the latter expression is valid in the limit that gravitational focusing dominates the encounter rate. The rate of encounters with stars that interact strongly with the binary, i.e. that satisfy r p < a , is approximately n π π p 2 σ σ = 2 π π G M 12 n a / σ σ where n and σ σ are the number density and velocity dispersion of the field stars and a is the semi-major axis of the binary.