Real‐space multiple‐scattering Hubbard model calculations for d‐ and f‐state materials

Calculations are presented of the electronic structure and X‐ray spectra of materials with correlated d‐ and f‐electron states based on the Hubbard model, a real‐space multiple‐scattering formalism and a rotationally invariant local density approximation. Values of the Hubbard parameter are calculated ab initio using the constrained random‐phase approximation. The combination of the real‐space Green's function with Hubbard model corrections provides an efficient approach to describe localized correlated electron states in these systems, and their effect on core‐level X‐ray spectra. Results are presented for the projected density of states and X‐ray absorption spectra for transition metal‐ and lanthanide‐oxides. Results are found to be in good agreement with experiment.     

Compton profiles of electron momentum distribution inβ-Ga

We report for the first time the Compton profiles of electron momentum distribution inβ-gallium calculated along the crystallographic directions (100), (110) and (111). The conduction electron states for this purpose are determined in the energy band calculations using model potential. The core states, on the other hand, are represented each by a single tight-binding function. The results show that the Compton profiles are nearly isotropic with very little directional dependence, which is suggestive of a free-electron-like distribution of the conduction electrons in this system. The latter conclusion is in close confirmity with similar conclusions drawn in augmented plane wave (APW) calculation of energy bands and the derived Knight-shift results inβ-Ga.     

The effect of a transverse electric field on the electronic properties of an armchair carbon nanoscroll

In this work, we use the tight-binding model to study the low-energy electronic properties of carbon nanoscrolls subject to the influences of a transverse electric field. A carbon nanoscroll can be considered as an open-ended spirally wrapped graphene nanoribbon. The inter-wall interactions will alter the subband curvature, create additional band-edge states, modify the subband spacing or energy gap, and separate the partial flat bands. Furthermore, the energy band symmetry about the Fermi level is lifted by such interactions. The truncated Archimedean spiral ρ?=?r _a θ?+r is used to describe the spiral structures of carbon nanoscrolls. The energy gap is found to oscillate significantly with r, and exhibits complete energy gap modulations. With the inclusion of a transverse electric field, the band structures are further altered. Inter-wall hoppings will cause electron transfers between different atoms leading to distortions of the electron wavefunctions. The main features of the energy dispersions are directly reflected in the density of states. The numbers, heights, and energies of the density of states peaks are dependent on the electric field strength.     

Ion-dipole dynamics

A unified semi-classical theory applicable to ion-polar molecule reaction kinetics and electron-dipole spectroscopy is presented within a planar ion/point-dipole model. The forms of the trapped periodic orbits that constitute dividing surfaces between internal and external regions of phase space are determined and their properties are shown to be well represented by a semianalytical adiabatic theory. Subsequent applications of the adiabatic theory to electron-dipole dynamics (a) yield a good approximation to the critical dipole for electron capture and (b) predict an exponential gap law for the excited states of electron/fixed dipole states, in good agreement with recent ab initio calculations. Extension of the theory to include dipoles of finite length, d, provides a correlation of the critical strength with d/I ^1/2 where I is the molecular moment of inertia.     

A new cluster model interpretation of the anomalous lifetime of <Superscript>14</Superscript>C

A new cluster model solution to the long-standing nuclear structure problem of describing the anomalously long lifetime of ¹⁴C is presented. Related beta-decay data for ¹⁴O to states in ¹⁴N, gamma-decay data between low-lying positive parity states in ¹⁴N and the elastic and inelastic magnetic dipole electron scattering from ¹⁴N data are all shown to be very accurately described by the model. The shapes of the beta spectra for the A = 14 system are also well reproduced by the model. The model invokes four-nucleon tetrahedral symmetric spatial correlations arising from three- and four-nucleon interactions, which yields a high degree of SU(4) singlet structure for the clusters and a tetrahedral intrinsic shape for the doubly magic ¹⁶O ground state. The large quadrupole moment of the ¹⁴N ground state is obtained here for the first time and arises because of the almost 100% d-wave deuteron-like-hole cluster structure inherent in the model.     

