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, Dandekar et al. (Celest Mech Dyn Astron 134(6): 55, 2022. https://doi.org/10.1007/s10569-022-10108-1) (Paper I) showed that a regularized version can be defined. Building on Paper I, which determined the regularized phase-volume for a given energy σ¯(E), this paper extends the analysis to its distribution over angular momentum, σ¯(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 σ¯(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 σ¯(E,L).