= Empty and full loss-cone capture rates
{title2=$\Gamma_{\rm empty}\sim\dfrac{N}{t_{\rm rel}\log(1/\mathcal R_{\rm lc})},\quad\Gamma_{\rm full}\sim\dfrac{N\mathcal R_{\rm lc}}P$}
Here $\mathcal R_{\rm lc}=J_{\rm lc}^2/J_c^2$ is the orbital <loss cone> fraction, $P$ an <orbital period>, and $t_{\rm rel}$ a <stellar relaxation time>. When angular diffusion per orbit is small relative to the cone, a steady two-dimensional diffusion solution is logarithmic and gives the empty-cone flux. Rapid refilling maintains an approximately isotropic full cone and gives the second rate. Numerical total rates need a stellar density and orbital-energy distribution, not merely a star count.
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