Correlation diagrams in collisions of three identical particles

TL;DR

This paper develops a framework using correlation diagrams and quantum number analysis to understand three-particle collisions, including recombination processes, across different configurations and coordinate systems.

Contribution

It introduces a method to derive collision selection rules and construct correlation diagrams for three identical particles in various configurations.

Findings

Derived quantum number conservation and change rules during collisions.

Constructed correlation diagrams linking initial and final states.

Identified conditions for recombination into dimers and free particles.

Abstract

We discuss collision of three identical particles and derive scattering selection rules from initial to final states of the particles. We use either laboratory-frame, hyperspherical, or Jacobian coordinates depending on which one is best suited to describe three different configurations of the particles: (1) three free particles, (2) a quasi-bound trimer, or (3) a dimer and a free particle. We summarize quantum numbers conserved during the collision as well as quantum numbers that are appropriate for a given configuration but may change during the scattering process. The total symmetry of the system depends on these quantum numbers. Based on the selection rules, we construct correlation diagrams between different configurations before and after a collision. In particular, we describe a possible recombination of the system into one free particle and a dimer, which can be used, for example, to identify possible decay products of quasi-stationary three-body states