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Direct collisions between finite-sized particles occur commonly in many areasof astrophysics. Such collisions are typically mediated by chaotic, boundgravitational interactions involving small numbers of particles. An importantapplication is stellar collisions, which occur commonly in dense star clusters,and their relevance for the formation of various types of stellar exotica. Inthis paper, we return to our study of the collision rates and probabilitiesduring small-number chaotic gravitational interactions ($N$ $\lesssim$ 10),moving beyond the small-number particle limit and into the realm of largerparticle numbers ($N$ $\gtrsim$ 10$^3$) to test the extent of validity of ouranalytic model as a function of the particle properties and the number ofinteracting particles. This is done using direct $N$-body simulations ofstellar collisions in dense star clusters, by varying the relative numbers ofparticles with different particle masses and radii. We compute the predictedrate of collisions using the mean free path approximation, adopting thepoint-particle limit and using the sticky-star approximation as our collisioncriterion. We evaluate its efficacy in the regime where gravitational-focusingis important by comparing the theoretical rates to numerical simulations. Usingthe tools developed in previous papers in this series, in particular CollisionRate Diagrams, we illustrate that our predicted and simulated rates are inexcellent agreement, typically consistent with each other to within onestandard deviation.

Small-N Collisional Dynamics V: Beyond the Realm of Not-So-Small-N