The Nuclear Finite–Size Corrections to Energies of n = 1, n = 2 AND n = 3 States of Hydrogen Atom

Abstract

The first order perturbative approach has been applied and the finite-size nuclear corrections of order of the scaling factors, ξ, ξ² and ξ³ for n = 1, n = 2 and n = 3 energy levels respectively for the hydrogen atom, have been computed. Results show that as the energy levels increases, the effects of the finite – size nucleus on the orbiting electron is diminishing. This procedure has shown that the concept of finite nuclear size model has an extremely small impact on the energy spectrum of the hydrogen atom. Electron – nucleus interactions, beyond the coulomb potential, modify the atomic property and due to the change from point-charge to finite-size nuclear model the energy level of nucleus is shifted upwards and thus the atomic spectral line for a finite-size nucleus will not coincide with that of its point-size nucleus. This gives us more information on the nuclear charge distribution. Another observation from this work is that with a higher probability of being farther from the nucleus of finite – size charge, the orbiting electrons feel the same effect as the effects due to the point – charge nucleus. Here the finite – size nuclear model have some relevance with the Schrödinger model of hydrogen atom at large distances from the
nucleus.

Keywords: Schrodinger; perturbation; Hamiltonian; wave function; nucleus; point-size; finite–size; potential energy