investigating $1s$ initial states. In this case the $s$- and $p$-type final density of states can be characterized by measurements at a small number of momentum transfers. This is in contrast to the case of more complex initial states for which measurements at a large number of momentum transfers are needed to separate the rich admixture of accessible and contributing final-state symmetries.

Exciton spectroscopy of hexagonal boron nitride using nonresonant x-ray Raman scattering

We report nonresonant x-ray Raman scattering (XRS) measurements on the boron $K$ edge of hexagonal boron nitride for transferred momentum $(\mathbf{q})$ from 2 to $9\text{ }{\text{\AA{}}}^{\ensuremath{-}1}$ along directions both in and out of the basal plane. A symmetry-based argument, together with real-space full multiple scattering calculations of the projected density of states in the spherical harmonics basis, reveals that a strong pre-edge feature is a dominantly ${Y}_{10}$-type exciton with no other $s$, $p$, or $d$ components. This conclusion is supported by a second, independent calculation of the $\mathbf{q}$-dependent XRS cross section based on the Bethe-Salpeter equation. This study demonstrates methods which should be applicable to the determination of final-state symmetries for localized resonances in other $\mathbf{q}$-dependent XRS studies of anisotropic single-crystal systems.

Dynamics of pp collisions at small impact parameters, universality of cross sections of hadron-hadron collisions and critical phenomena at superhigh energies

Studies of the small x dynamics at HERA energies allow one to quantify the range of momentum transfers and energies for which strength of the interaction approaches the maximum strength allowed by the unitarity in the gluon channel (black disk limit-BDL). Implications for the proton-proton interactions at collider energies (Tevatron, LHC) include a dominance of BDL up to transverse momenta of hadrons (jets) in the final state of a few GeV for collisions at small impact parameters, and explanation of proximity of the profile function of pp interaction to one at small impact parameters, leading to the universality of cross sections at superhigh energies. We discuss briey theoretical challenges in the applications of pQCD to small x phenomena, the onset of BDL for hard processes at large energies and universal limiting behavior: F 2, xG ∝ ln3(x o/x), σ(γ T) ∝ ln3(s/s o). We explain that the onset of BDL should be accompanied by generic nonlinear phenomena for the produced states such as kinks, different symmetry of final states, etc and related tunneling transitions. Characteristic features of QCD physics of central collisions at ultrahigh energies correspond to a new regime: (i) interaction is dominated by hard interactions of quarks and gluons leading to disappearance of the soft physics and hadronic degrees of freedom, (ii) change with energy of the space-time evolution of produced quark-gluon states, (iii) change of the avor composition of the produced system, (iv) formation of a color network, etc. Hence, such collisions are likely to result in the production of new forms of the QCD matter. We also comment on the implications of the discussed physics for cosmic ray interactions at ultrahigh energies and on the methods to get information necessary for modeling cosmic rays at energies much higher than LHC using planned experiments at LHC.

Momentum-dependent low energy losses in angle-resolved core level photoemission spectra

Angle-resolved photoemission spectra of the Sb 4d and Bi 5d core levels show spectral features split-off in energy by Δ E∼170–320 meV from the main peaks. The appearance of a second component in the Bi 5d spectrum was previously assigned to a surface related binding energy shift. However, use of synchrotron radiation ranging from 30 to 150 eV and angular scans along different symmetry directions of the (1 1 1) surface Brillouin zone show that the split-off peaks disperse as a function of the electron momentum k . Additionally, the peak width and intensity of the split-off peak oscillates between final state symmetry points. Since the d 5/2 and d 3/2 components show the same features symmetry arguments rule out crystal-field effects as the source of the observed peak splitting. The data can be explained by a k-dependent loss function consisting of several characteristic direct and indirect low energy interband transitions excited in various parts of the bulk Brillouin zone.

The probabilistic symmetry breaking of periodic regimes rapidly passing through a zone of chaos into the transparency window

The problem of transition of a noisy dynamical system to a periodic oscillatory regime through a zone of chaos is considered. Using the noisy logistics map as an example, domains of attraction of energetically equivalent regimes of period three are found for various transition rates and various noise levels. The fine structure of the domains of attraction under the condition of fast transitions is revealed. It is discovered that the settling time of the stable cycle of period three heavily depends on the initial conditions, i.e., on the structure of the domains of attraction. The critical transition rate that separates the region of the probabilistic symmetry of final states from the region of the dynamic behavior of trajectories is estimated.

