Hypertriton states from inverse scattering theory

Abstract

The primary goal of this paper is to demonstrate that inverse scattering theory is a viable method for the simulation of lambda-nucleon potentials in hypernuclear few-body studies. To this end, we investigate the hypertriton, modelled as a $\Lambda np$ three-body system in the $J^{\pi }=1/2^{+}$ and $3/2^{+}$ channels. This three-body problem is solved using a hyperspherical-harmonic expansion of the Faddeev equations. The $\Lambda p$ and $\Lambda n$ interactions are modelled by the GLM-YN0 potentials. These simulated potentials were recovered through Gel'fand--Levitan--Marchenko inverse scattering theory as phase-equivalent simulations of the NSC97f meson-exchange model. The neutron-proton interaction is described by the semi-realistic Malfliet--Tjon I/III potential, with both singlet and triplet channels retained. For the ground state ($J^{\pi }=1/2^{+}$), we obtain a binding energy of $-2.335$~MeV, corresponding to a $\Lambda$ separation energy of $B_{\Lambda }=+0.104$~MeV relative to the $\Lambda +d$ breakup threshold. This value is comparable to those from lambda-nucleon potentials that are simulated through G-matrix methods. The excited $J^{\pi }=3/2^{+}$ state is found to have a lambda separation energy of $B_{\Lambda }=-1.444$~MeV relative to the $\Lambda +d$ breakup threshold, confirming that there is no bound excited hypertriton state.