Weakly bound states with spin-isospin symmetry

TL;DR

This paper explores the behavior of weakly bound states in a three-fermion system with spin-isospin symmetry, extending Efimov physics to nuclear-like systems with large scattering lengths.

Contribution

It introduces a model to analyze three-fermion bound states along a specific ratio of scattering lengths, extending Efimov physics to nuclear systems.

Findings

Estimated three-nucleon binding energies along the scattering length ratio plane.

Extended Efimov plot for three fermions with spin-isospin symmetry.

Demonstrated the impact of large scattering lengths on bound state properties.

Abstract

We discuss weakly bound states of a few-fermion system having spin-isospin symmetry. This corresponds to the nuclear physics case in which the singlet, $a_0$, and triplet, $a_1$, $n-p$ scattering lengths are large with respect to the range of the nuclear interaction. The ratio of the two is about $a_0/a_1\approx-4.31$. This value defines a plane in which $a_0$ and $a_1$ can be varied up to the unitary limit, $1/a_0=0$ and $1/a_1=0$, maintaining its ratio fixed. Using a spin dependant potential model we estimate the three-nucleon binding energy along that plane. This analysis can be considered an extension of the Efimov plot for three bosons to the case of three $1/2$-spin-isospin fermions.