Hyperradial distribution function of few-body problems: a new arena for extreme value theory

In this work, after studying the capture hyperradius of few-body processes, including van der Waals and charged-neutral interactions, we found that the distribution of the hyperrardius follows a Frechet distribution. In other words, the distribution of the capture hyperradius is independent of the underlying interparticle interaction. We then rationalized and generalized our findings following the Fisher–Tippett–Gnedenko theorem, connecting the extreme value theory and few-body physics. In particular, we use a Monte Carlo technique in hyperspherical coordinates to properly sample all the initial configurations of the particles to extract the capture hyperradius and, with it, the hyperradial distribution.