A SEARCH FOR ANALYTICAL SOLUTIONS OF KLEIN-GORDON EQUATION FOR A PIONIC ATOM

Abstract

This thesis (research work) explores the solutions of the Klein-Gordon equation for a spin-zero particles in the presence of a Coulomb potential. The equation is derived and modified to incorporate electromagnetic interactions. Through mathematical transformations, the radial Klein-Gordon equation is obtained and further manipulated to match Kummer's equation, allowing for the determination of bound state solutions and energy levels. The binding energies of negatively charged pions in various bound states of mesonic atoms are numerically computed. The results demonstrate the significance of relativistic effects in determining binding energies, particularly at high nuclear charge (𝑍), highlighting how relativistic corrections give rise to pronounced deviation from the non-relativistic binding energies specifically for the s states of the pionic atom. As recommendation, future studies may include strong nuclear interactions and incorporating higher-order relativistic corrections