Size dependent electron momentum density distribution in ZnS

In this paper, we present size dependent electron momentum density distribution in ZnS. ZnS nanoparticles of size 3.8 nm and 2.4 nm are synthesized using the chemical route and characterized by X-ray diffraction (XRD). The Compton profile measurements are performed on both the nano-sized as well as bulk ZnS samples employing 59.54 keV gamma-rays from ²⁴¹Am source. The results reveal that the valence electron density in momentum space becomes narrower with reduction of particle size. To evaluate the charge transfer on compound formation, the ionic model based calculations for a number of configurations of Zn^+xS^−x (0.0≤x≤2) are also performed utilizing free atom Compton profiles. These results suggest different amounts of charge transfer in these materials varying from 1.2 to 2.0 electron from Zn to S atom.     

Analysis of the electronic structure of ZrO2 by Compton spectroscopy

The electronic structure of ZrO₂ is studied using the Compton scattering technique. The first-ever Compton profile measurement on polycrystalline ZrO₂ was obtained using 59.54 keV gamma-rays emanating from the ²⁴¹Am radioisotope. To explain the experimental data, we compute theoretical Compton profile values using the method of linear combination of atomic orbitals in the framework of density functional theory. The correlation scheme proposed by Perdew-Burke-Ernzerhof and the exchange scheme of Becke are considered. The ionic-model-based calculations for a number of configurations, i.e., Zr^+x (O^?x/2)₂ (0 ≤ x ≤ 2), are also performed to estimate the charge transfer on compound formation, and the study supports transfer of 1.5 electrons from Zr to O atoms.     

Anisotropy in the compton profile of copper

Directional Compton profiles of high statistical accuracy are measured by means of a 412 keV gamma-ray Compton spectrometer. The experimental anisotropies are in very satisfactory agreement with earlier measurements and there is good qualitative agreement between the experimental data and a recent band structure calculation. Quantitatively, however, the experimental anisotropy is significantly smaller than predicted by theory.A simple model calculation based on the Seitz approximation, in which higher order Fermi surface volumes all of spherical shape are taken into account in obtaining the momentum density, demonstrates that the major contribution to the Compton profile anisotropy in copper is due to the hybridization which has mixedd-electrons and nearly-free electrons in the top band. Any fine structure in the theoretical anisotropy due to the detailed shape of the Fermi surface cannot be resolved in the present experiment.The potential of analysing the electronic structure of transition metals in terms ofB(r), the Fourier transform of the momentum density, is discussed in detail. The major contribution to the anisotropy arises from localised peaks inB(r) centered on the sites of the translational lattice. Within the Seitz approximation it could be shown that these secondary maxima are caused by the presence of localisedd-electrons in the highest partly occupied band. In conclusion we anticipate that a proper treatment of electron correlation would produce a marked quantitative improvement in the agreement between the present experimental data and the Compton profiles obtained from current band structure calculations.     

Observation of ionic deformation and bonding from compton profiles

We describe a new method of interpreting Compton profile data using a function B(r) which is the autocorrelation function of the one-electron wave function Ψ(r). In any particular direction B(r) can be obtained by a one-dimensional Fourier transform of the corresponding directional Compton profile. The technique is applied to LiF and it provides a means of determining the ionic radii, as well as locating some inadequacies in the tight-binding overlap model for ionic crystals.     

Analysis of the 3-dimensional electron distribution in silicon using directional Compton profile measurements

A method of reconstructing the electron momentum density (p), and its Fourier transform,B(t), from a series of directional Compton profiles is described. It is based on a double Fourier inversion technique and an expansion in lattice harmonic functions. The effect of random errors has been analysed, and the implications for the data collection discussed. We have used the reconstruction technique to obtain (p) andB(t) for silicon from six directional Compton profiles measured with 412 KeV gamma-radiation. The experimental result is in good agreement with earlier measurements and with available solid state theories. A recent Wannier function calculation for silicon using orthogonalised bond orbitals provides a useful tool for identifying the physical origins of the observed anisotropies. A comparison between the information presented in position and momentum space shows that the ease of interpretation depends upon the degree to which the various interactions give rise to localised features in each representation.     

Compton scattering study and electronic properties of vanadium carbide: A validation of hybrid functional

In this paper, we have reported the isotropic Compton profile of VC measured using high energy (661.65 keV) γ-radiations from a ¹³⁷Cs isotope. To compare the experimental momentum densities, we have also employed the linear combination of atomic orbitals (LCAO). In addition, energy bands, density of states and Fermi surface topology of VC have been computed using FP-LAPW and LCAO methods. It is seen that the LCAO with hybridization of density functional theory and Hartree-Fock (so called B3LYP) gives a better agreement with the present Compton profile experiment. This shows validation of an exact exchange part in hybrid density functional. On the basis of energy bands, we have discussed the microscopic origin for the anomalous behavior of hardness of VC. The relative nature of bonding in VC and NbC is also discussed in terms of valence charge densities and Mulliken′s population analysis. To establish the role of Compton profiles in computation of cohesive properties of refractory materials, we have also calculated for the first time the cohesive energy using the present experimental Compton profile and compared it with the existing data.     

