$\Lambda NN $ three-body problem within $s$-wave inverse scattering on theoretical data

$\Lambda N$ potentials recovered through the application of $s$-wave inverse scattering on theoretical data are demonstrated on the $\Lambda NN$ three-body problem. The spin-dependent Malfliet-Tjon I/III potential, with benchmark parameters that bind the deuteron at -2.2307 MeV, represents the $NN$ interaction. The three-body problem is solved through the hyperspherical method. From spin-averaged effective $\Lambda N$ potentials with one-quarter spin singlet and three-quarters spin triplet contributions, the binding energy and root-mean-square radius of $\Lambda n p$ ($J^{\pi}=1/2^+$) computed is found to be -3.0759 MeV and 7.7 fm, respectively. This is higher than the current experimental binding energy for $\Lambda n p$ ($J^{\pi}=1/2^+$), but consistent with recent trends in high-precision measurements on the lifetime of the same hypernucleus. With charge symmetry breaking in the $\Lambda N$ potentials, this $\Lambda n p$ ($J^{\pi}=1/2^+$) binding energy was found to be consistent with a bound $\Lambda n n$ ($J^{\pi}=1/2^+$) state.