At the moment of deepest core collapse, a star cluster core contains less than ten stars. This small number makes the traditional treatment of hard binary formation, assuming a homogeneous background density, suspect. In a previous paper, we have found that indeed the conventional wisdom of binary formation, based on three-body encounters, is incorrect. Here we refine that insight, by further dissecting the subsequent steps leading to hard binary formation. For this purpose, we add some analysis tools in order to make the study less subjective. We find that the conventional treatment does remain valid for direct three-body scattering, but fails for resonant three-body scattering. Especially democratic resonance scattering, which forms an important part of the analytical theory of three-body binary formation, takes too much space and time to be approximated as being isolated, in the context of a cluster core around core collapse. We conclude that, while three-body encounters can be analytically approximated as isolated, subsequent strong perturbations typically occur whenever those encounters give rise to democratic resonances. We present analytical estimates postdicting our numerical results. If we only had been a bit more clever, we could have predicted this qualitative behaviour.
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