(updated for 2013)
Collisions are of key importance in the ISM:
- cause most of the excitation
- can cause recombinations (electron + ion)
- lead to chemical reactions
Three types of collisions
- Coulomb force-dominated ( potential): electron-ion, electron-electron, ion-ion
- Ion-neutral: induced dipole in neutral atom leads to potential; e.g. electron-neutral scattering
- neutral-neutral: van der Waals forces -> potential; very low cross-section
We will discuss (3) and (2) below; for ion-electron and ion-ion collisions, see Draine Ch. 2.
In general, we will parametrize the interaction rate between two bodies A and B as follows:
In this equation, is the collision rate coefficient in , where is the velocity-dependent cross section and is the particle velocity distribution, i.e. the probability that the relative speed between A and B is v. For the Maxwellian velocity distribution,
where is the reduced mass. The center of mass energy is , and the distribution can just as well be written in terms of the energy distribution of particles, . Since , we can rewrite the collision rate coefficient in terms of energy as
These collision coefficients can occasionally be calculated analytically (via classical or quantum mechanics), and can in other situations be measured in the lab. The collision coefficients often depend on temperature. For practical purposes, many databases tabulate collision rates for different molecules and temperatures (e.g., the LAMBDA databsase).
For more details, see Draine, Chapter 2. In particular, he discusses 3-body collisions relevant at high densities.