Correlation among low-energy four-nucleon observables

Abstract

We study the correlation among $s$-wave low-energy four-nucleon observables by using a simplified dispersion theoretic ($\frac{N}{D}$) approach. We find that the triton binding energy, its asymptotic normalization parameter, the deuteron exchange left-hand cut, and the nucleon-trinucleon ($N\ensuremath{-}t$) scattering length control the low-energy $N\ensuremath{-}t$ system. The isospin one channel is insensitive to the asymptotic normalization parameter of the triton. The effective range function $kcot\ensuremath{\delta}$ for the isospin zero spin singlet $N\ensuremath{-}t$ system has a pole whose position and residue are strongly correlated with the $N\ensuremath{-}t$ scattering length. In this case the four-nucleon system (in our model) has an excited state whose binding energy and asymptotic normalization parameter are also correlated with the $N\ensuremath{-}t$ scattering length.[NUCLEAR REACTIONS $s$-wave nucleon-trinucleon systems, spin-isospin channels, $\frac{N}{D}$ approach, low-energy correlations.]