Distribution of regularized three-body phase-volume

TL;DR

This paper extends the regularized three-body phase-volume analysis to include angular momentum distribution, providing analytical and numerical results that support the validity of the regularization method and reveal suppression at high angular momentum.

Contribution

It introduces the distribution of regularized three-body phase-volume over angular momentum, expanding previous work that focused only on energy dependence.

Findings

Regularized phase-volume remains positive across tested parameters.

Distribution shows strong suppression at high angular momentum.

Validated regularization procedure through an $L$-integration test.

Abstract

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 $\bar\sigma(E,L)$.