Numerical study of three-body recombination for systems with many bound states

TL;DR

This study numerically investigates three-body recombination in systems with many bound states, revealing complex potential structures and modified threshold laws, with implications for understanding ultracold bosonic systems.

Contribution

It introduces a numerical approach combining SVD and adiabatic methods to handle complex potentials with many bound states in three-body recombination.

Findings

Recombination into deeply bound states is dominated by a single decay pathway.

Sharp avoided crossings in potentials are effectively managed using SVD.

Modified Wigner threshold law applies to excited incident channels.

Abstract

Three-body recombination processes are treated numerically for a system of three identical bosons. The two-body model potentials utilized support many bound states, a major leap in complexity that produces an intricate structure of sharp nonadiabatic avoided crossings in the three-body hyperradial adiabatic potentials at short distances. This model thus displays the usual difficulties of more realistic systems. To overcome the numerical challenges associated with sharp avoided crossings, the slow variable discretization (SVD) approach is adopted in the region of small hyperradii. At larger hyperradii, where the adiabatic potentials and couplings are smooth, the traditional adiabatic method suffices. Despite the high degree of complexity, recombination into deeply bound states behaves regularly due to the dominance of one decay pathway, resulting from the strong coupling between different recombination channels. Moreover, the usual Wigner threshold law must be modified for excited incident recombination channels.