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.