Geometric Algebra and Einstein’s Electron

This thesis entitled Geometric algebra and einsteins electron: Deterministic field theories .The work in this thesis clarifies an important part of Koga’s theory.Koga also developed a theory of the electron incorporating its gravitational field, using his substitutes for Einstein’s equation.The third chapter deals with the application of geometric algebra to Koga’s approach of the Dirac equation. In chapter 4 we study some aspects of the work of mendel sachs (35,36,37,).Sachs stated aim is to show how quantum mechanics is a limiting case of a general relativistic unified field theory.Chapter 5 contains a critical study and comparison of the work of Koga and Sachs. In particular, we conclude that the incorporation of Mach’s principle is not necessary in Sachs’s treatment of the Dirac equation.

Semiclassical theory of shot noise in ballistic n+in+ semiconductor structures: relevance of Pauli and long range Coulomb interactions

We work out a semiclassical theory of shot noise in ballistic n+-i-n+ semiconductor structures aiming at studying two fundamental physical correlations coming from Pauli exclusion principle and long-range Coulomb interaction. The theory provides a unifying scheme which, in addition to the current-voltage characteristics, describes the suppression of shot noise due to Pauli and Coulomb correlations in the whole range of system parameters and applied bias. The whole scenario is summarized by a phase diagram in the plane of two dimensionless variables related to the sample length and contact chemical potential. Here different regions of physical interest can be identified where only Coulomb or only Pauli correlations are active, or where both are present with different relevance. The predictions of the theory are proven to be fully corroborated by Monte Carlo simulations.

Self-consistent theory of current and voltage noise in multimode ballistic conductors

Electron transport in a self-consistent potential along a ballistic two-terminal conductor has been investigated. We have derived general formulas which describe the nonlinear current-voltage characteristics, differential conductance, and low-frequency current and voltage noise assuming an arbitrary distribution function and correlation properties of injected electrons. The analytical results have been obtained for a wide range of biases: from equilibrium to high values beyond the linear-response regime. The particular case of a three-dimensional Fermi-Dirac injection has been analyzed. We show that the Coulomb correlations are manifested in the negative excess voltage noise, i.e., the voltage fluctuations under high-field transport conditions can be less than in equilibrium.

Theoretical modeling of photon and electron-stimulated Na and K desorption from SiO2

The mechanism of generation of atomic Na and K from SiO2 samples has been studied using explicitly correlated wave function and density functional theory cluster calculations. Possible pathways for the photon and electron stimulated desorption of Na and K atoms from silicates are proposed, thus providing new insight on the generation of the tenuous Na and K atmosphere of the Moon.

Acid-Base. Surface Electron Donatin6 &.Catai.Ytlc Properties Of Some Binary Mixed Oxides Containing Rare Earth Elements

Catalysis research underpins the science of modern chemical processing and fuel technologies. Catalysis is commercially one of the most important technologies in national economies. Solid state heterogeneous catalyst materials such as metal oxides and metal particles on ceramic oxide substrates are most common. They are typically used with commodity gases and liquid reactants. Selective oxidation catalysts of hydrocarbon feedstocks is the dominant process of converting them to key industrial chemicals, polymers and energy sources.[1] In the absence of a unique successfiil theory of heterogeneous catalysis, attempts are being made to correlate catalytic activity with some specific properties of the solid surface. Such correlations help to narrow down the search for a good catalyst for a given reaction. The heterogeneous catalytic performance of material depends on many factors such as [2] Crystal and surface structure of the catalyst. Thermodynamic stability of the catalyst and the reactant. Acid- base properties of the solid surface. Surface defect properties of the catalyst.Electronic and semiconducting properties and the band structure. Co-existence of dilferent types of ions or structures. Adsorption sites and adsorbed species such as oxygen.Preparation method of catalyst , surface area and nature of heat treatment. Molecular structure of the reactants. Many systematic investigations have been performed to correlate catalytic performances with the above mentioned properties. Many of these investigations remain isolated and further research is needed to bridge the gap in the present knowledge of the field.

Theory for the change of bond character in divalent-metal clusters

To determine the size dependence of the bonding in divalent-metal clusters we use a many-electron Hamiltonian describing the interplay between van der Waals (vdW) and covalent interactions. Using a saddle-point slave-boson method and taking into account the size-dependent screening of charge fluctuations, we obtain for Hg_n a sharp transition from vdW to covalent bonding for increasing n. We show also, by solving the model Hamiltonian exactly, that for divalent metals vdW and covalent bonding coexist already in the dimers.

Double-autoionization decay of resonantly excited single-electron states

Perturbation theory in the lowest non-vanishing order in interelectron interaction has been applied to the theoretical investigation of double-ionization decays of resonantly excited single-electron states. The formulae for the transition probabilities were derived in the LS coupling scheme, and the orbital angular momentum and spin selection rules were obtained. In addition to the formulae, which are exact in this order, three approximate expressions, which correspond to illustrative model mechanisms of the transition, were derived as limiting cases of the exact ones. Numerical results were obtained for the decay of the resonantly excited Kr 1 3d^{-1}5p[^1P] state which demonstrated quite clearly the important role of the interelectron interaction in double-ionization processes. On the other hand, the results obtained show that low-energy electrons can appear in the photoelectron spectrum below the ionization threshold of the 3d shell. As a function of the photon frequency, the yield of these low-energy electrons is strongly amplified by the resonant transition of the 3d electron to 5p (or to other discrete levels), acting as an intermediate state, when the photon frequency approaches that of the transition.