Electron momentum density, band structure, and structural properties of SrS

The electron momentum density, the electronic band structure, and the structural properties of SrS are presented in this paper. The isotropic Compton profile, anisotropies in the directional Compton profiles, the electronic band structure and density of states are calculated using the ab initio periodic linear combination of atomic orbitals method with the CRYSTAL06 code. Structural parameters of SrS—lattice constants and bulk moduli in the B1 and B2 phases—are computed together with the transition pressure. The computed parameters are well in agreement with earlier investigations. To compare the calculated isotropic Compton profile, measurement on polycrystalline SrS is performed using 5Ci-²⁴¹Am Compton spectrometer. Additionally, charge transfer is studied by means of the Compton profiles computed from the ionic model. The nature of bonding in the isovalent SrS and SrO compounds is compared on the basis of equal-valenceelectron-density profiles and the bonding in SrS is found to be more covalent than in SrO.     

Compton scattering and charge transfer in Er substituted DyAl2

A unique applicability of Compton spectroscopy in probing the electronic states of rare earth aluminides using high energy (662 keV) γ-rays is reported. We have measured first-ever Compton profiles of Dy_1-xEr_xAl₂ (x=0, 0.2) using 20Ci ¹³⁷Cs Compton spectrometer. The charge reorganization in Dy_1−xEr_xAl₂ (x=0, 0.2), on the formation of compound, has been discussed using the valence band Compton profile data. The experimental Compton profile data unambiguously establish charge transfer from Al to Dy (Dy and Er) on formation of x=0.0 (0.2) compound, which is in tune with spin polarized relativistic Korringa–Kohn–Rostoker (SPR-KKR) calculations. A reasonable agreement between SPR-KKR based Compton profiles and the experimental data show applicability of the Green function method in predicting the electronic properties of rare earth compounds.     

Electronic properties and compton profiles of silver iodide

We have carried out an extensive study of electronic properties of silver iodide in β- and γ-phases. The theoretical Compton profiles, energy bands, density of states and anisotropies in momentum densities are computed using density functional theories. We have also employed full-potential linearized augmented plane-wave method to derive the energy bands and the density of states. To compare our theoretical data, isotropic Compton profile measurement on γ-AgI using ¹³⁷Cs Compton spectrometer at an intermediate resolution of 0.38 a.u. has been undertaken. The theoretical anisotropies are also interpreted on the basis of energy bands.     

Energy, momentum, and force in classical electrodynamics: Application to negative-index media

The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M — these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r, t) and M(r, t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with special relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. The Abraham momentum density p_EM(r,t) = E(r,t) × H(r,t) / c² emerges as the universal electromagnetic momentum that does not depend on whether the field is propagating or evanescent, and whether or not the host media are homogeneous, transparent, isotropic, linear, dispersive, magnetic, hysteretic, negative-index, etc. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.     

High momentum transfer approach to inelastic electron scattering on nuclei and model-independent description of nuclear transition densities

A method of approximating the DWBA transition amplitude at higher momentum transfers is given. It leads to quantitative agreement with the DWBA values, combined with a considerable saving of computing time. The method permits model-independent analyses of inelastic data at higher momentum transfers. The influence of uncertainties in the ground state charge density on the inelastic cross section is studied and found to be negligible. Regardless of the magnitude of Coulomb distortions, the multipole moments B(τ; L, q) are shown to be model-independent quantities for those values of q which lie in the region of measured momentum transfers.     

Momentum densities and Compton profiles of alkali-metal atoms

It is assumed that the dynamics of valence electrons of alkali-metal atoms can be well accounted for by a quantum-defect theoretic model while the core electrons may be supposed to move in a self-consistent field. This model is used to study the momentum properties of atoms from³Li to³⁷Rb. The numerical results obtained for the momentum density, moments of momentum density and Compton profile are found to be in good agreement with the results of more detailed configuration-interaction calculations for the atom³Li. Similar results for¹¹Na,¹⁹K and³⁷Rb are compared with the corresponding Hartree-Fock-Roothaan values only, for want of data from other realistic calculations     

On a low intensity <Superscript>241</Superscript>Am Compton spectrometer for measurement of electron momentum density

In this paper, a new design and construction of a low intensity (100 mCi) ²⁴¹Am γ-ray Compton spectrometer is presented. The planar spectrometer is based on a small disc source with the shortest geometry. Measurement of the momentum density of polycrystalline Al is used to evaluate the performance of the new design. The measured profile is in good agreement with the existing theoretical data and our density functional calculations.      

