Energy Transitions and Mixed States

Our next step is to further examine selection rules for forced eleetric dipole transitions. We need to account for the actual energy observed, in terms of the two terminal states possible, i.e.- yellow = [17560 cm i Hi3/2l VS [green = 21,020 em 6H15/2]. We can see that if an excitation energy of 40,000 cm were to be used, the 2Hh/2 level would be 

You might ask why this state is the emitting state. Remember that a photon is a significant amount of energy and Nature would prefer to emit 

The composition of the three states, i.e.- emitting and terminal states, are shown in the following  

Note that the excited state has a component. It turns out that strong transition intensities in the lanthanides occur due to a transition termed forced-electric-dipole transitions, where AJ s 2. This rule holds in all cases where strong intensities have been observed. Thus, for our case, the transition involves the 6H13/2 state, because of the AJ = 2 restriction. 

We have already shown in Chapter 5 that spectral Intensities, I, are proportional to oscillator strength, f, which is inversely proportional to half-life,, namely- 

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