Estimation of Relativistic Mass Correction for Electronic and Muonic Hydrogen Atoms with Potential from Finite Size Source

Abstract

The simplest atom known to exist in nature is electronic hydrogen atom, which helps us to study fundamental properties and structure of atoms. We can also have muonic hydrogen by replacing electron with muon. In this paper, we revisit Schrodinger equation as an attempt to address the relativistic mass correction to electronic and muonic hydrogen-like atoms with potentials from finite size sources. This study is done with the assumption that the changes in both energy eigenvalues and eigenfunctions are negligible when considering the finite size of the nuclei. The relativistic mass corrections to and states using potential from finite size source are obtained and compared with corrections using potential from point-like source. The results show that, for hydrogen-like atoms with light nuclei the relativistic mass corrections due to the finite size source roughly coincides with that of point-like source. However, for atoms with heavy nuclei the two corrections display strong disagreement in which the corrections with finite size nuclei are significantly smaller than that of point-like nuclei.

Keywords

• Atomic structure; Charge distributions; Finite size source; Hydrogen-like atom; Muonic hydrogen; Point-like source; Relativistic mass correction.