Investigating Muonic Hydrogen Atom Energy Spectrum Using Perturbation Theory in Lowest Order

Abstract

This work presents a quantum mechanical calculation of corrections in energy levels of muonic hydrogen atom using a potential due to finite size proton. Muonic hydrogen (μ-p) is an exotic atom in which the muon (μ⁻) replaces the electron "orbiting around" the proton in normal atomic hydrogen. Corrections in energy levels of Muonic hydrogen atom are calculated using a potential due to finite size proton. This Thesis analyzes the implications of Muonic hydrogenic atoms compared to standard hydrogenic atoms. These calculations are performed with Schrödinger wave functions with Coulomb potential using perturbation theory. The finite size of proton gives values of Lamb shift higher than that of point charge. The fine structure correction is very small compared to the Lamb shift values of Muonic hydrogen as we can see from the literature review. Therefore, as we have seen through all the above calculation of 1s, 2s and 2p, the application of perturbation theory has shown us that the energy correction is very small at each state. So the perturbation at higher order become small and small compared to the zero order at each state and even it can be ignored for higher orders. From this we can say that the interaction of electron with proton at higher state will be low which justifies that proton is not a large spherical shaped but it has finite size.

Keywords: coulomb potential; Point proton; Finite size proton; muonic hydrogen atom; Energy levels corrections;  Lamb shift.

DOI: 10.7176/APTA/83-02

Publication date: February 29^th 2020