X-ray photoelectron spectra of halogens in coordination compounds

X-ray photoelectron data on C12p energies for more than 200 coordination compounds of transition metals have been analysed. The effects of the central atom, other ligands, and the geometrical location of the chlorine atom on the C12p energy have been considered and certain regularities have been observed. The data on Br3d and F1s lines in coordination compounds have also been considered.     

The effective ion-ion interaction of heavy alkali metals

The effective ion-ion interaction for the heavy alkali metals is calculated by a full non-local model potential, including exchange and correlation in the screening according to Vashishta and Singwi and in the RPA. The inclusion of the s-d hybridization effects merely following Harrison's theory for transition metals turns out to be inadequate for these metals.     

Systematics of the rare-gas core contributions to the positron annihilation spectra of some simple and transition metals

Taking into account the core electron enhancement factor the rare-gas core contribution to the angular correlation positron annihilation spectra and to the total annihilation rate in some simple and transition metals are calculated. It is shown that the valence high-momentum part of the Gaussian fraction is not negligible in simple metals. In 3d and 4d metals, the rare-gas core part of the total annihilation rate amounts from 9 to 37%. The results are expected to help in the correct interpretation of the positron annihilation data.     

KLL auger and core level (1s and 2p) photoelectron shifts in a series of gaseous sulfur compounds

Core (1s and 2p) X-ray photoelectron shifts and KLL (¹D₂) Auger shifts for 22 sulfur compounds have been measured. The values have been correlated by means of atomic charge plus remote potential or central atom potential models. Either approach is equally effective tor binding energy correlations. The relaxation corrected and transition state models are in general superior to ground state models. Auger shift predictions are however poor in all cases. Absolute total static relaxation and extra-atomic relaxation values have been assessed by using the Auger parameter of Lang and Williams and relativistic atomic calculations for the free atom and its ions. These extra-atomic relaxation components are not additive but rather obey an average contribution behavior. The relaxation shift values have been compared with those obtained from the original Auger parameter (α) of Wagner. The correlation of 1s and 2p binding energies suggested a revised relationship for the Wagner Auger parameter and an equivalent simple form of the Lang and Williams parameter which can be used with satisfactory results when only the usual experimental binding energy (2p) is available in conjunction with the Auger shift.     

Asymptotic potential coefficients for rare gas and alkali atoms and simple molecules interacting with metallic surfaces

Values of the coefficients C₃ and C₅ which describe the asymptotic potential energy between an atom or molecule and a surface, and the constants C_s1 and C_s2 which characterize the surface mediation of the long-range atom(molecule)-atom(molecule) interaction, are calculated for rare gas and alkali or simple molecules, such as NO, H₂, and H₂O, adsorbed on noble and transition metals. These calculated results are obtained using analytic representations of the atomic polarizability and a numerical treatment of the substrate dielectric response obtained from measured optical constants.     

Intrinsic magnetostriction and phase transitions

A new possibility of first-order magnetic phase transitions in simple systems, based on the concept of intrinsic volume-magnetostriction Ω_s ≡ ? V_n/V_n, is suggested. The net volume V_n is defined as the difference between the total lattice volume and the sum of the individual atomic volumes. A magneto-volume equation of state for the net volume: Ω_s = Q₀η^s with s < 2, as well as the dependence of the effective exchange integral on the long-range order parameter η, are postulated. The value s ? 1.5 accounts well for the experimental values of the critical exponents β and δ, as well as for the deviation from linearity of the Arrott—Belov plots obtained for the ferromagnetic transition metals. The model leads to an order—order transition just below the order—disorder transition, thus providing an explanation for the two experimentally found temperatures, the forromagnetic Curie temperature and the paramagnetic Curie—Weiss temperature.     

An ESCA investigation of some thiocyanato complexes

A series of simple thiocyanato complex ions have been investigated as their tetraphenylphosphonium and potassium salts. The binding energies of N, C and S were determined as well as those of the metals. From the first-mentioned data effective charge-values were estimated for the atoms of the ligands. For this purpose linear relations E_b = kq + E_b0 were used that had been previously established within a scheme having C_1s (phenyl) as the internal standard.From the data thus obtained the effective charge on the metal atoms was estimated. For elements where we have sufficient data the same type of linear relation seems to he followed. Tentatively valid examples are E_b(Ni) = 6.74q_Ni + 848.3 eV and E_b(Pd) = 4.45q_Pd + 333.9 eV.In this interpretation the atoms of the metals are considered to be positively charged and surrounded by the negative charge of the electrons occupying the s band.It is further suggested for complexes with pronounced π backbonding (Pt(SCN)₄^2?, Pd(SCN)₄^2? and Hg(SCN)₄^2?) that the C 1s binding energy measured for the carbon atom of the SCN^? ligand is composed of the ionisation energy from the 1s level and an additional term corresponding to the intraligand π → π* transition.     

