Exponential freeze-out sensitivity ($d\ln n_0/dP=3/(2P)-1$)

In a supplied equilibrium-cutoff model with $P=m{c}^2/(k_B{T}_f)$, present number density can contain $P^{3/2}{e}^{-P}$. The logarithmic derivative is $3/(2P)-1$, making small changes in a large cosmological particle freeze-out parameter important for the inferred abundance.