Photoelectron intensity oscillation as a probe to monitor Si layer-by-layer growth

Photoelectron intensities from the surface state on Si(100)2 × 1 periodically oscillate during Si epitaxial growth, for which an alternation between 2 × 1 and 1 × 2 surface reconstructions has been proposed as an origin [Y. Enta et al., Surf. Sci. 313 (1994) L797]. To confirm the scheme more directly, we have performed synchrotron radiation ultraviolet photoelectron spectroscopy (UPS) measurements on both 2 × 1 and 1 × 2 surfaces. As a result, an apparent difference between the two valence-band spectra was observed, whose difference spectrum presented a good agreement with the dependence of the oscillation amplitude on the photoelectron energy, proving the validity of our previous proposal. A selection rule argument on the initial and final state symmetries yields an insight on the origin for the oscillation. With its very high sensitivity, UPS oscillation can be a powerful tool for monitoring the layer-by-layer growth at surfaces.

Symmetry characterization of unoccupied states in thick alkaline layers by spin-resolved Auger electron spectroscopy using primary excitation by circularly polarized light

CVV Auger electrons emitted from K, Rb and Cs layers are studied using spin-resolved spectroscopy. Oriented 3p, 4p and 5p hole states are excited by circularly polarized radiation in normal incidence. The photon energies range from 12 to 24 eV. With all three materials, the degree and sign of the Auger electron spin polarization vary with the photon energy. As an atomic model of the Auger process predicts, and as a comparison of measurements with the calculated densities of states shows, the spin polarization is essentially determined by the symmetry of the final states reached in the primary (photo)excitation. Just above the excitation threshold, the preferential spin direction of the Auger electrons is measured to be parallel to the spin of the exciting photons corresponding to a predominantly s-like symmetry of the unoccupied final states reached by the excitation. At higher photon energies the preferential spin direction changes to be antiparallel to the photon spin, corresponding to the mainly d-like symmetry of unoccupied states reached by the excitation.

Final-state symmetry and polarization effects in angle-resolved photoemission spectroscopy

Certain collection geometries used in photoemission experiments on oriented single crystals imply, in the one-electron picture, a definite selection of initial-and final-state symmetries. The principle is applied to recent polarization experiments on W(001) surfaces.

Photoionization of the 5d6p 3D1 state of barium.

We have carried out a relative measurement of the photoionization cross section of the 5d6p $^{3}$${\mathit{D}}_{1}$ state of barium from the 6s ionization threshold to 875 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ (\ensuremath{\sim}0.109 eV) above the 5${\mathit{d}}_{5/2}$ ionization threshold. The cross section was measured for two different final-state symmetries by varying the angle between the laser polarization vectors. Both photoionization cross sections contain ``forbidden lines'' which arise through a breakdown of the selection rules on J and ${\mathit{M}}_{\mathit{J}}$ due to the hyperfine interaction in the odd isotopes of barium. These experimental results are compared with jj-coupled eigenchannel R-matrix calculations and show good agreement. Approximate incorporation of the hyperfine effects into the calculations was necessary for a complete understanding of the measured photoionization cross sections. We found that for the odd isotopes (\ensuremath{\sim}18% of natural barium) the excited 5d6p $^{3}$${\mathit{D}}_{1}$ state was substantially depolarized by the effect of the hyperfine interaction.

Differential and integral cross sections for electron impact excitation of the n3S, n1S and n3P (n=2,3) levels in He

Differential and integral electron impact excitation cross sections are reported for the n3S, n1S and n3P (n=2,3) levels in He. Differential cross sections were measured at 30, 50 and 100 eV impact energies in the 10' to 135' angular range, extrapolated to 0 and 180', and then integrated over all angles to obtain integral cross sections at these three incident electron energies. In addition, differential cross sections were measured by excitation of the n3S (n=2,3,4,5), n1S and n3P (n=2,3,4) levels at 60 eV impact energy and 30' scattering angle. Theoretical cross sections based on first-order many-body theory (FOMBT) are also reported for these three final state symmetries for the 30-500 eV impact energy range. These new experimental and theoretical results are compared with other data.