Photoionization of Kr near 4s threshold: II. Intermediate-coupling theory

The Kr 4s-electron photoionization cross section as a function of the exciting-photon energy in the range between 30 eV and 90 eV was calculated using the configuration interaction (CI) technique in intermediate coupling. In the calculations the 4p spin-orbital interaction and corrections due to higher orders of perturbation theory (the so-called Coulomb interaction correlational decrease) were considered. Energies of Kr II states were calculated and agree with spectroscopic data within less than 10 meV. For some of the Kr II states new assignments were suggested on the basis of the largest component among the calculated CI wavefunctions.

Photoionization of Kr near the 4s threshold: I. Experiment and LS coupling theory

Absolute cross sections for the transitions of the Kr atom into the 4s^1 and 4p^4nl states of the Kr^+ ion were measured in the 4s-electron threshold region by photon-induced fluorescence spectroscopy (PIFS). The cross sections for the transitions of the Kr atom into the 4s^1 and 4p^4nl states were also calculated, as well as the 4p^4nln'l' doubly excited states, in the frame of LS-coupling many-body technique. The cross sections of the doubly-excited atomic states were used to illustrate the pronounced contributions of the latter to the photoionization process, evident from the measurements. The comparison of theory and experiment led to conclusions about the origin of the main features observed in the experiment.

Three-electron radiative transitions

A new type of many-electron radiative transitions involving three electrons is predicted. The results of their investigation by many-body perturbation theory are presented. New spectral lines observed in the wavelength range of 37.5 to 54.0 nm by means of photon-induced fluorescence spectroscopy (PIFS) following the excitation of the Kr I 3d{^-1}np resonances are reported and compared with the predictions.

Application of inclusive probability theory to heavy ion-atom collisions

Using the independent particle model as our basis we present a scheme to reduce the complexity and computational effort to calculate inclusive probabilities in many-electron collision system. As an example we present an application to K - K charge transfer in collisions of 2.6 MeV Ne{^9+} on Ne. We are able to give impact parameter-dependent probabilities for many-particle states which could lead to KLL-Auger electrons after collision and we compare with experimental values.

Study of 3d - 4f and 3d - 5f quartet and doublet transitions of doubly excited three-electron ions

We present the first observation of optical transitions between doubly excited doublet states in the term systems N V, 0 VI and F VII. The spectra were produced by foil excitation of fast ion beams. The assignment of the spectral lines was made by comparison with the results of MCDP calculations along the isoelectronic sequence. The same method also led to the identification of two 3d - 4f quartet transitions in Mg X.

Transitions between quintet states of doubly excited four-electron ions

Following an earlier observation in F VI we identified the line pair 1s2s2p^2 {^5P}-1s2s2p3d {^5P^0} , {^5D^0} for the elements N, O, Mg, and tentatively for A1 and Si in beam-foil spectra. Assignment was established by comparison with Multi-Configuration Dirac-Fock calculations along the isoelectronic sequence. Using this method we also identified some quartet lines of lithium-like ions with Z > 10.

Electron-Nuclear Correlation in Laser-Driven Diatomic Molecules

The interaction of short intense laser pulses with atoms/molecules produces a multitude of highly nonlinear processes requiring a non-perturbative treatment. Detailed study of these highly nonlinear processes by numerically solving the time-dependent Schrodinger equation becomes a daunting task when the number of degrees of freedom is large. Also the coupling between the electronic and nuclear degrees of freedom further aggravates the computational problems. In the present work we show that the time-dependent Hartree (TDH) approximation, which neglects the correlation effects, gives unreliable description of the system dynamics both in the absence and presence of an external field. A theoretical framework is required that treats the electrons and nuclei on equal footing and fully quantum mechanically. To address this issue we discuss two approaches, namely the multicomponent density functional theory (MCDFT) and the multiconfiguration time-dependent Hartree (MCTDH) method, that go beyond the TDH approximation and describe the correlated electron-nuclear dynamics accurately. In the MCDFT framework, where the time-dependent electronic and nuclear densities are the basic variables, we discuss an algorithm to calculate the exact Kohn-Sham (KS) potentials for small model systems. By simulating the photodissociation process in a model hydrogen molecular ion, we show that the exact KS potentials contain all the many-body effects and give an insight into the system dynamics. In the MCTDH approach, the wave function is expanded as a sum of products of single-particle functions (SPFs). The MCTDH method is able to describe the electron-nuclear correlation effects as the SPFs and the expansion coefficients evolve in time and give an accurate description of the system dynamics. We show that the MCTDH method is suitable to study a variety of processes such as the fragmentation of molecules, high-order harmonic generation, the two-center interference effect, and the lochfrass effect. We discuss these phenomena in a model hydrogen molecular ion and a model hydrogen molecule. Inclusion of absorbing boundaries in the mean-field approximation and its consequences are discussed using the model hydrogen molecular ion. To this end, two types of calculations are considered: (i) a variational approach with a complex absorbing potential included in the full many-particle Hamiltonian and (ii) an approach in the spirit of time-dependent density functional theory (TDDFT), including complex absorbing potentials in the single-particle equations. It is elucidated that for small grids the TDDFT approach is superior to the variational approach.