Graduate Cross section-temperature equivalence

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The discussion centers on the interaction rate between particles, defined by the equation Γm=<nlσv>, incorporating the density of species l, the cross-section σ, and their relative velocity v. A key point of contention is the assumption that <σv>∼G²T², with G representing Fermi's constant, which is argued to only apply under weak interaction conditions. The validity of this equivalence relation is questioned, as it may not hold true for all particle interactions. Participants seek clarification on the origins of this assumption and its general applicability. The conversation highlights the need for a deeper understanding of the conditions under which these relations are derived.
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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 ?
 
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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.
 

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