Semi-analytic Faddeev solution to the $N$-boson problem with zero-range interactions

TL;DR

This paper develops a semi-analytic approach using hyperspherical methods to analyze two-body correlations in N-boson systems with zero-range interactions, revealing stability conditions and Efimov states.

Contribution

It introduces a semi-analytic Faddeev solution for the N-boson problem with zero-range interactions, incorporating correlations and renormalization techniques.

Findings

Derived a transcendental equation for hyperradial potential

Provided stability conditions for Bose-Einstein condensates

Demonstrated the presence of Efimov states at large scattering lengths

Abstract

We study two-body correlations for $N$ identical bosons by use of the hyperspherical adiabatic expansion method. We use the zero-range interaction and derive a transcendental equation determining the key ingredient of the hyperradial potential. The necessary renormalization is for both repulsive and attractive interactions achieved with an effective range expansion of the two-body phase-shifts. Our solutions including correlations provide the properties of Bose-Einstein condensates exemplified by stability conditions as established by mean-field Gross-Pitaevskii calculations. The many-body Efimov states are unavoidable for large scattering lengths.