Hyperradial Distribution Function of Few-Body Problems: A New Arena for Extreme Value Theory

This work explores classical capture models for few-body systems via a Monte Carlo method in hyperspherical coordinates. In particular, we focus on van der Waals and charged-induced dipole interactions. As a result, we notice that, independently of the number of particles and interparticle interaction, the capture hyperradial distribution function follows a Fréchet distribution, a special type of the generalized extreme value distribution. Besides, we elaborate on the fundamentals of such universal feature using the general extreme value theory, thus, establishing a connection between extreme value theory and few-body physics.