A general theoretical description of N-body recombination

TL;DR

This paper derives a general theoretical formula for N-body recombination processes, providing insights into threshold behaviors, energy scaling, and resonance effects, with applications to four-boson systems and Efimov states.

Contribution

It introduces a universal S-matrix based formula for N-body recombination cross sections and rates, extending Wigner threshold laws and including resonance effects from borromean states.

Findings

Derived a general cross section formula for N-body recombination.

Revealed threshold scaling laws for N bosons.

Applied model to four-boson recombination into Efimov states.

Abstract

A formula for the cross section and event rate constant describing recombination of N particles are derived in terms of general S-matrix elements. Our result immediately yields the generalized Wigner threshold scaling for the recombination of N bosons. A semi-analytic formula encapsulates the overall scaling with energy and scattering length, as well as resonant modifications by the presence of borromean N-body states near the threshold collision energy in the entrance channel. We then apply our model to the case of four-boson recombination into an Efimov trimer and a free atom.