Abstract
It is shown that second-order perturbation theory leads to the usual quadratic and bilinear terms in the spin-Hamiltonian for a spatially non-degenerate state even when excited states differing in multiplicity from the ground states are included. The form of the spin-Hamiltonian adequate to represent arbitrary splittings of the ground manifold is considered and explicit results given for the fine structure and for those interactions with nucleus and external magnetic field which are linear in I and H respectively.
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