Initial collisional excitation can make up the energy shortfall allowing optical excitation to be used to select the final state.
2.
For example, collisional excitation of the " n " = 2 level of hydrogen will release a Ly-? photon upon de-excitation.
3.
With a good approximation, the number of occupied states at the superior level n _ u and the number of states at the inferior energy level n _ l are given by the equilibrium between collisional excitation and spontaneous emission
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