### Re: What is the nature of an atomic collision?

Date: Tue Dec 14 10:47:12 1999
Posted By: Georg Hager, Grad student, Theoretical Particle Physics
Area of science: Physics
ID: 943296432.Ph
Message:

Dear Chris!

You ask a question one could write whole books about, but I'll try to be concise ;-)

Let us first investigate the difference between elastic and inelastic collisions, and how it comes about. When two objects start to collide, their kinetic energy is first converted into elastic potential energy; it is `stored' inside the objects, in the atomic bonds which hold molecules together. When the objects start to depart from each other, the potential energy is converted back into kinetic energy. If those two conversion processes happen without loss into other forms of energy (e.g. heat or sound), we speak of an elastic collison. In this case, the overall kinetic energy of the colliding objects before and after the collision is the same.

On the other hand, if the collision leads to a significant heating of one or both objects, the energy for this must come from the previous kinetic energy, and is subsequently not avalable any more. To put it in a more abstract context, one could say that a part of the kinetic energy was used for `inner excitation' (in this case, heating) of the collision partner(s). But if and how strongly this effect takes place depends heavily on the composition of the material. Rubber balls collide much more inelastically that steel balls, because of their strong deformation. In the case of a completely inelastic collision, the partners stick together after the hit. There is no way a collision can get more inelastic than that. The amount of energy that is `lost' can be calculated easily using momentum conservation.

How about molecules then? First of all you have to understand that there are significant differences between collisions of `classical' objects like balls, cars etc. and quantum objects like atoms and molecules. An atom consists mainly of nothing - the nucleus is incredibly small (about 10-15m for hydrogen) and the electron(s) are distributed across a large space compared to that, 100000 times larger in the hydrogen case. So, atoms do not hit each other at some certain moment, but they `feel' each other's presence from quite far apart and react accoringly, sometimes even overlapping each other. Atomic collisions are quite complicated to describe exactly; for most cases, one is satisfied with approximate solutions. It is even not evident from the start whether two atoms repel or attract at very low collision energy. The laws of quantum mechanics govern this world, but there are features which can nevertheless be `carried over' from classical mechanics: energy and momentum conservation! In atomic collisions, it is entirely possible to have elastic, inelastic and even completely inelastic collisions:

• If two atoms collide (better use the word `scatter') elastically, they might be the same in any aspect after the collision as they were before. They are not even in an excited state, so this must be an elastic process.
• An inelastic collision can occur when the atoms get excited, i.e. when electrons are pushed to higher energy levels. Eventually, those electrons will return to their ground state, but the energy is `lost' for some time, it is especially not available for kinetic energy right after the collision. Molecules, whose vibrational and rotational modes can be excited as well, are even more prone to this kind of inelasticity.
• Two atoms might collide and then form a bound state. This is the equivalent to a completely inelastic collision.
Collisions between elementary objects like quarks and leptons can be interesting as well. They cannot be excited `internally' - an electron is an electron is an electron. But it is possible to convert one particle into another (for instance, the weak decay of a neutron comes about because an up quark is converted into a down quark, emitting a W- boson). Nevertheless, all collisions are elastic on this level, because there is always energy and momentum conservation. If you, however, choose to perform an experiment in which you do not control or measure all particles which take part, you may think you have encountered an inelastic process. Take, for example, scattering of an electron off a nucleus (at moderate energies, so that the nucleus can be regarded as pointlike). You will notice that in the scattering process, some of the initial kinetic energy is lost. This is because the electron gets accelerated in the field of the nucleus, and, because of its nonvanishing charge, must consequently radiate photons. This phenomenon is called bremsstrahlung (deceleration radiation). You can measure those photons if you want - or choose to ignore them. In the first case, energy and momentum is conserved, in the second case it is not (not even the momentum - this might give you a hint, if you didn't know about photons in the first place, that there must be something you have missed, and that it cannot be an inner excitation of the electron or the nucleus).

Now I hope I haven't confused you too much. If I did, feel free to submit another question to the MSN. It is hard to give references for such a broad subject - you'd have to cover a lot of material from classical mechanics to quantum fields -, but I suggest taking a look at an entry-level quantum field theory book like Mandl and Shaw, and a book about atomic physics like Haken and Wolf.

Hope that helps,
Georg.

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