Soft X-ray transition matrix elements: The role of approximation of the valence states

The coordinate, momentum and potential forms of the interband transitions matrix elements are equivalent when the initial and the final states are exactly known. For the soft X-ray transitions we assume exact core states, and approximate valence states. Then the three different forms of the matrix elements are no longer equivalent and are related by new, more general expressions. From these the qualitative conclusions regarding the appropriate form of the approximated valence states are derived. It turns out, that the orthogonalization of the approximate valence wave function to the core states is very important for the correct behaviour of the photon energy dependence of the soft X-ray emission. These results are illustrated by simple numerical examples.     

Electronic structure of PbI2 from photoelectron spectra and the exciton problem

The valence band density of states for PbI₂ is determined from X-ray and u.v. induced photoelectron spectra. It is shown that the band derived from Pb 6s states is at 8 eV binding energy and not at the top of the valence bands as suggested by band structure and charge density calculations. A rigid shift in the predominantly iodine 5p derived bands to lower binding energy brings the band structure calculations into essential agreement with experiment. Pb 5d core level binding energies determined here are used to derive core level exciton energies of 0.7 eV from published reflectivity spectra.     

On the self-energy of electrons in metals

The electron self-energy of unoccupied states is investigated taking into account dynamical screening and nonlocal exchange. To obtain agreement with experiment it is crucial to go beyond the framework of the homogeneous electron gas and include the nonlocal exchange with electrons in valence and core shells. This contribution of atomic origin gives rise to a considerable, almost linear energy dependence of the self-energy over a wide energy range in agreement with experimental findings for many substances and in disagreement with the local density approximation. Quantitative results are presented for Ag.     

Application of the method of asymptotic projection to the calculation of vertical ionization potentials

An alternative method is proposed for the calculation of ionized states corresponding to the excitation of both valence and core electrons. Unlike the well-known approaches, in which such states are constructed by removing an electron from the corresponding spin orbital, the method proposed employs the requirement that all the spin orbitals of the ionized system are orthogonal to the spin orbitals of the neutral system. The proper spin symmetry and the orthogonality of the wave functions of these states to the wave function of the neutral molecule are ensured by a simple-to-use method of taking into account the orthogonality that was proposed by us earlier. The adequacy of the proposed scheme is demonstrated by the calculation of 15 ionization potentials of diatomic and triatomic molecules at different levels of the theory. The results of the calculations, performed in optimized basis sets including three to five Gaussian s functions per electron, are in good agreement with experimental data and state-of-the-art results obtained by other methods in extended basis sets.     

Arbitrary /-state approximate solutions of the Hulthén potential through the exact quantization rule

In this paper, using the Exact Quantization Rule, we present approximate analytical solutions of the radial Schrödinger equation with non-zero l values for the Hulthén potential in the frame of an approximation to the centrifugal potential for any l states. The energy levels of all bound states can be easily calculated from the Exact Quantization Rule. Specifically, the normalized analytical wave functions are also obtained. Some energy eigenvalues are numerically calculated and compared with those obtained by other methods such as asymptotic iteration, supersymmetry, numerical integration methods, and the schroedinger Mathematica package.     

Comparison of site-specific valence band densities of states determined from Auger spectra and XPS-determined valence band spectra in GeS (001) and GeSe (001)

Auger lineshapes of the Ge M₁M_4,5V and M₃M_4,5V and Se _M1M_4,5V transitions in GeS (001) and GeSe (001) are measured and compared to XPS valence band spectra. Distortions in both types of spectra due to inelastic scattering, analyzer and source broadening, and core level lifetime broadening are removed by deconvolution techniques. The valence band consists of three main peaks at ?2 eV, ?8 eV, and ?13 eV. There is excellent agreement of peak positions in AES and XPS spectra. The Auger lineshapes can be interpreted in terms of site-specific densities of states. They indicate that the states at ～?8 eV and at ～?13 eV are associated with the cation and anion sites respectively. The bonding p-like states at the top of the valence band have both cation and anion character. The Auger lineshapes indicate that the states closest to the valence band maximum are preferentially associated with Ge.     

