Exact solution of the three-boson problem at vanishing energy

TL;DR

This paper provides an exact analytical solution for the three-boson problem at zero energy using a zero-range model, enabling precise calculation of three-body recombination rates across all scattering lengths.

Contribution

It introduces a novel exact solution method for the three-boson problem at zero energy, incorporating a dimensionless phase for boundary conditions and deriving an explicit recombination rate formula.

Findings

Exact zero-energy solution valid for all scattering lengths

Analytical expression for three-body recombination rate

Applicable to both positive and negative scattering lengths

Abstract

A zero range approach is used to model resonant two-body interactions between three identical bosons. A dimensionless phase parametrizes the three-body boundary condition while the scattering length enters the Bethe-Peierls boundary condition. The model is solved exactly at zero energy for any value of the scattering length, positive or negative. From this solution, an analytical expression for the rate of three-body recombination to the universal shallow dimer is extracted.