What Does t→0 Mean in Neutron Freeze-Out?

[AuraCrystal]

Hello,

I was reading about big bang nucleosynthesis recently (If it helps, I'm using Mukhanov) and it was calculating the abundance of neutrons. It seems to say that X_n→X_n^{eq} (It says that X_n^{eq} is the equilibrium abundance of neutrons) as t→0. So...does that mean that the neutrons have an abundance when they are first created and that is changed by the interactions with the protons?

 

[mathman]

I am not familiar with the context. However, free neutrons are radioactive with a half life of a little under 15 minutes, decaying into proton + electron + anti-neutrino.

 

[BillSaltLake]

Due to pair production, at around t = 1μ sec, neutrons would have existed (along with antineutrons) in roughly the same number as photons. Then after ~ 10 μ sec, the antineutrons were gone and the neutrons were down to around 1 per billion photons. (There were also proton- antiproton pairs but they should have completely annihilated.) Then the neutrons began to decay with half life ~900 sec. Most decayed into protons (+ electron & neutrino), but some were captured as the (stable) nuclei of ²H, ³He, ⁴He, and ⁷Li.
I'm not sure which "t→0" is referred to (wrt 900 sec or 1μ sec).