# Embedding nuclear physics inside the unitary window

## TL;DR

This paper explores the universal low-energy properties of nuclear systems near the unitary limit, analyzing how nuclear binding energies evolve from this limit using a potential model across different nuclei.

## Contribution

It introduces a potential model to study the spectrum of nuclei near the unitary limit, highlighting the universality of low-energy nuclear dynamics and the emergence of observed levels.

## Key findings

- Binding energies form from the unitary limit as the control parameters vary.
- The low-energy observables are universal and insensitive to interaction details.
- Correlations between three- and four-nucleon observables are explained by scale invariance.

## Abstract

The large values of the singlet and triplet scattering lengths locate the two-nucleon system close to the unitary limit, the limit in which these two values diverge. As a consequence, the system shows a continuous scale invariance which strongly constrains the values of the observables, a well-known fact already noticed a long time ago. The three-nucleon system shows a discrete scale invariance that can be observed by correlations of the triton binding energy with other observables as the doublet nucleon-deuteron scattering length or the alpha-particle binding energy. The low-energy dynamics of these systems is universal; it does not depend on the details of the particular way in which the nucleons interact. Instead, it depends on a few control parameters, the large values of the scattering lengths and the triton binding energy. Using a potential model with variable strength set to give values to the control parameters, we study the spectrum of $A=2,3,4,6$ nuclei in the region between the unitary limit and their physical values. In particular, we analyze how the binding energies emerge from the unitary limit forming the observed levels.