Low-energy neutron scattering on light nuclei and $^{19}$B as a $^{17}$B-$n$-$n$ three-body system in the unitary limit

TL;DR

This paper investigates neutron scattering on light nuclei, modeling $^{19}$B as a three-body system near the unitary limit, predicting low-lying resonances and exploring connections to Efimov physics.

Contribution

It introduces a three-body model for $^{19}$B near the unitary limit, reproduces its ground state energy, and predicts low-lying resonances linked to Efimov physics.

Findings

Reproduces the ground state energy of $^{19}$B

Predicts two low-lying resonances in $^{19}$B

Suggests a connection to Efimov physics

Abstract

We consider the evolution of the neutron-nucleus scattering length for the lightest nuclei. We show that, when increasing the number of neutrons in the target nucleus, the strong Pauli repulsion is weakened and the balance with the attractive nucleon-nucleon interaction results into a resonant virtual state in $^{18}$B. We describe $^{19}$B in terms of a $^{17}$B-$n$-$n$ three-body system where the two-body subsystems $^{17}$B-$n$ and $n$-$n$ are unbound (virtual) states close to the unitary limit. The energy of $^{19}$B ground state is well reproduced and two low-lying resonances are predicted. Their eventual link with the Efimov physics is discussed. This model can be extended to describe the recently discovered resonant states in $^{20,21}$B.