Hypertriton states from inverse scattering theory

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 $\mathrm{\Lambda }np$ three-body system in the $J^{\pi }=1\mathrm{/}{2}^{+}$ and $3\mathrm{/}{2}^{+}$ channels. This three-body problem is solved using a hyperspherical-harmonic expansion of the Faddeev equations. The $\mathrm{\Lambda }p$ and $\mathrm{\Lambda }n$ 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 ($J^{\pi }=1\mathrm{/}{2}^{+}$), we obtain a binding energy of $-2.335$~MeV, corresponding to a $\mathrm{\Lambda }$ separation energy of $B_{\mathrm{\Lambda }}=+0.104$~MeV relative to the $\mathrm{\Lambda }+d$ breakup threshold. This value is comparable to those from lambda-nucleon potentials that are simulated through G-matrix methods. The excited $J^{\pi }=3\mathrm{/}{2}^{+}$ state is found to have a lambda separation energy of $B_{\mathrm{\Lambda }}=-1.444$~MeV relative to the $\mathrm{\Lambda }+d$ breakup threshold, confirming that there is no bound excited hypertriton state.