Hello.
The standard way of expressing collisional freq is n*sigma*v where n, sigma and v represents target species density, collisional scattering cross section and mean incident particle velocity, respectively.
Normally v is expressed in terms of incident particle temperature and mass.
When I looked at this expression, I thought it doesn't consider temperature of the target particles. This looked to be derived from the picture that incident species are going on the "cold" target species.
What if target species are not cold, for example, collisional frequency between same species like neutral-neutral collision?
I simply thought mass in the expression of v becomes the reduced mass but It could be wrong.
Could you help me to get a kind of general expression of collision frequency including target species temperature?
For neutron collision you can use the following expression relating the cross section with temperature:
s=s0(T0/T)1/2
where T0 is the temperature at which the cross section s0 is referred to.
When you have hot target your cross section cold depend on the internal state of the target, therefore the equation of the state-specific frequency is n(i)v s(v,i), where n is the index of internal state. where n(i) are the number of specie in the level. Consider f(i)=n(i)/n the distribution function the total frequency is
n sum(f(i) v s(v,i))
If the distribution is a Boltzmann the frequency depend on the temperature.
As an example applied to transport properties look at this paper.
In the frequency
Reactive and internal contributions to the thermal conductivity of local thermodynamic equilibrium nitrogen plasma: The effect of electronically excited states
D Bruno, G Colonna, A Laricchiuta, M Capitelli
Physics of Plasmas 19 (2012) 122309
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