Spin Hamiltonian for a Many-Center Imperfection with Applications to the VK Center

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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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