Rigorous solution of a Hubbard model extended by nearest‐neighbour Coulomb and exchange interaction on a triangle and tetrahedron

The Hubbard model extended by both nearest‐neighbour (nn) Coulomb correlation and nearest‐neighbour Heisenberg exchange is solved rigorously for a triangle and tetrahedron. All eigenvalues and eigenvectors are given as functions of the model parameters in a closed analytical form. For fixed electron numbers we found a multitude of level crossings, both in the ground state and in the excited states in dependence on the various model parameters. By coupling an ensemble of clusters to an electron bath we get the cluster gas model or the cluster gas approximation, if an extended array of weak‐interacting clusters is considered. The grand‐canonical potential Ω (μ, T, h) and the electron occupation N (μ, T, h) of the related cluster gases were calculated for arbitrary values (attractive and repulsive) of the three interaction constants. For the cluster gases without the additional interactions we found various steps in N (μ, T = 0, h = 0) higher than one. The reason is the degeneration of ground states differing in their electron occupation by more than one electron. For the triangular cluster gas we have one such degeneration point. For the tetrahedral cluster gas two. As a consequence, we do not find areas with one electron in the μ‐U ground‐state phase diagram of the triangular cluster gas or with one, two and five electrons in the case of the tetrahedral cluster gas. The degeneration point of the triangular cluster gas can not be destroyed by an applied magnetic field. This holds also for the lower degeneration point of the tetrahedral cluster gas. Otherwise, the upper degeneration point breaks down at a critical magnetic field h_c. The dependence of h_c on U shows a maximum for strong on‐site correlation. The influence of nn‐exchange and nn‐Coulomb correlation on the ground‐state phase diagrams is calculated. Whereas antiferromagnetic nn‐exchange breaks the degeneration points of the tetrahedral cluster gas partially only, a repulsive nn‐Coulomb correlation lifts the underlying degeneracies completely. Otherwise both ferromagnetic nn‐exchange and attractive nn‐Coulomb interaction stabilise the degeneration points. The consequences of the cluster gas results for extended cluster arrays are discussed.     

Alkali metal oxides: Occupied,unoccupied and excited states

The occupied and unoccupied electronic states of NaO₂ and KO₂ have been investigated by UV photoemission spectroscopy and inverse photoemission spectroscopy, respectively. In addition single electron excitations from occupied into empty levels have been probed by x-ray absorption and electron energy loss spectroscopy. The experimental data are augmented by LCGTO-X model cluster calculations. A detailed assignment of initial and final states is given. The excitation cross sections and an inversion of the ligand field induced3d level splitting in NaO₂ are discussed.     

Excitation spectrum of one-dimensional extended ionic Hubbard model

We use perturbative continuous unitary transformations (PCUT) to study the one dimensional extended ionic Hubbard model (EIHM) at half-filling in the band insulator region. The extended ionic Hubbard model, in addition to the usual ionic Hubbard model, includes an inter-site nearest-neighbor (n.n.) repulsion, V. We consider the ionic potential as unperturbed part of the Hamiltonian, while the hopping and interaction (quartic) terms are treated as perturbation. We calculate total energy and ionicity in the ground state. Above the ground state, (i) we calculate the single particle excitation spectrum by adding an electron or a hole to the system; (ii) the coherence-length and spectrum of electron-hole excitation are obtained. Our calculations reveal that for V = 0, there are two triplet bound state modes and three singlet modes, two anti-bound states and one bound state, while for finite values of V there are four excitonic bound states corresponding to two singlet and two triplet modes. The major role of on-site Coulomb repulsion U is to split singlet and triplet collective excitation branches, while V tends to pull the singlet branches below the continuum to make them bound states.     

Polarised hot electron luminescence in p-GaAs: Electric field effects

Electrons photo-excited to high-energy conduction band states of GaAs exhibit complex energy and momentum distributions determined by the anisotropic valence band structure and the optical matrix elements. In p-type GaAs a fraction of these hot electrons combine with localised acceptor states, producing a hot electron luminescence (HEL) spectrum with a cascade of peaks corresponding to discrete energy losses resulting from LO-phonon emission. The highest peak involves unscattered electrons, and their energy distribution is due to warping of the initial heavy-hole (HH) bands. We report measurements of the line shape of this 0-HH peak, and its polarisation profile which identifies emission from electrons along particular directions. An applied electric field of 1 kV cm⁻¹ distorts the hot electron momentum distribution, and this is reflected in the polarisation profile. These line shapes and profiles, with and without field, are calculated using a computer model incorporating a band structure and optical matrix elements, the effect of electric field being included using a k-broadening model. The data and model are in good quantitative agreement assuming an electron lifetime of 100 fs, and confirm the expected differences in the profiles for different excitation polarisation states and applied field directions.     

