Weakly bound states with spin-isospin symmetry

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 $a_0\mathrm{/}{a}_1\approx -4.31$. This value defines a plane in which $a_0$ and $a_1$ can be varied up to the unitary limit, $1\mathrm{/}{a}_0=0$ and $1\mathrm{/}{a}_1=0$, 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 $1\mathrm{/}2$-spin-isospin fermions.