Cross section-temperature equivalence

[karmion]

It's assumed that interaction rate between a species of particule m and l is expressed as:

Γm=<nlσv>,

where nl is the density of the species l, σ the cross-section of species m (=probability of interaction) and v the relative velocity between the two particles.

It's also assumed that <σv>∼G²T², where G is fermi's constant.

I need to know where comes from this last equivalence relation, is there anyone that can help me please ?

 

[Vanadium 50]

I don't know where this came from, but it is not true in general, as GF assumes a weak interaction, That's not true for particles in general.

 

[Demystifier]

It's assumed that ...

Where is it assumed?