Radially dependent antishielding factor γ(r) of the Sc3+ ion in the solid state

We report the results of our calculation of γ(r), the radially dependent antishielding factor of Sc³⁺ ion in the crytalline environment. Watson sphere model is used to approximately represent the crystal potential. Differential equations resulting from non-orthogonal Hartree-Fock perturbation theory are solved to obtain perturbations to core electron states. Contribution to γ(r) from electron self-consistency effect has been evaluated by using the latter wave-functions in the many-body expression of Schmidtet al.     

Local environment and electron correlation effects on the magnetic properties of clusters

The electronic and magnetic properties of clusters are investigated in the framework of the Hubbard model by treating electron correlations effects in a saddle-point slave-boson approximation. The size dependent single-particle spectrum is calculated using a third moment real-space expansion of the local density of states. Results for the magnetic moments, magnetic order, average number of double occupations and hopping renormalizations are given as a function of the local coordination number z, for different representative values of the Coulomb interaction strength U/t and band filling n. Several transitions between paramagnetic, ferromagnetic and antiferromagnetic behaviors are obtained as a function of z. The environment dependence of the magnetic behavior and of the degree of electron delocalization is analyzed. Advantages and limitations of the present approach are discussed. Received: 8 January 1998 / Revised: 22 June 1998 / Accepted: 6 August 1998     

Single and double electron capture processes in slow Ne q+-He (q=10, 6) collisions

The cross sections for single and double electron capture to the states Ne⁹⁺ n) with n=3–6 and Ne⁸⁺(3l,n′l′), Ne⁸⁺(4l,n′l′) with n′⩾4 and also the cross sections for single electron capture to the states Ne⁵⁺(3) in collisions of Ne¹⁰⁺ and Ne⁶⁺ with He atoms are calculated for collision energies in the interval from 10 to 150 keV. The calculation is carried out in the multichannel Landau-Zener, Nikintin, and Landau-Zener-Chaplik models with allowance for the radial coupling of the channels at crossing points of the energies of the quasidiabatic twoelectron states of the quasimolecule. The energies of the two-electron states are calculated in the effective potential method to first order in perturbation theory in the residual electron-electron interaction. The energies of the adiabatic states in the neighborhoods of the crossings of quasidiabatic terms are determined by the configuration interaction method. It is found that in Ne¹⁰⁺-He collisions the electron is captured mainly to the n=5 state of the Ne⁹⁺ ion. The cross section for double electron capture to the 3lnl′ state (n⩾4) of the Ne⁸⁺ ion is an order of magnitude smaller than the cross section for single electron capture. The contribution to the total cross section for double electron charge transfer from the 4l4l′ 4l5l′, and 4l6l′ states is approximately 25%. The dependence of the cross sections for double electron charge transfer on the values of l and l′ is investigated. Zh. Tekh. Fiz. 69, 15–28 (January 1999)     

Conductivity-dependent cathodoluminescence in BaTiO3, SrTiO3 and TiO2

It is reported that similar cathodoluminescence spectra are excited by an electron beam striking BaTiO₃, SrTiO₃ and TiO₂ ceramics at room temperature. The energy location of the luminescence bands does not depend on various doping or reduction treatments. The luminescence intensity increases with the electron beam current as well as with the conduction electron density. The luminescence is interpreted as a fundamental transition of local character in the TiO₆ octahedron; the conduction electrons localized at the Ti sites in polaron states recombine with the 0–2p valence electron defects. The shape and energy location of the luminescence spectra are qualitatively in accordance with an explanation in terms of a configuration coordinate model.     

On Algebraic Integrability of the Deformed Elliptic Calogero-Moser Problem

Abstract

We discuss stationary solutions of the discrete nonlinear Schrödinger equation (DNSE) with a potential of the ? ⁴ type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a 1D chain of atoms — the (Rashba)–Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another relevant example is that of superconducting states in layered superconductors described by the same DNSE. Amongst many other applications the typical example for a classical lattice is a system of coupled nonlinear oscillators. We present the exact energy spectrum of this model in the strong coupling limit and the corresponding wave function. Using this as a starting point we go on to calculate the wave function for moderate coupling and find that the energy eigenvalue of these structures of the wave function is in exquisite agreement with the exact strong coupling result. This procedure allows us to obtain (numerically) exact solutions of the DNSE directly. When applied to our typical example we find that the wave function of an electron on a deformable lattice (and other quantum or classical discrete systems) may exhibit incommensurate and irregular structures. These states are analogous to the periodic, quasiperiodic and chaotic structures found in classical chaotic dynamics.     

