Analytical solution of the bosonic three-body problem

TL;DR

This paper provides an analytical solution to the three-boson problem near a narrow Feshbach resonance, yielding exact results for binding energies, thresholds, and recombination rates in a universal three-body system.

Contribution

It introduces a novel analytical approach by transforming the three-body integral equation into a Schrödinger-type equation, enabling precise solutions for key physical quantities.

Findings

Exact trimer binding energies obtained

Precise three-body parameter determined

Threshold and recombination rate accurately calculated

Abstract

We revisit the problem of three identical bosons in free space, which exhibits a universal hierarchy of bound states (Efimov trimers). Modelling a narrow Feshbach resonance within a two-channel description, we map the integral equation for the three-body scattering amplitude to a one-dimensional Schr\"odinger-type single-particle equation, where an analytical solution of exponential accuracy is obtained. We give exact results for the trimer binding energies, the three-body parameter, the threshold to the three-atom continuum, and the recombination rate.