A relativistic effective Hamiltonian for S-state ions

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This paper uses the 'effective operator technique' to develop a relativistic formulation to describe the crystalline electric field splitting of an S-state ion. This formulation leads to an effective Hamiltonian which is capable of describing the EPR and ENDOR spectra observed from S-state ions such as Gd3+. It replaces the traditional phenomenological spin Hamiltonian and reveals that all those total angular momentum tensor operators permitted by symmetry considerations are included. It is shown that Kramer's theorem which is valid only for spin states must be modified to apply to only the lowest degenerate level of the ground state of any ion since all tensor operators Tqk(J) where k is odd and k not=1 are allowed because J, and not S, is a good relativistic quantum number.