Abstract—

Light hypernuclei play the role of a natural laboratory for the study of YN and NN interactions. The repulsive nature of the ΛN interaction leads to the fact that possible bound states in hypernuclei arise due to the three-body nucleon-hyperon-nucleon interaction. The leading role in this interaction is assigned to the conversion ΛN → ΣN of one type of hyperon to another. In this work, the binding energies of light hypernuclei are obtained by solving the homogeneous Faddeev integral equation for three particles with both realistic and phenomenological YN and NN potentials. The conversion of Λ and Σ hyperons is considered exactly. A numerical technique has been developed for the solution of the homogeneous integral Faddeev equation with three particles of different masses for the local form of pair potentials. A procedure generalized to local potentials for the approximate solution of integral equations by the Noyes–Kowalski method is presented. In order to speed up the numerical calculation, a procedure of four-dimensional spline interpolation of the obtained two-body T-matrices has been introduced and tested. Numerical calculations of binding energies are carried out both with charge-dependent separable potentials and with charge-dependent local potentials. The impact of higher partial waves of the NN potentials on the binding energy of light nuclei is discussed. The obtained values of the binding energies of the simplest nuclei ³H, ³He, are in good agreement with the available experimental values. In addition, four-body calculations with a partial-wave expansion of the pair potentials used have been carried out. It is shown that the approach developed can also be successfully applied when searching for the binding energies of four-body \({}_{{{\Lambda }}}^{4}{\text{H}},{}_{{{\Lambda }}}^{4}{\text{He}}\) hypernuclei.

中文翻译：

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轻超核的结合能

摘要——

轻超核扮演着研究 YN 和 NN 相互作用的天然实验室的角色。ΛN 相互作用的排斥性质导致超核中可能的束缚态是由于三体核子-超子-核子相互作用而产生的。这种相互作用中的主导作用被分配给一种超子到另一种超子的转换 ΛN → ΣN。在这项工作中，轻超核的结合能是通过求解具有现实和唯象 YN 和 NN 势的三个粒子的齐次 Faddeev 积分方程获得的。Λ 和 Σ 超子的转换被精确考虑。已经开发了一种数值技术，用于求解具有不同质量的三个粒子的齐次积分 Faddeev 方程，用于对势的局部形式。提出了一种通过 Noyes-Kowalski 方法推广到积分方程近似解的局部势的过程。为了加快数值计算，引入并测试了所得二体T-矩阵的四维样条插值程序。结合能的数值计算是通过电荷依赖的可分离电位和电荷依赖的局部电位进行的。讨论了NN势的较高分波对轻核结合能的影响。获得的最简单原子核的结合能值 介绍并测试了所得二体T矩阵的四维样条插值程序。结合能的数值计算是通过电荷依赖的可分离电位和电荷依赖的局部电位进行的。讨论了NN势的较高分波对轻核结合能的影响。获得的最简单原子核的结合能值 介绍并测试了所得二体T矩阵的四维样条插值程序。结合能的数值计算是通过电荷依赖的可分离电位和电荷依赖的局部电位进行的。讨论了NN势的较高分波对轻核结合能的影响。获得的最简单原子核的结合能值³ H, ³ He 与现有实验值非常吻合。此外，已经进行了对所使用的电势对的部分波展开的四体计算。结果表明，所开发的方法在搜索四体\({}_{{{\Lambda }}}^{4}{\text{H}},{}_的结合能时也可以成功应用。{{{\Lambda }}}^{4}{\text{He}}\)超核。