Spin-Orbit Coupling - The Free Ion Case

In general, when there is a signihcant orbital angular momentum contribution (i.e. for free ions), the value of the magnetic moment is not given by Eq. 8.21. This is a relativistic effect that increases with the atomic number. The result is that the measured magnetic moments of heavy ions are expected to be lower than the spin-only moment. This is because the spin and orbital momenta couple via the spin-orbit interaction  

In the Russell-Saunders approximation introduced earher, which is appropriate for the 4-d, 5d, and fighter rare-earth elements, the coupling of L and S give a total angular momentum quantum number J that takes on integer values from (L + S) through L — 5  

The total magnetic moment, including spin-orbit coupling, is then given by  

In using Eqs. 8.23 and 8.25, the mles for determining the ground-state configuration of an isolated atom, in the order they must be followed are  

Hund s first rule. S has the maximum value consistent with the Pauli exclusion principle. 

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