The geometric and electronic structure of oxygen on a Re(10[formula omitted]0) surface investigated by LEED and ARUPS

The geometric and electronic structure of oxygen dissociatively adsorbed on a Re(1010) surface has been studied by means of LEED and ARUPS. Five ordered oxygen LEED phases could be observed, namely, a (2×3)-O structure at θO = 16, a c(2×4)−20 structure at θO = 14, a (1×5)−20 structure at θO = 25, a (1×4)−20 structure at θO = 12, and a (1×3)−20 structure at θO = 23. The two dimensional band structures of the (1×5)−20 and the (1×3)−20 phase were mapped at BESSY. Both ordered oxygen overlayers showed quite similar band structures with a pronounced dispersion along Σ ([1210]-direction) but a lack of any dispersion along Δ ([0001]-direction). The oxygen-induced bands could be assigned to certain symmetric and antisymmetric states of two chemisorbed oxygen atoms per unit cell by considering dipole selection rules in combination with final state symmetries. The uniform behaviour of both band structures can be interpreted by a similar local arrangement of the oxygen atoms in the unit cells of both structures.

Final state effects in photoemission of the 4f levels of terbium and dysprosium

Many electron excitations in photoemission are observed to occur at selected photon energies leading to resonant photoemission enhancements of the 4f multiplet levels of terbium and dysprosium. The authors find that final state symmetry effects can alter the photon energy of the photoemission resonances of the 4f levels creating a slightly different photon energy dependence for the various 4f multiplets. Additional complications are observed because of unresolved multiplets resulting from inter-atomic correlation effects. It is final state 5d-4f interactions that give rise to a variety of valence band 4f multiplets not predicted by one-electron theory.

Molecular photo cross sections with the LCGTO–Xα method using Stieltjes imaging

A method for calculating and symmetry analyzing total molecular photoionization cross sections is presented. The technique is based on the LCGTO–Xα method and employs Stieltjes imaging. It allows applications to molecular systems comparable in size to those treated so far with the continuum multiple-scattering Xα method, but avoids the pitfalls of the muffin-tin approximation to the electronic potential. Photo cross sections for valence ionization of CO are found in good agreement with experiment and with previous calculations. From a final state symmetry analysis for the 1π level, the absence of kσ* shape resonance which appears in the 4σ and the 5σ ionization channels is attributed to small transition moments. This is in contrast to a previous treatment where this difference has been rationalized as caused by a channel dependent final state potential. The photoionization cross sections for the four highest valence orbitals of benzene were calculated in better agreement with experiment than found in a previous Xα–SW treatment. The improvement is especially significant for the 1e1g(π) highest occupied molecular orbital where at least part of the experimentally observed structures are attributed to shape resonances. Some of the observed resonance features in the valence orbital photo cross sections of benzene were identified with resonances found in carbon K-shell ionization.

Final-state symmetry effects in photoemission of thin Gd overlayers

The 4f valence band and shallow core levels of ultrathin Gd overlayers on Cu(100) and on crystalline nickel overlayers on Cu(100) have been investigated using angle-resolved photoemission. The authors have observed a definite selection of final-state symmetries which, for one-half to four-monolayer-thick Gd films, indicates that the occupied Gd 5d band is predominantly 3z2-r2 and j=3/2 in character. The 5p3/2 appears to be predominantly z in character for thin Gd overlayers on Cu(100). This occurs as a consequence of final-state interactions between the Gd5d and 5p eigenstates. These results, together with the observed screening processes of the photoemission hole state, are discussed and applied to the understanding of photoemission resonance from the valance bands.

The D-Band Exchange Splitting for Thin Gadolinium Overlayers

ABSTRACTThin (0–6 monolayer) films of gadolinium on Cu(100) have been investigated using synchrotron radiation photoemission. From the definite selection of final state symmetries in photoemission, we have been able to determine a lower bound to the exchange splitting of the gadolinium 5d band. The gadolinium films on Cu(100) exhibit an exchange splitting that changes from approximately 1.1 eV to 0.6 eV as the overlayer thickness increases. The results for thicker films agree with the accepted values for the 5d exchange splitting of bulk gadolinium.