Lifetime Matrix in Collision Theory

The duration of a collision is usually a rather ill-defined concept, depending on a more or less arbitrary choice of a collision distance. If the collision lifetime is defined as the limit, as $R\ensuremath{\rightarrow}\ensuremath{\infty}$, of the difference between the time the particles spend within a distance $R$ of each other and the time they would have spent there in the absence of the interaction, a well-defined quantity emerges which is finite as long as the interaction vanishes rapidly enough at large $R$.