Few-body calculations of $\hat{I}\cdot$-nuclear quasibound states

Abstract

We report on precise hyperspherical-basis calculations of $\hat{I}\cdot NN$ and $\hat{I}\cdot NNN$ quasibound states, using energy dependent $\hat{I}\cdot N$ interaction potentials derived from coupled-channel models of the $S_{11}$ $N^{\ast }(1535)$ nucleon resonance. The $\hat{I}\cdot N$ attraction generated in these models is too weak to generate a two-body bound state. No $\hat{I}\cdot NN$ bound-state solution was found in our calculations in models where Re $a_{\hat{I}\cdot N}\lesssim 1$ fm, with $a_{\hat{I}\cdot N}$ the $\hat{I}\cdot N$ scattering length, covering thereby the majority of $N^{\ast }(1535)$ resonance models. A near-threshold $\hat{I}\cdot NNN$ bound-state solution, with $\hat{I}\cdot$ separation energy of less than 1 MeV and width of about 15 MeV, was obtained in the 2005 Green-Wycech model where Re $a_{\hat{I}\cdot N}\approx 1$ fm. The role of handling self consistently the subthreshold $\hat{I}\cdot N$ interaction is carefully studied.

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