= Unordered-pair collision rate
{title2=$\Gamma_{ii}=K_{ii}N_i(N_i-1)/2$}
For a dilute phase-mixed population, an identical-species <collision> rate counts unordered pairs: $\Gamma_{ii}=K_{ii}N_i(N_i-1)/2$. Different species have rate $\Gamma_{ij}=K_{ij}N_iN_j$. Here $K_{ij}=\langle\sigma_{ij}v_{ij}\rangle/V$ uses the <collision cross-section> and relative speed. Destroying both identical particles gives $\dot N_i=-2\Gamma_{ii}$, not $-\Gamma_{ii}$. This distinction prevents inconsistent factors when using one kinetic kernel for several particle sizes.
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