Boltzmann suppression of a nonrelativistic relic ($n_{\mathrm{eq}}\simeq g(mT/2\pi {)}^{3/2}{e}^{-m/T}$)

A nonrelativistic species with $g$ states and negligible chemical potential has equilibrium density $g(mT/(2\pi ){)}^{3/2}{e}^{-m/T}$. If particle-antiparticle annihilation maintains equilibrium after the species becomes massive, its eventual freeze-out population can be much smaller than a relativistically decoupled population. The nonrelativistic annihilation rate and any asymmetry determine the final abundance.