Charge displaced by a one-body potential in a Fermion assembly in terms of the highest occupied state

For (i) a slowly varying potential V(r) in a Fermi gas and (ii) N particles moving in a linear harmonic-oscillator potential, the total displaced charge and the particle density are respectively written in terms of the highest occupied state.     

Density functional calculation of Compton profiles of metals using phase-space approach

Spherically averaged electron momentum densities (EMD) in Al, V and Cu metals have been calculated by using density functional theory in the phase-space approach. Compton profiles, J(q) and expectation values 〈pⁿ〉 have been computed. These theoretical results show satisfactory agreement with the experimental data for Al, V and Cu.     

Nuclear matter approach to the heavy-ion optical potential: (II). Imaginary part

The heavy-ion optical potentials are constructed in a nuclear matter approach, for the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O and ⁴⁰Ca + ⁴⁰Ca elastic scattering at the incident energies per nucleon E^lab/A ? 45 MeV. The energy density formalism is employed assuming that the complex energy density of colliding heavy ions is a functional of the nucleon density ?(r), the intrinsic kinetic energy density τ⁽²⁾(r) and the average momentum of relative motion per nucleon K_r(≦ 1.5 fm^?1). The complex energy density is numerically evaluated for the two units of colliding nuclear matter with the same values of ρ, τ⁽²⁾ and K_r. The Bethe-Goldstone equation is solved for the corresponding Fermi distribution in momentum space using the Reid soft-core interaction. The “self-consistent” single-particle potential for unoccupied states which is continuous at the Fermi surface plays a crucial role to produce the imaginary part. It is found that the calculated optical potentials become more attractive and absorptive with increasing incident energy. The elastic scattering and the reaction cross sections are in fair agreement with the experimental data.     

Study of two-phonon excitations in superfluid 4He

We explain the second branch of excitations in superfluid ⁴He observed by Cowley and Woods, by accounting for two-phonon contributions to the dynamic structure function, S(k, ω). Our theory gives a good fit with the experimental data in the high energy region for several values of momentum transfer. It is observed that the contribution to S(k, ω) due to two-phonon excitations is of the order of k² as against its k⁴ dependence reported in earlier theories.     

Electron momentum density in Cu<Subscript>0.9</Subscript>Al<Subscript>0.1</Subscript>

A reconstruction technique based on the solution of the Radon transform in terms of Jacobi polynomials is used to obtain the 3D electron momentum density, ϱ(p), from nine high-resolution Compton profiles (CPs) for a Cu_0.9Al_0.1 disordered alloy single crystal. The method was also applied to theoretical CPs computed within the Korringa–Kohn–Rostoker coherent potential approximation (KKR-CPA) first-principles scheme for the same nine orientations of the crystal. The experimental ϱ(p) is in satisfactory agreement with the theoretical ϱ(p), shows most details of the Fermi surface (FS) and exhibits electron correlation effects. We comment on the map of the FS obtained by folding the reconstructed ϱ(p) into the first Brillouin zone, which yields the occupation number density, ϱ(k). A test of the validity of data via a consistency condition (within our reconstruction algorithm) as well as the propagation of experimental noise in the reconstruction of both ϱ(p) and ϱ(k) are investigated. Received: 24 October 2001 / Accepted: 20 January 2002 / Published online: 3 June 2002 RID="*" ID="*"Corresponding author. Fax: +48-71/344-10-29, E-mail: samsel@int.pan.wroc.pl     

Photoelectron (He(I), He(II) and X-ray) spectroscopy of γ-pyrone and its related sulphur derivatives: valence and core ionization energies and shake-up satellites

The photoelectron He(I) and He(II) spectra of 4H-pyran-4-one (1), 4H-thiopyran-4-one (2), 4H-pyran-4-thione (3) and 4H-thiopyran-4-thione (4) are reported. The assignments are based on experimental evidence, taking into account the results of theoretical calculations. The outermost orbital sequences proposed (X = O, S) are n_X (σ), 3b₁ (π), 1a₂(π) for 1, 2 and 4; and 3b₁(π), n_X(σ) and 1a₂(π) for 3. The shifts of the core-ionization energy values for 1–4 are ascribed to a drift of π-charge from the intracyclic heteroatom towards the carbonyl or thiocarbonyl group. Low-energy shake-up satellites (up to 25% with respect to the main line) are observed in the various energy regions of the XPS spectra. They are qualitatively reproduced by CNDO/2 calculations. The most important satellites derive from the transition in the ion corresponding to the 3b₁ (π) → 4b₁(π*) transition in the UV-visible spectra of the neutral molecules. Charge rearrangements accompanying this transition lead to charge depletion of the core-ionized atom.