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.