How Should I Incorporate Neutrino Decoupling into My Function?

[DrunkenMaster]

Background:
Neutrinos decouple at around 10^10 K (or 1 MeV). This is normally shown as the interaction rate (between neutrinos and electrons) over the Hubble constant: Gamma/H = (T/10^10 K)^3

My problem:
I have a function which is dependent on the neutrino-electron interaction. But it does not take the neutrino decoupling into account. I am unsure about how I should (very simply) incorporate this into my function.
1) Should I add a stepfunction from 1 to 0 at 1 MeV?
2) Should I use a smoother function? Like e^-(10^10 K / T)^3 ?
3) Something else?

Cheers! :)

 

[AndyW]

I would suggest using a smoother function rather than a step function. The decoupling of neutrinos is not a sudden event, but rather a gradual process. Using a smoother function, such as the one you suggested (e^-(10^10 K / T)^3), would better reflect the gradual decrease in interaction rate as the temperature decreases. This would also be more accurate and realistic in representing the decoupling process. Additionally, you could also consider incorporating other factors such as the expansion of the universe and the change in particle number density. Overall, the key is to use a function that accurately reflects the gradual decrease in interaction rate as the temperature decreases.