Annihilation Cross Sections for Relic Densities in the Low Velocity Limit

A simple method to calculate the total annihilation cross section of massive cold relics is presented. Exact expressions for $\arel$, $\brel$, and $\crel$ of $\sigma \vrel=\arel+\brel \vrel^2+\crel \vrel^4$ are obtained from simple derivatives of the squared annihilation amplitude. Three examples are given. In one example, the computed annihilation cross section of massive Dirac neutrinos confirms recent correct calculations.