Abstract
A spin Hamiltonian containing the interaction of a one-electron defect center with the surrounding ions is derived. It is shown, by means of the gauge invariance of perturbation theory that for a many-center imperfection in a magnetic field, that one may choose a different gauge for each force center such that the orbital angular-momentum operators refer to the individual force centers. The above result is found to be a consequence of the gauge transformation properties when orbital angular-momentum operators occur in the Hamiltonian. The spin Hamiltonian is applied to the g shift of the VK center and some qualitative results are obtained for the case of nonorthogonal atomic orbitals.
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