The Analytical Modeling of Nuclear Size Effect on Relativistic Electron in Hydrogen Atom

Abstract

The effects of relativistic motion, the spin-orbit interaction and Zitterbewegung of an electron, which are of the same order of magnitude, defined the fine structure correction to hydrogen spectra. In this work, perturbation theory, as an approximation method is applied to examine the effects of finite sized of atomic nucleus on relativistic motion of electron in hydrogen atom. The nuclear finite corrections to 1s, 2s, 3s, 4s and 5s energy states in hydrogen atom due to the finite size of nucleus were computed and the results showed that the nuclear size effects, which is of order of 10 -6 eV, depends on the size, A(N, Z) of the nucleus and energy states, n of relativistic electron. This suggested that the nuclear size is more effective on relativistic electron in the lower energy levels of heavy nuclei, as the effect varied directly with the nuclear size and inversely with the electron states, n. Thus, the finite size of atomic nucleus has an impact on relativistic motion of an electron. Moreover, a simple model was developed to predict the energy level variation as a function of the size of the nucleus. Therefore, this study justifies the effects of nuclear size on relativistic electron and the measured values are of greatest interest since it will reveal significant changes of the nuclear structure and may also improve the knowledge of fine structure correction.