So I'm pretty sure I'm approaching this problem in the wrong way and I need some guidance (my first hint is that I think I'm thinking about a quantum mechanical problem too classically)
Suppose there is an isolated molecule in the gas phase with an average cross-sectional area to be exposed to radiation of $A$. (For my specific problem, the molecule is trapped in a superfluid Helium droplet, but I think the calculation should be roughly the same). If the radiation source has a flux $f$ (in units of photons/second/square area/0.1% BW) at energy $E$, what is the probability of the molecule absorbing a photon within a given interaction time $t$ if the absorption probability at a given energy is $P(E)$?
This is pretty easy to calculate if I treat the whole problem classically, i.e. like a ball and a target model. For some reason, though, I get numbers that seem to be way too low if I do this. I know it has to be more complicated than that, since light is a wave also. What am I missing?
I understand that transition probabilities are related to wavefunction overlap, etc. Also, I should note that the radiation in my specific problem is in the hard x-ray region, though I don't think that should change the answer.
Thanks in advance for your help.