http://ir.haramaya.edu.et//hru/handle/123456789/120 Mon, 22 Jun 2026 10:35:24 GMT 2026-06-22T10:35:24Z http://ir.haramaya.edu.et//hru/handle/123456789/8700 The Central Field Approximation for Many Electron Atoms Assemahgn, Wondwosun The solution to the Schrodinger equation in case of Hydrogen atom (single particle) can be solved exactly. But if we consider many electron atoms the Schrodinger equation could not solved exactly due to the electron-electron term makes the solution inseparable in single-particle coordinates. However, we can estimate the solutions using different methods. so from those methods the Central Field Approximation provides an excellent starting point to deal with a many-electron system and even if further improvements on this are available and often employed, the Central Field Approximation scheme itself serves a very large number of applications. A set of Quantum defect were also performed and the results have been compared with that of the experimental values. the term quantum defect is a measure of the difference betwen an energy level and the corresponding one in hydrogen. That is the extent to which an outer (valence) electron of a given angular momentum penetrates the inner shell of the atom. While comparing the experimental and calculated values, we have stressed the role of centeral field approximation in Quantum defect theory, some suggestions for improvement of the results are also disscussed 62 Mon, 01 Jul 2019 00:00:00 GMT http://ir.haramaya.edu.et//hru/handle/123456789/8700 2019-07-01T00:00:00Z http://ir.haramaya.edu.et//hru/handle/123456789/8270 STUDYING THE EFFECTS OF RELATIVISTIC CORRECTIONS TO MUONIC-HYDROGEN ATOMS BULLO TOLA ADILA; Dr. Gashaw Bekele (PhD) In this thesis, we have examined the limitations of the nonrelativistic Schrödinger equation focusing on the study of relativistic effects in muonic hydrogen. Muonic hydrogen is an exotic atom where a muon replaces the electron in the orbit around a nucleus. The minimal coupling prescription has been used to incorporate the central potential into the Dirac equation, resulting in coupled Pauli spinor equations. By applying operators for angular momentum and properties of spherical spinors, radial Dirac equations have been derived. The study has addressed the nonrelativistic limit and demonstrated the reduction of the Dirac equation to the Schrödinger equation with first-order relativistic corrections, including the kinetic energy correction, spin orbit coupling, and Darwin term. Python programming language has been employed to generate data for electronic and muonic hydrogen atoms, examining shifts in muonic hydrogen spectra due to relativistic effects. The results have revealed that the relativistic effects are more prominent in muonic hydrogen atom when compared to the ordinary hydrogen due to large rest mass of muon. Moreover, the findings of this work offer insights into muonic hydrogen spectroscopy and have implications for understanding the fine structure of atomic energy levels. 90 Sat, 01 Jun 2024 00:00:00 GMT http://ir.haramaya.edu.et//hru/handle/123456789/8270 2024-06-01T00:00:00Z http://ir.haramaya.edu.et//hru/handle/123456789/8269 ELECTROWEAK THEORY OF NEUTRINO INDUCED PRODUCTION OFF FREE NUCLEON: CASE OF NEUTRAL CURRENT PROCESS ASFAW MEKONNEN BELETE; Gashaw Bekele (PhD) This thesis presents a relativistic description of the neutral current (NC) neutrino-induced associated production of strange particles, in the framework of the Glashow-Salam Weinberg (GSW) model. In the Laboratory (Lab) frame, where the target nucleon is at rest, the kinematics and dynamics of the process were derived separately. The differential cross-section (DCS) was expressed in terms of the norm squared of the invariant matrix element (IME), which was manipulated into the contraction between leptonic and hadronic tensors. In turn, these tensors were evaluated by employing the Casimir’s trick and Feynman trace techniques. In addressing the complexity at hadronic vertex, first it was parameterized by eighteen unknown form factors, which were then extracted from the Born term model by employing the SU(3) symmetry and Cabibbo V-A theory. MATLAB R2016a software was implemented to perform numerical analysis of the production process. The numerical results have led to the identification of the dominant reaction channels in the neutrino-induced associated production of off free proton. The analysis reveals that the -channel is the dominant contributor to the total DCS, followed by the -channel, while the t-channel contribution remains negligible. The total DCS exhibits suppression in the forward scattering region due to destructive interference between these channels. Moreover, increasing the incident neutrino energy leads to an overall increase in the total DCS. Future studies should focus on refining the hadronic vertex parameterization and exploring other NC neutrino-induced strangeness production processes to further advance research in this field. 112 Sat, 01 Jun 2024 00:00:00 GMT http://ir.haramaya.edu.et//hru/handle/123456789/8269 2024-06-01T00:00:00Z http://ir.haramaya.edu.et//hru/handle/123456789/8003 STUDYING THE EFFECT OF UNIFORM BACKGROUND MAGNETIC FIELD ON THE ANTIMUON DECAY WITHIN THE FRAMEWORK OF ELECTROWEAK THEORY DEGINET MATHEWOS DINIKO; Gashaw Bekele (PhD) This thesis examines the impact of uniform background magnetic fields on antimuon decay within the precision framework of electroweak theory. Through analytical derivation of matrix elements from first principles via Feynman diagrams and the exact Dirac equation solution in magnetic fields, novel numerical computations elucidate rich interplay between electroweak forces and intense astrophysical-scale fields. Specifically, a MATLAB 2013a code evaluates kinematics and computes differential decay rates in the laboratory frame as a function of squared four momentum transfer across diversified field strengths for various Landau level initial and final state fermion configurations up to the tenth level. Results reveal the decay rate achieves sharp maxima at moderate momentum transfers before increasing further with augmented fields and momentum, occasionally exhibiting modified peak positions. Differential decay plots uncover distinct rising and oscillating patterns dictated by initial states. This groundbreaking work establishes an unprecedented rigorous theoretical and computational framework to model exotic electroweak transformations at the particle-plasma-gravity astrophysics intersection, providing deeper understanding of decay dynamics under cosmological conditions with profound implications. 116 Sat, 01 Jun 2024 00:00:00 GMT http://ir.haramaya.edu.et//hru/handle/123456789/8003 2024-06-01T00:00:00Z