Modified cascade model of resonant Raman scattering: a case study of UV Raman scattering in Zn1−xMnxO thin films

The cascade model of inelastic resonant Raman scattering considers real electronic states in the conduction band (CB) as intermediaries to explain multiple longitudinal optical (LO) Stokes‐shifted lines in the emission spectra. In this study, we report modification in the cascade model under conditions where the scattered photons after multiple transitions have energy lower than the bandgap (E_g) and give rise to higher order n‐LO lines. The higher order n‐LO lines involve electron transition between the trap levels, which are created by impurities or defects in the forbidden energy gap, and are analogous to the real electronic states in CB, depending on the density of defects or impurities in the lattice. The presence of traps in the forbidden gap (1) acts as virtual intermediate states giving rise to higher order n‐LO modes and (2) tends to decrease the radiative recombination probability leading to quenching of the luminescence emission and line width (full‐width at half‐maximum) broadening. Ultraviolet Raman scattering in Mn‐doped ZnO (Zn_1−xMn_xO) thin films were investigated and the experimental observations analyzed in the domain of the modified cascade model. Copyright © 2011 John Wiley & Sons, Ltd.     

Quasistationary states of an electron in a spherical β-HgS/β-CdS/β-HgS nanoheterosystem

The electron scattering matrix for spherically symmetric states in a spherical β-HgS/β-CdS/β-HgS nanoheterosystem is calculated. The positions of the energy levels and the lifetimes of an electron in the corresponding states are found as functions of the geometric parameters of the system and analyzed. Fiz. Tverd. Tela (St. Petersburg) 41, 2081–2083 (November 1999)     

Theoretical calculation of atomic spectrum for 1s23l4l′ states of beryllium-like ions

Using the saddle-point variation and saddle-point complex-rotation methods, energies, radiative, and Auger rates are calculated for the doubly-excited states 1s²3l4l′ of beryllium-like ions. The total wave function is expanded by the restricted variation method to saturate the functional space and improve the nonrelativistic energy. Relativistic corrections and mass polarization effects are taken into account by the first-order perturbation theory. The partial Auger rates for these states are studied. The calculated Auger electron energies are compared with the experimental results which are observed in high resolution electron spectroscopy. The total radiative rates and the total Auger rates for these doubly-excited states 1s²3l4l′ in the beryllium-like ions are also analyzed along with the increase of atomic number Z. Calculated results show that the total Auger rates are several orders of magnitude larger than the total radiative rates for these low-Z systems.     

Deconvolution of appearance potential spectra

Soft x-ray appearance potential spectra from solids carry information on the local density of unoccupied states in the surface region of the sample. The intensity of the emitted characteristic radiation is, according to a simple model, proportional to a convolution product of the transition densities of the incoming electron and the ionized core electron. In a first approximation, the two transition densities are proportional to the density of states in the unoccupied part of the conduction band. Attempts to retrieve the density of states from measured spectra must rely on deconvolution procedures. In this paper, we introduce a new simple method. It is essentially a stabilized version of the Hagstrum-Becker method which appears to work quickly and reliably. As an example, the method is applied to an ironL _III appearance potential spectru. Comparison of the results with a theoretical calculation of the density of states and with measured Bremsstrahlungsisochromats obtained by Turtle and Liefeld strongly supports the self-convolution model in this case.     

Near-threshold electron-impact ionization of calcium atoms

The electron-impact ionization of calcium atoms is studied in the near-threshold energy range (from 6.11 to 16 eV). Experiments were performed by the method of intersecting electron and atomic beams with the recording of formed positive calcium ions. The electron beam (ΔE _1/2 = 0.15 eV) was formed using a hypocycloidal electron monochromator. An analysis of the specific features of ionization cross sections revealed a contribution from the excitation and decay of low-lying autoionization atomic states, which converge to the excitation thresholds of the 3d, 4p, and 5s ionic levels, and resonances (long-lived states of negative ions). The specific features of cross sections are identified using the experimental and theoretical data on photoionization (photoabsorption).