Scaling of the $^{19}$B two-neutron halo properties close to unitarity

TL;DR

This paper investigates the properties of the $^{19}$B isotope as a three-body system near unitarity, using universal scaling functions to describe its radii and providing model-independent estimates of its structure.

Contribution

It introduces universal scaling functions for $^{19}$B's radii based on Efimov physics, demonstrating their model independence near unitarity.

Findings

Scaling functions depend only on dimensionless parameters near unitarity.

Model independence of radii scaling functions is confirmed.

Estimated root-mean-square radii and separation distances for $^{19}$B.

Abstract

We explore the description of the bound $^{19}$B isotope in terms of a $^{17}$B+n+n three-body system where the two-body subsystems $^{17}$B+n and neutron-neutron (nn) have virtual states close to the continuum. Dimensionless scaling functions for the root-mean-square (rms) radii are defined and studied for different parameters of the neutron-core potential and considering three different models for neutron-neutron interaction. The scaling functions for the radii are rooted on the universal behavior of three-body systems close to the Efimov limit and depend only on dimensionless quantities formed by the two-neutron separation energies and scattering lengths. Our results show in practice the model independence of these scaling functions close to unitarity. We provide an estimation of the different rms relative separation distances between the constituents, as well as of the proton and matter radii.