The form of the collision function 
can be found [11, 12, 14]
by assuming that the gas has a low density so only
binary collisions need be considered. It is also assumed that
the molecules are completely
uncorrelated before the collision, this assumption is called `molecular
chaos'. With these assumptions the collision function is given by
[11, 12, 14]
where 
and 
are the
velocities of the two particles before a collision,
and 
are their velocities
after the collision,
,
,
,
,
g is the magnitude of the particles relative velocity before the collision,
is the solid angle the particles are scattered into,
and
is the differential cross section in the centre of mass
reference frame,
where b and 
are the impact parameter and the scattering angle
respectively in the
centre of mass reference frame, as defined in figure 2-1,
is the azimuthal angle.
Figure 2-1: Two particles (of equal mass) before and
after a collision in the centre of mass reference frame. The impact parameter
b and the angle are shown.