Numerical calculation of soft-X ray transition probability for the muffin-tin potential

The matrix elements of the coordinate, the momentum and the gradient of the potential were used to calculate the optical transition probability between the valence and core states, obtained for the muffin-tin model of the crystal potential. It has been found that gradV is the most suitable form for the numerical calculation while the other forms can yield substantial errors for both transition and simple metals when the core energy amounts few Rydbergs and the amplitude of the core function reaches at the muffin-tin radius 10^–3-10^–2 of its maximum value.     

Electron correlations in alloys of simple and transition metals

The effect of dynamical electron-electron correlations on the electronic structure of the paramagnetic disordered binary alloy of the transition and simple metals is studied for the Anderson model extended to arbitrary concentration of the transition metal impurities. We use the terminal-point approximation for the many-body quantities, which allows us to solve the random part of the problem within the single-site approximation. The many-body part of the problem is treated within the selfconsistent T-matrix approximation, valid for low, but finite concentration of particles ( ? 0.3/atom/spin). For low concentration of the transition metal impurities we obtain results identical with those for the Anderson model. The theory is illustrated numerically for a simple bandstructure model.     

Theory for superconductivity in amorphous transition metals

A theory is presented for superconductivity in amorphous transition metals. It is shown that in contrast to simple metals for transition metals the changes in the phonon spectrum, in the electronic density of states and in the electronic matrix elements which result from strong lattice disorder can enhance as well as decreaseT _c. The numerical results for the superconducting transition temperatureT _c of amorphous 4d-and 5d-transition metals agree well with the experimental results.     

Gaussian estimation of electron scattering cross sections on the basis of a Feynman path integral

A version of Gaussian estimation of a Feynman path integral is considered and its validity for a scattering problem is investigated. Test calculations of the differential and total cross sections are performed for the scattering of a plane wave by a three-dimensional spherically symmetric Gaussian potential and for the electron impact excitation of the 1s → 2s transition in the hydrogen atom. The data on the scattering by a potential are compared with the analogous results obtained using the first Born approximation and the method of phase functions (which gives almost exact results). The excitation cross sections for the transition in the hydrogen atom are compared with those obtained by the convergent close-coupling method. The validity of this approach is demonstrated. The accuracy of the method proposed is acceptable for many cases. For total cross sections, the result obtained in terms of the density matrix formalism turned out to be more exact than that derived from differential cross sections. Among all the above approaches using path integration to solve problems of scattering of electrons by atoms, the method proposed here.     

Heat of mixing in HfCxN1−x compounds from XPS core level binding energy shifts

The XPS core level binding energies for the Hf4f_{$\text{7}\text{2}$}, Cls and Nls level in several nearly stoichiometric HfC_xN_1?x compounds are reported. Using the thermochemical model to calculate core level binding energy shifts in metals the heat of mixing as function of the HfC/HfN ratio is calculated from the position of the Cls binding energies. In addition it is shown that the Hf4f_{$\text{7}\text{2}$} and Nls binding energies can be used to obtain further thermochemical data for these compounds.     

Electron shake-off in neon and the interaction of continuum states

Transition probabilities for shake-off of a 2p electron in a neon atom into the continuum following the creation of a vacancy in the 1s shell by an energetic electron or photon are calculated in the sudden approximation and include the electrostatic interaction between the shake-off electron and the residual ion core. The calculations is based on nonrelativistic Hartree-Fock-Slater wave functions, the residual interaction resulting from the electrostatic term being treated as a perturbation. In the first Born limit as well as in a complete calculation results for the ratio I(^3P)/I(1P = $\text{transition probability to continuum states with}{}^3\text{P}\text{core}\text{transition probability to continuum states with}{}^1\text{P}\text{core are lower than the value 3: 1 predicted by statistics in the independent particle limit}$.     

Transition probabilities for two-photon H(1s–2s) and He(11s–21s) transitions: A partial-closure approach

Transition amplitudes and transition probabilities for the two-photon 1s–2s transition in the hydrogen atom and 1¹ s–2¹ s transition in helium atom have been calculated using a partial-closure approach. The dominant term is calculated exactly and the remaining sum over intermediate states is calculated using a mean excitation energy. Our value of the transition amplitudes agree within 2% with the exact results for the hydrogen case. Our value of the transition probability for hydrogen is 8.50 s⁻¹ which is in good accord with its known value 8.226 s⁻¹. For helium, the photon energy distribution of the metastable 2¹ s state is in good agreement with the accurate values. The corresponding transition probability is 53.7 s⁻¹ which is in good agreement with the accurate value 51.3 s⁻¹.     

