How empty is an empty loss cone?

Understand

We consider two body relaxation in a spherical system with a loss cone.

• Considering two-dimensional angular momentum space, we focus on "empty loss cone" systems, where the typical scattering during a dynamical time $j_{d}$ is smaller than the size of the loss cone $j_{\rm lc}$.
• As a result, the occupation number within the loss cone is significantly smaller than outside.
• Classical diffusive treatment of this regime predict exponentially small occupation number deep in the loss cone.