Fine Structure and Spin Hamiltonian

The matrices in Table 16 and 17 (or Table 18 and 19 enable) us to ascertain the effect upon Ai when there is an admixture from Ti by spin-orbit coupling. 

Assume first that the Ti state has a three-fold orbital degeneracy as it would if the symmetry were truly cubic. Let this zero order energy be E(Ti) and let the corresponding zero order energy of Ai be E(Ai). Further let 

Since there is no spin-orbit coupling within the Ai term, there is no first order correction to the energy. The second order corrections to the energy ( )) may be read directly from Tables 16 and 17. In terms of C the spin-orbit coupling constant, they are 

It is seen that Ai is no longer six-fold degenerate but is split into three doublets which have different energies. The states with -1- Ms and — Ms are still degenerate and, according to Kramers theorem, there can be no further removal of degeneracies without the use of magnetic fields. It is convenient to define 

The level system may also be described by a spin Hamiltonian 

---