Distribution of regularized three-body phase-volume

The micro-canonical phase-space volume for the three-body problem is a topic of intrinsic interest. Within the flux-based statistical theory, it provides a means to predict the scale of disintegration times for non-hierarchical systems. While the bare phase-volume diverges, arXiv:2205.04294 (Paper I) showed that a regularized version can be defined. Building on Paper I, which determined the regularized phase-volume for a given energy $\bar\sigma(E)$, this paper extends the analysis to its distribution over angular momentum, $\bar\sigma(E,L)$. Through analytical integrations, we reduce the problem to a 3d numerical integration, a step up in complexity from the 2d integration required for $\bar\sigma(E)$. We provide regularized phase-volume values for several mass sets across a range of $E$ and $L$, validated through an $L$-integration test. Notably, the values remain positive for all tested parameters, lending further support to the validity of the chosen regularization procedure. For high values of $L$ at fixed masses and $E$, we observe a strong suppression of $\bar\sigma(E,L)$.