Interference in a three-level system

It is interesting to compare the Fano theory of autoionisation, which is an interference effect, with another kind of interference effect which is responsible for pronounced variations of intensity in certain molecular bands. Homogeneous perturbations arise when two excited electronic-vibrational states of a molecule are coupled by a perturbation in a manner which does not depend on the rotational quantum numbers of a molecule, but only on the rotational term and vibrational state, so that complete rotational bands can be enhanced or depressed in intensity. 

Now consider the dipole matrix element for the transition from the ground state 0 to the perturbed state +  

from equation (6.16), the avoided crossing occurs when AE = 0 or Ei = E2, in which case, by equation (6.35), cf = 4- Since it was assumed at the outset that hq2 — fj,01, the case of zero intensity will generally lie to one side of the avoided crossing. This can be compared with the minimum intensity which generally lies to one side of the Fano profile. The analogy with autoionisation is that, in a Beutler-Fano profile, all the possible values of AE are present simultaneously. 

In fig. 6.8, we show how the intensities evolve near the avoided crossing for different values of the energy difference AE in a typical situation for 

In a homogeneous molecular perturbation, V12 is the product of vibrational and electronic overlap elements, but is the same for all the rotational levels of a band. Thus, whenever a cancellation of intensity occurs, a complete rotational band may disappear from view. This situation arises for several bands in the N2 spectrum [297] which possess the same symmetries but originate from different electronic terms. An analysis based on the same principles as described above has been presented by Dressier [298]. 

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