When two excited carbon dioxide molecules collide will one of them emit a photon, or will both? As I understand it, collisions between two molecules can result in one becoming excited, or an excited molecule relaxing. But what happens if two excited molecules collide?
There's a probability that both will change state and there's a probability that only one will; this is a standard exercise. Just write down the states and the interaction Hamiltonian and compute the transition amplitude from any given initial state to any other desired state. There's nothing conceptually obscure about it.
Stam,
Thank you for your reply. I am afraid that Hamitonians are a bit beyond me. I was thinking in terms of semi-classical theory.
It occurred to me after I posted this question that if two CO2 molecule excited in the 667 cm-1 vibrational state collided then one could be excited into a higher state and the other relaxed to the ground state. I think that this is effectively what you are saying.
What I am really asking is can a collision result in the emission of a photon? As I understand it, photons are only emitted as a result of spontaneous and stimulated emissions. So collisions can result in spontaneous emissions, but only photons can cause stimulated emissions.
I think I may now have answered my own question, but I would be grateful if you could confirm that I am correct.
Regards, Alastair.
Of course, collisions of objects, that are bound states of electric charges, will, generically, produce electromagnetic waves. This isn't spontaneous emission-it's the collision that produces the non-uniform motion, that gives rise to them.
For classical systems such as molecules, it's not useful to talk about individual photons, but of electric and magnetic fields, since their quantum fluctuations aren't really relevant.
Whether such fields can describe radiation, is the question whose answer is the statement that these fields describe an energy flux that is non-zero at infinity. And this means that the limit r^2(E x B) as r->infinity is non-zero, where E and B are the fields produced by the fact that the molecules have collided. It's quite messy, of course.
Of course, if the question refers to the idealization of the molecules as N-state quantum systems, with N energy levels each, the answer is, apparently, much simpler:
Just take as interaction Hamiltonian H = sum am1m2n1n2|m1>|m2> and ending up with molecule 1 in state |n1> and molecule 2 in state |n2>. One then interprets the different levels as counting the number of photons.
The probability of such a transition is proportional to |am1m2n1n2|2
The mess is in the matrix elements am1m2n1n2, that describe the possible transitions.
A good reference for this is is http://www.feynmanlectures.caltech.edu/III_toc.html
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