Determining the Ξ-Nucleus Potential from the Measured Binding Energies of ^15_Ξ^C

TL;DR

The paper tackles the Ξ-nucleus interaction by leveraging the binding energies of the recently observed ^15_Ξ^-C hypernucleus to constrain the depth of the Ξ-nucleus potential. It solves the radial Schrödinger equation for a Ξ^- in a combined Woods-Saxon nuclear potential and Coulomb field using the Numerov method, extracting bound-state energies for the nuclear 0^+_1 and 1^-_1 configurations and comparing with IRRAWADDY, KINKA, KISO, and IBUKI data. A parameter study identifies a self-consistent depth $V_0=12$ MeV (with $a=0.65$ fm and $r_0=1.2$ fm) that reproduces both the deep IRRAWADDY binding of $B_{Ξ} ≈ 6.27$ MeV and the shallow KISO/IBUKI range around 1 MeV, while deeper potentials overbind the nuclear state. The work also predicts the $\Xi^0$ bound state in $^{15}$N by omitting the Coulomb interaction, yielding $B_{Ξ^0} ≈ 2.636$ MeV, thereby providing a benchmark for ΞN interaction models and informing the equation of state for dense baryonic matter.

Abstract

The recent observation of the deeply bound Ξ- hypernucleus ^15_Ξ^-C through the IRRAWADDY and KINKA events provided a crucial benchmark for determining the Ξ-nucleus interaction. This work aims to constrain the depth of this potential by calculating the binding energy B_Ξof the ^15_ΞC system, which forms a Ξ^- -^14 N bound state. We achieve this by numerically solving the Schroedinger equation for a Ξhyperon 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_Ξ= 6.27 \pm 0.27 MeV) and the shallower 1^-_1 states (KISO/IBUKI events, B_Ξ\approx 1 MeV), respectively. Assuming Ξ^0 instead of Ξ^-, we predict the ground state 0^+ of _{Ξ^0}^{15}N with (B_{Ξ^0} = 2.636 MeV) by omitting the Coulomb interaction as a first approximation.