Title: Determining the Ξ-Nucleus Potential from the Measured Binding Energies of ^15_Ξ^C Show Chinese title

Title: 从测量的^15_Ξ^C结合能确定Ξ-核势能

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. Show Chinese abstract

Abstract: 最近通过IRRAWADDY和KINKA事件观察到的深结合的\Xi -超核^15_\Xi ^-C为确定\Xi -核子相互作用提供了关键的基准。 本工作旨在通过计算^15_\Xi _C系统的结合能B_\Xi ，来约束该势的深度，该系统形成一个\Xi ^- -^14N束缚态。 我们通过数值求解一个\Xi _超子在现象学Woods-Saxon势中的薛定谔方程，使用稳定的Numerov方法，并包含库仑相互作用来实现这一点。 对于势阱深度V_0 = 12 MeV，我们的计算得到0^+_1态的结合能为6.35 MeV，以及1^-_1态的能量为0.87 MeV。 这些结果与IRRAWADDY事件（B_\Xi = 6.27 \pm 0.27 MeV）和较浅的1^-_1态（KISO/IBUKI事件，B_\Xi \approx 1 MeV）分别有很好的一致性。 假设将\Xi ^0 而不是\Xi ^-，我们通过忽略库仑相互作用作为第一步近似，预测了 _{\Xi ^0}^{15}N 的基态 0^+，其中 (B_{\Xi ^0} = 2.636 MeV)。