# Use of “rate function” as rate over density

Heggie (1975) uses the term rate function to express the ratio of the rate $$R$$ of some event (for example the dissociation of a given binary star by the interaction with a passing field star) with the density $$n$$ of relevant objects (field stars): $$R = Q n,$$ when the rate function can be calculated as integral over the speed $$v$$ of impactors (field stars) $$Q = \int_0^\infty v\,p(v)\,\sigma(v)\, \mathrm{d}v$$ from their speed distribution $$p(v)$$ and the speed-dependent cross-section $$\sigma(v)$$ for the event (binary dissociation).

The concept of the rate function $$Q$$ is useful, as it is often possible to calculate accurately, even if the rate $$R$$ is uncertain owing to uncertainty of the density $$n$$. However, I haven't come across this term before/elsewhere and wonder in how much this is standard terminology in similar contexts (scattering etc.) or whether there is another standard expression, such as possibly volume capture rate (in case of capture events), for the same thing.