STUDYING THE EFFECTS OF RELATIVISTIC CORRECTIONS TO MUONIC-HYDROGEN ATOMS

Abstract

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.