NON-LOCAL ELECTRON-POSITRON ENHANCEMENT FACTORS IN SOLIDS

Non-local electron-positron correlation effects in solids are studied. The weighted density approximation is applied to calculations of the non-local electron-positron correlation functions. The calculated weighted density approximation electron-positron enhancement factors for the core electrons are compared with those obtained within the local density approximation. Also, differences in the electron-positron enhancement factors due to the s, p, d and f angular momentum channels of the electron charge density are studied. The formalism is applied to ab initio calculations of positron lifetimes in a variety of metals and silicon. The influence of various approximations to the electron-positron interaction on the positron lifetimes is also presented. The weighted density approximation results are compared to those calculated within the local density approximation, the recent generalized gradient approximation and with experimental data. PACS numbers: 78.70. Bj, The positron lifetime, τ, is an important characteristic of electronic properties of solids. This parameter provides information on the electron density distribution in the host material, thus yielding also useful information on defects in metals and semiconductors. The positron annihilation rate, A = 1/r, is calculated as where nei(re ) is the electron density in the host material, φ+(r p ) is the wave function of a thermalised positron and g(re , rp ) denotes the correlation function of the positron at rp and electrons at re , and r0 and c are the classical electron radius and velocity of light, respectively

Many-body aspects of positron annihilation in the electron gas

We investigate positron annihilation in electron liquid as a case study for many-body theory, in particular the optimized Fermi Hypernetted Chain (FHNC-EL) method. We examine several approximation schemes and show that one has to go up to the most sophisticated implementation of the theory available at the moment in order to get annihilation rates that agree reasonably well with experimental data. Even though there is basically just one number to look at, the electron-positron pair distribution function at zero distance, it is exactly this number that dictates how the full pair distribution behaves: In most cases, it falls off monotonously towards unity as the distance increases. Cases where the electron-positron pair distribution exhibits a dip are precursors to the formation of bound electron--positron pairs. The formation of electron-positron pairs is indicated by a divergence of the FHNC-EL equations, from this we can estimate the density regime where positrons must be localized. This occurs in our calculations in the range 9.4 <= r_s <=10, where r_s is the dimensionless density parameter of the electron liquid.Comment: To appear in Phys. Rev. B (2003

Forecasting: theory and practice

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases

Forecasting: theory and practice

Forecasting has always been in the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The lack of a free-lunch theorem implies the need for a diverse set of forecasting methods to tackle an array of applications. This unique article provides a non-systematic review of the theory and the practice of forecasting. We offer a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts, including operations, economics, finance, energy, environment, and social good. We do not claim that this review is an exhaustive list of methods and applications. The list was compiled based on the expertise and interests of the authors. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of the forecasting theory and practice

Positron Annihilation Study of Defects in the Cage-Type Uranium Compound

The electron and positron properties of the $UIr_2Zn_{20}$ compound of the Fd-3m cage-type crystal structure are studied. The characteristics for the perfect crystal are compared with their counterparts in the elements containing Ir and Zn vacancy. The presence of the vacancy hardly influences the electron charge density around individual atoms. In contrast to electrons, the positron is strongly localized inside the vacancy and the transfer of positron charge is observed. The positron lifetime, τ, appears to be strongly sensitive to the presence and type of the vacancy. Furthermore, this parameter calculated for the perfect crystal is very close to the experimental value for Zn. Here the theoretical values of τ depend on the approach applied to the electron positron (e-p) correlations

Effect of the Positron Distribution on the Electron-Positron Momentum Density Calculated for SiC

To interpret positron annihilation data in solids in terms of the electron momentum density, both the electron-positron interaction and positron distribution have to be considered explicitly. In the present work the influence of the shape of the positron wave function on the calculated electron-positron momentum density in elemental SiC is discussed. It is shown that the form of the positron distribution in the Wigner-Seitz cell has a considerable effect on the resulting annihilation characteristics. Calculations were performed for SiC of 3C diamond structure within the linear muffin-tin orbital-atomic spheres approximation method

Influence of Atomic Sphere Radii on the Electron-Positron Momentum Density Calculated for SiC within the LMTO-ASA

The atomic sphere approximation consists in replacing the Wigner-Seitz polyhedron, containing individual atom, by the sphere of the same volume. In the case of several not equivalent atoms per primitive cell, e.g. for SiC, the radii of atomic spheres, centred at different atoms, are not uniquely determined and should be judiciously chosen. In the present work one studies the effect of choice of atomic sphere radii on the resulting electron band structure and momentum density as well as the electron-positron momentum density. Calculations were performed for SiC within the linear muffin-tin orbital atomic sphere approximation method

Electron-Positron Momentum Densities for Electrons from Individual Core Levels

In the present contribution I focus on various effects affecting the slope of calculated electron-positron momentum densities for electrons from individual core shells. In particular, I discuss the influence of positron distribution, of approximation used for the electron-positron correlation functions, as well as of finite apparatus resolution on the resulting spectra

Effect of the Positron Distribution on the Electron-Positron Momentum Density Calculated for SiC

To interpret positron annihilation data in solids in terms of the electron momentum density, both the electron-positron interaction and positron distribution have to be considered explicitly. In the present work the influence of the shape of the positron wave function on the calculated electron-positron momentum density in elemental SiC is discussed. It is shown that the form of the positron distribution in the Wigner-Seitz cell has a considerable effect on the resulting annihilation characteristics. Calculations were performed for SiC of 3C diamond structure within the linear muffin-tin orbital-atomic spheres approximation method

Influence of Atomic Sphere Radii on the Electron-Positron Momentum Density Calculated for SiC within the LMTO-ASA

The atomic sphere approximation consists in replacing the Wigner-Seitz polyhedron, containing individual atom, by the sphere of the same volume. In the case of several not equivalent atoms per primitive cell, e.g. for SiC, the radii of atomic spheres, centred at different atoms, are not uniquely determined and should be judiciously chosen. In the present work one studies the effect of choice of atomic sphere radii on the resulting electron band structure and momentum density as well as the electron-positron momentum density. Calculations were performed for SiC within the linear muffin-tin orbital atomic sphere approximation method