Valence and core state modifications in Pt3Ti

XPS data for the valence band, the Pt 4? states, and the Ti 2p states are presented for the intermetallic Pt₃Ti. Relative to the Pt valence band, the Pt₃Ti band shows a decrease in the density of states just below the Fermi level and a shift of the centroid to higher (binding) energy. Ti 2p and Pt 4? binding energies showed relatively large shifts with respect to the pure metals. These changes in the valence band density of states and core level binding energies are interpreted as arising from hybridization of the d-orbitals in both metals to form strong intermetallic bonds.     

Manifestation of auger processes in C1s-satellite spectra of single-walled carbon nanotubes

Using the equipment of the Russian-German beamline of the synchrotron radiation at the BESSY II electron storage ring, satellite spectra accompanying the C1s core lines in the cases of single-walled carbon nanotubes and highly ordered pyrolytic graphite have been measured with a high energy resolution. The Auger spectra corresponding to shaking of the valence system of carbon by the core vacancy have been found and investigated. The Auger spectra of the studied single-walled carbon nanotubes and highly ordered pyrolytic graphite are caused by annihilation of the excited π* electron with a hole in the π subband. It has been established that the electron states in the conduction band have 3π* (gT, K, M) symmetry; i.e., they correspond to flat 3π* subband, which is localized by 12–13 eV above the Fermi level. It has been revealed that the general regularities of the distribution of electron states in the valence system insignificantly change during its shake-up by the excited core.     

The formation of heavy-fermion states in non-Fermi-liquid impurity systems

A mechanism for the occurrence of heavy-fermion states in non-Fermi-liquid (NFL) metals with f-shell impurities is proposed. The impurity with an unstable valence is suggested to have an energy spectrum consisting of a deep f-level and quasicontinuum states (narrow band) in resonance with the Fermi energy. Depending on the impurity concentration, the single-site NFL states are generated by the two-channel Kondo scattering for the low concentration (the Kondo regime) or by the screening interaction for a relatively high concentration (the X-ray-edge regime). It is shown that the NFL states are unstable against the scattering of the NFL excitations by electron states of the narrow band. This scattering generates additional narrow Fermi-liquid (FL) resonances at/near the Fermi level in the Kondo regime and in the X-ray-edge regime. The mixed-valence states are shown to be induced by new FL resonances. The mixed valence mechanism is local and is related to the instability of single-site NFL states. The FL resonances lead to the existence of additional energy scales and of pseudogaps near the Fermi level in the mixed-valence states. They also considerably narrow the region with a nearly integer valence.     

Many-body calculations of the hyperfine interaction of some excited states of alkali atoms,using approximate Brueckner or natural orbitals

The theory of maximum-overlap or Brueckner orbitals and of natural Orbitals is reviewed for closed-shell systems. A technique is described to calculate approximate Brueckner or natural orbitals for systems with a single valence electron, and this is applied together with the linked-diagram expansion of effective operators to evaluate the hyperfine interaction of some excited states of alkali atoms. It is found that it is in this way possible to reproduce reasonably well also the highly perturbed interactions of the excitedd states, which is not possible in a low-order expansion based on HF orbitals. Numerical results are given for the 5d state in K and the 4d state in Rb, where good experimental information is available.     

Full inclusion of symmetry in constructing Wannier functions: Chemical bonding in MgO and TiO<Subscript>2</Subscript> crystals

Chemical bonding in MgO and TiO₂ crystals is analyzed using a minimal basis consisting of atomic-type Wannier functions (AWFs) centered at atomic sites in the crystal and constructed from Bloch states of the energy bands originating from the valence states of the atoms. A method proposed earlier for constructing Wannier functions is improved. Symmetrization of the initial Bloch function basis and symmetrical orthogonalization of the generalized Bloch functions greatly reduces computational effort. The prior symmetrization of the Bloch function basis is of fundamental importance in constructing AWFs, because the latter functions have to be centered at the atomic sites and possess the symmetry of the atomic functions in the crystal. The principle that should be followed in selecting the conduction bands originating from the valence states of the atoms of the crystal is formulated. The Bloch functions are calculated using the LCAO approximation within the Hartree-Fock method and density-functional theory. Using the calculated Bloch functions, a minimal valence AWF basis is constructed and calculations of the local characteristics of the electronic structure (atomic charge, bond order, atomic valence) are performed for the MgO and TiO₂ crystals. According to the analysis performed, the covalent component of the chemical bonding in the MgO crystal is negligibly small and TiO₂ is a mixed ionic and covalent crystal with pronounced covalent bonding.     

