(updated for 2013)

Short range forces involving “neutral” particles (neutral-ion, neutral-neutral) are inherently quantum-mechanical. Neutral-neutral interactions are very weak until electron clouds overlap (cm). We can therefore treat these particles as hard spheres. The collisional cross section for two species is a circle of radius r1 + r2, since that is the closest two particles can get without touching.

What does that collision rate imply? Consider the mean free path:

This is about 100 AU in typical ISM conditions ()

In gas at temperature T, the mean particle velocity is given by the 3-d kinetic energy: , or

, where is the mass of the neutral particle. The mean free path and velocity allows us to define a collision timescale:

.

- For (n,T) = (), the collision time is
**500 years**
- For (n,T) = (), the collision time is
**1.7 months**
- For (n,T) = (), the collision time is
**45 years**

So we see that density matters much more than temperature in determining the frequency of neutral-neutral collisions.

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