Confinement of atoms under general boundary conditions

The energy spectrum of a nonrelativistic quantum particle and hydrogen-like atom is considered under the most general conditions of confinement in a spatial box (vacuum cavity). It is shown that the rearrangement of the lowest energy levels occurring in this case turns out to be considerably more significant when compared with the case of confinement achieved by the impenetrable potential barrier. The role in the rearrangement of this level, played by the von Neumann-Wigner level repulsion effect, is emphasized. For an atom confined in a spherical cavity of radius R, it is also shown that, when the role of the cavity boundary is played by the surface layer of nonzero depth d, the atomic ground state possesses a deep and pronounced minimum for the physically reasonable width and depth of that surface layer, in which the binding energy turns out to be an order of magnitude larger than that of the lowest 1s-level of a free atom E _1s . Also, it becomes possible to achieve a mode when the binding energy of an atom is noticeably higher than E _1s at R on the order of 10–100 nm.     

Vibrational properties of vacancy in bcc transition metals using embedded atom method potentials

The embedded atom method (EAM) potentials, with the universal form of the embedding function along with the Morse form of pair potential, have been employed to determine the potential parameters for three bcc transition metals: Fe, Mo, and W, by fitting to Cauchy pressure (C ₁₂???C ₄₄)/2, shear constants $G_\textrm{v} =({C_{11} -C_{12} +3C_{44}})/5$ and C ₄₄, cohesive energy and the vacancy formation energy. The obtained potential parameters are used to calculate the phonon dispersion spectra of these metals. Large discrepancies are found between the calculated results of phonon dispersion using the EAM and the experimental phonon dispersion results. Therefore, to overcome this inadequacy of the EAM model, we employ the modified embedded atom method (MEAM) in which a modified term along with the pair potential and embedding function is added in the total energy. The phonon dispersions calculated using potential parameters obtained from the MEAM show good agreement with experimental results compared to those obtained from the EAM. Using the calculated phonons, we evaluate the local density of states of the neighbours of vacancy using the Green’s function method. The local frequency spectrum of first neighbours of vacancy in Mo shows an increase at higher frequencies and a shift towards the lower frequencies whereas in Fe and W, the frequency spectrum shows a small decrease towards higher frequency and small shift towards lower frequency. For the second neighbours of vacancy in all the three metals, the local frequency spectrum is not much different from that of the host atom. The local density of states of the neighbours of the vacancy has been used to calculate the mean square displacements and the formation entropy of vacancy. The calculated mean square displacements of the first neighbours of vacancy are found to be higher than that of the host atom, whereas it is lower for the second neighbours. The calculated results of the formation entropy of the vacancy compared well with other available results.     

Excitation of rubidium atoms by electron impact

An analytic central potential containing two adjustable parameters is used to generate wave functions for the ground and excited states of the rubidium atom. The two parameters are chosen so that the potential reproduces accurately known values of optical oscillator strengths for the 5s?np (n≧5) transitions. Using the Born approximation, we calculate generalized oscillator strengths and integrated cross sections up to 5 keV for the 5s?np excitations. Reasonable agreement with experimental data is obtained.     

Self-energy correction to the wave function in the effect of parity violation for the amplitude of the 6s–7s transition in the 133Cs atom

The quantum electrodynamic self-energy correction to the wave function in the effect of parity violation for the amplitude of the 6s–7s transition in the ¹³³Cs atom is calculated in explicit form without using the nonrelativistic approximation for the self-energy operator. The result obtained refines some previous estimates and indicates that the correction to the parity violation may be comparable with the corresponding correction to the vacuum polarization. The necessity of taking complete relativistic account of all the quantum electrodynamic corrections in calculations of the electroweak charge Q _W in atomic systems is shown.     

A theorem for the existence of Majorana fermion modes in spin-orbit-coupled semiconductors

We prove an index theorem for the existence of Majorana zero modes in a semiconducting thin film with a sizable spin-orbit coupling when it is adjacent to an s-wave superconductor. The theorem, which is analogous to the Jackiw-Rebbi index theorem for the zero modes in mass domain walls in one-dimensional Dirac theory, applies to vortices with odd flux-quantum in a semiconducting film in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect. The momentum space construction of the zero-mode solution presented here is complementary to the approximate real space solution of the Bogoliubov-de Gennes equations at a vortex core (Sau et al., arXiv:0907.2239 [17]), proving the existence of non-degenerate zero-energy Majorana excitations and the resultant non-Abelian topological order in the semiconductor heterostructure. With increasing magnitude of the proximity-induced pairing potential, the non-Abelian superconducting state makes a topological quantum phase transition to an ordinary s-wave superconducting state which no topological order.