Manifestations of the Efimov Effect for Three Identical Bosons

TL;DR

This paper presents numerical calculations of three identical boson systems at large scattering lengths, analyzing Efimov states by solving the hyperangular Schrödinger equation and characterizing their effective potentials and couplings.

Contribution

The study provides detailed numerical analysis of Efimov states for three bosons at very large scattering lengths, expanding understanding of their asymptotic behavior.

Findings

Quantified the asymptotic behavior of Efimov states.

Characterized three-body effective potentials and nonadiabatic couplings.

Tested assumptions related to the Efimov effect.

Abstract

In this paper we present results from numerical calculations for three identical boson systems for both very large and infinite two-body s-wave scattering length $a$. We have considered scattering lengths up to $2\times 10^5$ a.u. and solved the hyperangular part of the Schr\"odinger equation for distances up to $10^6$ a.u.. Form these, we obtained the three-body effective potentials, hyperspherical channel functions and the asymptotic behavior of the nonadiabatic couplings in order to to characterize the main aspects of the Efimov states. These results allow us to test and quantify the assumptions related to the Efimov effect.