Adsorbate characterisation by correlation of various photoelectron spectroscopies: CO on W(110)

As a test of the value of various electron spectroscopies and their combination for the characterisation of adsorption states, UPS valence spectra, XPS core spectra (O (1s) and C (1s)) and core satellite spectra (O (1s)), and X-ray induced Auger spectra (O KLL) were measured for various adsorption layers of CO on W(110) prepared at and above room temperature and, for comparison, of oxygen on the same surface. Virgin- and β-CO can readily be distinguished in all four kinds of spectra, while α-CO shows spectra very similar to those of virgin-CO. The conversion of virgin- to β-CO and their desorption can be followed in some detail. For all four techniques, the oxygen derived spectra of β-CO are identical to those of adsorbed oxygen, at about half the intensity. This makes it very likely that CO is dissociated in the β-layer on W(110). Virgin- and α-CO show the typical features of molecularly-adsorbed CO.     

Numerical study of pseudowavefunctions for alkali atoms

Smooth pseudowavefunctions based on known valence and core functions are calculated and displayed for atomic Li, Na and K. These are used to examine some of the approximations employed in pseudopotential calculations; in particular, that of replacing the pseudowavefunction by a constant in the core region. The possibility of neglecting inner core states in pseudopotential calculations is discussed in the light of pseudowavefunctions calculated using only the core state of highest energy.     

First-principles study of electronic structure and magnetism of cubic Al1−xErxN using the LSDA+U approach

First-principles calculations, by means of the full-potential augmented plane wave method using the LSDA+U approach (local spin density approximation with Hubbard-U corrections), have been carried out for the electronic structure of the Al_0.75Er_0.25N. The LSDA+U method is applied to the rare-earth 4? states. We have investigated the electronic and magnetic properties.The Al_0.75Er_0.25N is shown to be a semiconductor, where the filled ? states are located in the valence bands and the empty ones above the conduction band edge. The magnetic interaction of the rare-earth ion with the host states at the valence and conduction band edges has been investigated and discussed.     

Theoretical form factors of metallic aluminum

The form factors of metallic aluminum are obtained from two APW calculations of the density in the solid. The first one is a standard self-consistent Kohn-Sham calculation. The second one includes an exact Hartree-Fock core-valence exchange potential and an approximate local valence—valence exchange-and-correlation potential. The second model decreases the valence contribution and increases the core contribution. But the total form factors are nearly equal in the two schemes. The ‘non-muffin-tin’ contributions to the form factors are shown to be important. The results remain too large compared with experiment.     

Core-hole screening effects in the initial state of Auger emission across the transition metal series

Supercell method is used to study the relaxation and screening effects on the initial state of the Auger transition in metals. Our consideration is based on the assumption that when a core-hole exists long enough before the Auger transition occurs, the occupied valence states relax to screen the core-hole which results in a redistribution of the valence electrons, in particular within the atom that contains the core-hole. In order to make the interaction between the core-holes sites at different atoms negligible, the real metal is simulated by supercells repeated periodically. In each supercell one atom is considered to have a core-hole and many others not to have one. The electronic states concerned by the Auger transition are calculated by the self-consistent full-potential linearized augmented plane wave (FLAPW) method. Different responses of the local valence band on the site of the core-hole have been shown depending on whether the d-bands are partially or completely filled. According to the final state rule, the screening to the two holes in the local valence band after the Auger transition has also been considered, as examples, for Ni and Cu metals. The result shows that, with the existence of two holes in them, the states of the local valence band of Cu relax to atomic-like impurity states, while the local valence band of Ni changes to a much narrow band at the bottom of the original band. As examples, L₃VV and M₁VV Auger spectral profiles of Cu have been calculated in reasonably good agreement with the experiment.     

Continuum shell-model calculation for 14C including core excitations

Elastic and inelastic cross sections for neutron scattering on ¹³C have been calculated up to 10 MeV including excitations of the ¹²C core. The core properties are taken from experiment while the additional neutrons are described in a shell-model basis. Antisymmetrization between the valence particles and the core is taken into account as a second-order perturbation effect. All results including those for the target and the bound states of ¹⁴C are compared to experimental data. The differences between a gaussian and a δ interaction for the valence particles is investigated. The calculation was only feasible with a modified continuum shell model, i.e. approximating the single-particle resonances by bound states. The remaining modified continuum states are damped in amplitude within the resonance region. The residual interaction between modified continuum states is neglected.