Universality of isolated $N$-body resonances at large scattering length

TL;DR

This paper investigates universal properties of non-Efimovian N-body resonances at large scattering lengths, introducing a contact model with two parameters that accurately describes bound states, including those not square-integrable.

Contribution

It introduces a universal contact model for N-body resonances at large scattering lengths, extending the description to non-square-integrable states with a modified scalar product.

Findings

The contact model accurately normalizes bound states.

The model applies to states that are not square-integrable.

Universal behavior of N-body resonances is established.

Abstract

Non Efimovian $N$-body resonances are investigated in the regime of a large two-body s wave scattering length. In view of a universal description of low-energy bound and quasi-bound states, a contact model is introduced. The modeling requires two parameters in addition to the scattering length. Using a modified scalar product, the contact model provides a normalization of bound states, possibly not square-integrable, that coincides with that of the corresponding finite range model.