Atomic and nuclear Ξ− bound states

Abstract

An study of the Ξ−-nucleus interaction is done for the purpose of expanding the knowledge on how strangeness S = −2 hyperons interact with nuclear media. Our work is based on some recent two-body capture events (Ξ−p → ΛΛ) on 12C and 14N nuclei measured at KEK and J-PARC in which a pair of single-Λ hypernuclei are formed. By developing an algorithm, based on Numerov’s method, able to resolve numerically the radial Schr¨odinger’s equation with a potential composed by a finite-size Coulomb potential and a nuclear potential shaped as a Woods-Saxon function, we conclude that this capture events occur from 1pΞ− nuclear states with a corresponding potential depth of V0 ∼ 14−17 MeV. Developing a program able to find the Ξ-nuclear energy levels and their dependence on V0, which is at the same time easy to adapt to other interacting particles or nuclei, is part of our intention here too