$ΛNN $ three-body problem within $s$-wave inverse scattering on theoretical data

Abstract

ΛN potentials recovered through the application of s-wave inverse scattering on theoretical data are demonstrated on the ΛNN three-body problem. The spindependent 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 ΛN potentials with one-quarter spin singlet and three-quarters spin triplet contributions, the binding energy and root-mean-square radius of Λnp (J π = 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 Λnp (J π = 1/2 + ), but consistent with recent trends in high-precision measurements on the lifetime of the same hypernucleus. With charge symmetry breaking in the ΛN potentials, this Λnp (J π = 1/2 + ) binding energy was found to be consistent with a bound Λnn (J π = 1/2 + ) state.