Investigations on the Relativistic Interactions in One-Electron Atoms with Modified Yukawa Potential for Spin 1/2 Particles

Abstract

Energy levels of one electron atoms have been re-examined by applying an alternative perturbative scheme in solving the modified Dirac equation (m.d.e.) for the modified Yukawa potential model with a arbitrary spin-orbit quantum number (see equation in the paper) by means Bopp’s shift method instead to solving (m.d.e.) with star product, in the framework of noncommutativity three dimensional real space (NC: 3D-RS). It is observed that the obtained corrections of energies are depended on the new discrete atomic quantum numbers (see equation in the paper) under spin-symmetry and pseudospin symmetry and two infinitesimal parameters (see equation in the paper) which induced by position-position noncommutativity. Furthermore, in limit of parameters (see equation in the paper), the new energy equations for modified Yukawa potential are consistent with the results of ordinary relativistic quantum mechanics for ordinary Yukawa potential. Keywords: Yukawa potential, noncommutative space, star product, Bopp’s shift method and Dirac equation.