Radius of effect of atomic interactions

[jshrager]

Suppose that I have an atom in one corner of a room, and I fire a photon toward the opposite corner (and assume that it is absorbed there into the wall). There is essentially zero probability that that photon will interact with the atom (either be captured, or stimulate emission, or whatever). As the angle at which I fire the photon relative to the position of the atom becomes smaller, this probability increases until I'm aiming essentially at the nucleus of the atom, at which (I assume) the interaction probability will be largest. Several questions: 1. Am I framing this correctly? That is, it is a matter of interaction probabilities and the spatial relations determine these. 2. (Here's my real question) How does one frame this mathematically, esp. regarding the excitation state of the atom? 3. Suppose that instead of an atom and a photon I'm shooting another atom at the first one, say, I'm shooting one ground state H at another the same, v. H+ at H+, or an excited H at another? In these cases I'm hoping to find an equation that relates the excitation state of the atoms to the angles of interaction and the interaction probabilities.

Thanks!

 

[mfb]

The photon is not a classical point-like particle, but the basic idea is right - the interaction probability depends on the direction of your photon emission, aiming as precise as possible should give the largest interaction probability.

2. (Here's my real question) How does one frame this mathematically, esp. regarding the excitation state of the atom?

Depends on the theory you use to describe the interaction. For single photons, probably quantum electrodynamics, and then it gets complicated (you first need some superposition of planar waves to describe your localized particles, and then scattering amplitudes for all those planar waves, ...
Nonrelativistic quantum mechanics with continuous light is easier.

3. Suppose that instead of an atom and a photon I'm shooting another atom at the first one, say, I'm shooting one ground state H at another the same, v. H+ at H+, or an excited H at another? In these cases I'm hoping to find an equation that relates the excitation state of the atoms to the angles of interaction and the interaction probabilities.

I guess that's possible, but probably complicated. For two charged H+ (=just the nuclei): if the energy is not too high, you get the Coulomb repulsion only, and you can solve the system with classical mechanics.