Signatures of few-body resonances in finite volume

TL;DR

This paper demonstrates how finite-volume energy spectra of few-body systems can reveal the existence and properties of multi-body resonances, providing a new computational approach for studying such states.

Contribution

The authors introduce a method using finite-volume spectra and avoided level crossings to identify and analyze few-body resonances, validated with known models and applied to new systems.

Findings

Avoided level crossings indicate multi-body resonances.

Method accurately reproduces known two- and three-body resonance properties.

Predicts three- and four-body resonances in Gaussian potential models.

Abstract

We study systems of bosons and fermions in finite periodic boxes and show how the existence and properties of few-body resonances can be extracted from studying the volume dependence of the calculated energy spectra. Using a plane-wave-based discrete variable representation to conveniently implement periodic boundary conditions, we establish that avoided level crossings occur in the spectra of up to four particles and can be linked to the existence of multi-body resonances. To benchmark our method we use two-body calculations, where resonance properties can be determined with other methods, as well as a three-boson model interaction known to generate a three-boson resonance state. Finding good agreement for these cases, we then predict three-body and four-body resonances for models using a shifted Gaussian potential. Our results establish few-body finite-volume calculations as a new tool to study few-body resonances. In particular, the approach can be used to study few-neutron systems, where such states have been conjectured to exist.