Determining the \Xi-Nucleus Potential from the Measured Binding Energies of ^15_\Xi^C
Abstract
The recent observation of the deeply bound \Xi - hypernucleus ^15_\Xi^-C through the IRRAWADDY and KINKA events provided a crucial benchmark for determining the \Xi-nucleus interaction. This work aims to constrain the depth of this potential by calculating the binding energy B_\Xi of the ^15_\Xi C system, which forms a \Xi^- -^14 N bound state. We achieve this by numerically solving the Schroedinger equation for a \Xi hyperon within a phenomenological Woods-Saxon potential, using the stable Numerov method, incorporating the Coulomb interaction. For a potential well depth V_0 = 12 MeV, our calculations yield a 0^+_1 state binding energy of 6.35 MeV and a 1^-_1 state energy of 0.87 MeV. These results are in excellent agreement with the IRRAWADDY event (B_\Xi = 6.27 \pm 0.27 MeV) and the shallower 1^-_1 states (KISO/IBUKI events, B_\Xi \approx 1 MeV), respectively. Assuming \Xi^0 instead of \Xi^-, we predict the ground state 0^+ of _{\Xi^0}^{15}N with (B_{\Xi^0} = 2.636 MeV) by omitting the Coulomb interaction as a first approximation.
Cite
@article{arxiv.2510.08077,
title = {Determining the \Xi-Nucleus Potential from the Measured Binding Energies of ^15_\Xi^C},
author = {Paing Thit Nyein and Kyaw Kyaw Naing and Htun Htun Oo and M. Yamaguchi and Hiroyuki Kamada},
journal= {arXiv preprint arXiv:2510.08077},
year = {2025}
}
Comments
5page,no figure