How can a non-resonant monochromatic light induce an atomic transition?

[Abu Abdallah]

Hello
How can a monochromatic light induce a transition ( absorption ) between two energy levels whose energy difference doesn't match the frequency of the incident light ?? A treatment using time dependent perturbation theory shows that the transition will occur even when the incident radiation frequency and hence the energy of its photons is less than the difference between the two levels !

 

[inha]

A transition like that could not happen. It'd violate conservation of energy. Maybe you've misunderstood something? From what exactly did you read this?

 

[CarlB]

It's been a long time since I've done this problem, but I believe that the OP is correct.

Let me try and remember, and please forgive me, it's been nearly 30 years...

The first thing one must note is that the "energy eigenstates" of an atom are only energy eigenstates in the absence of any interactions that might allow them to decay. That is, energy eigenstates are stable, but excited atoms are not. Excitations are only stable when you ignore the ways that they can decay. This all gets back to the dE dT > h-bar rule. Energy eigenstates implies that dE = 0, and therefore that dT = infinity, and thus you are considering states that have infinite lifetimes (i.e. states that are stable).

Of course that is only an approximation, but it can be a very good one.

Now consider what happens when you add a small oscillating E&M field to the system. (I.e. monochromatic light.) The effect is that the energy eigenstates that you had before are now going to be slightly mixed. The mixtures will give you the transition probabilities. As Abu Abdallah said, you don't have to have these energies exactly matched in order to have a positive probability of inducing a transition. Heck, if the energies always had to match exactly we'd never get anything done.

The thing to remember is that you are dealing with a transitory state, so it doesn't have to satisfy energy conservation exactly.

Carl

 

[inha]

Sure non-resonant transitions happen but you can't have a transition unless the photon's energy is atleast the difference between the energy levels of the atom. You can't get the K alpha out of molybednum unless you supply more than the 17 something keVs for example.