In general the terms involving the scattering operator cannot
be expressed as a simple function of, for instance, the
parabolic moments .
Here we use a macroscopic relaxation time approximation
for the closure which gives the system
of moment equations a structure resembling the drift
diffusion system.
In a deliberate way the scattering integral stemming from an
observable is
modeled as
Here
denotes the moment from the equilibrium
solution.
A discussion on the validity of this
approximation is given in [Lun00].
Note that the
odd equilibrium moments vanish and hence
the expression simplifies in this case.