Modification of Clebsch- Gordan Coefficients For Heavy Elements

Abstract

In this work, a semi classical expression for the energy shift is obtained. The ground state, Clebsch- Gordan coefficients, angular momentum, matrix elements and the energy shift of some elements like Ag+, Lu3+, Gd3+ and Pr3+ is evaluated. The multiplicity of these elements is found to be strongly dependent on J, so in heavy atoms the LS coupling scheme begins to break down. A similar breakdown occurs in strong external magnetic fields (typically ~ 10 T) in the limit of the failure of LS coupling jj coupling occurs.