= Geometric galaxy-encounter rate
{title2=$\Gamma=\pi R^2N\langle v_{\mathrm{rel}}\rangle$}
A target <galaxy> with geometric encounter cross section $\pi R^2$ in a population of number density $N$ has encounter rate $\Gamma=\pi R^2N\langle v_{\mathrm{rel}}\rangle$. A <Poisson process> gives merger probability $1-e^{-\Gamma T}$, approximated by $\Gamma T$ only for rare encounters. Counts of distinct pairs across the whole population additionally require a factor of one-half.
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