Weakly bound states with spin-isospin symmetry

Abstract

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 ≈ −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.

Nuclear Physics Around the Unitarity Limit

“…As an exception, Refs. [7,8] use potential models to map out correlations between observables in three-and fournucleon systems as the limit is approached at fixed a t =a s .Here, we argue that the typical particle binding momentum Q A of the A-nucleon system satisfies 1=a s;t < Q A < 1=R so that a combined expansion in Q A R and 1=ðQ A a s;t Þ converges quickly and quantitatively reproduces the physical systems. With this, the gross features of states in the nuclear chart are determined by a very simple leading-order interaction (governed by a single parameter), whereas, much like the fine structure of atomic spectra, observables are moved to their physical values by small perturbative corrections.…”

“…As an exception, Refs. [7,8] use potential models to map out correlations between observables in three-and fournucleon systems as the limit is approached at fixed a t =a s .…”