One-electron atoms with spin

Similar considerations show that the magnetic quantum number m must obey the rule 

The polarization and angular distribution of radiation satisfying a given Am selection rule are the same as those discussed in section 5.2.2. 

In the special case where the total angular momentum of the initial and final states is zero, j=j =0, it is obviously impossible to satisfy the principle of conservation of angular momentum. These transitions are therefore strictly forbidden, a fact which can be expressed symbolically by 

This rule is responsible for the metastability of the lowest Pq levels in mercury, cadmium, zinc, neon, argon, etc. 

This derivation of the selection rules, equations (5.14), (5.15), and (5.16), has necessarily been rather qualitative and a more rigorous treatment is given in section 5.4.1 below. Meanwhile by using the explicit wave-functions of equation (3.64) and the recursion relations (5.11) and (5.12), it is possible to evaluate the electric dipole matrix elements directly and to verify that these selection rules are in fact correct (Problem 5.5). 

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