Systematic investigation of energy levels of Λ hypernuclei enables physicists to determine a considerable number of details about the inner structure of these particles as well as the interaction dynamics of Λ nucleon. Of importance is to develop the theoretical tools to study spectroscopy of hypernuclei. In this regard, our aim is to specify the mass spectra and the binding energies of Λ hypernuclei in their ground and excited states. Then, we first present an analytical solution for the Bethe–Salpeter equation of single Λ hypernuclei taking the Woods–Saxon interaction potential. Through a good approximation, we present an analytical expression for the binding energies in the ground and excited states, i.e., 1p, 1d, 1f and 1g shells. We also give numerical results for Λ binding energies of light and heavy hypernuclei. Our numerical analysis is compared with experimental data so that good consistencies between both results confirm the approach used to analysis the Λ–nucleon interaction.

对Λ超核能级的系统研究使物理学家能够确定有关这些粒子内部结构以及Λ核子相互作用动力学的大量细节。重要的是开发研究超核光谱的理论工具。在这方面，我们的目标是确定 Λ 超核在基态和激发态的质谱和结合能。然后，我们首先提出一个采用 Woods-Saxon 相互作用势的单 Λ 超核 Bethe-Salpeter 方程的解析解。通过良好的近似，我们提出了基态和激发态（即 1 p、 1 d、 1 f和 1 g壳层）结合能的解析表达式。我们还给出了轻超核和重超核的 Λ 结合能的数值结果。我们的数值分析与实验数据进行了比较，两个结果之间的良好一致性证实了用于分析 Λ 核子相互作用的方法。