How empty is an empty loss cone?
  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. We revisit this classical derivation
of occupancy distribution of objects in the empty loss cone regime. We
emphasize the role of the rare large scatterings and show that the occupancy
does not decay exponentially within the loss cone, but it is rather flat, with
a typical value $\sim [(j_d/j_{\rm lc})]^2\ln^{-2}(j_{\rm lc}/j_{\min})$
compared to the occupation in circular angular momentum (where $j_{\min}$ is
the smallest possible scattering). Implication are that although the loss cone
for tidal break of Giants or binaries is typically empty, tidal events which
occurs significantly inside the loss cone ($\beta\gtrsim 2$), are almost as
common as those with $\beta\cong 1$ where $\beta$ is the ratio between the
tidal radius and the periastron. The probability for event with penetration
factor $>\beta$ decreases only as $\beta^{-1}$ rather than exponentially. This
effect has no influence on events characterized by full loss cone, such as
tidal disruption event of $\sim 1m_\odot$ main sequence star.
