The Alt–Grassberger–Sandhas equations for the five-body problem are solved for the case of the driving two-body potentials limited to s-waves. The separable pole expansion method is employed to convert the equations into the effective quasi-two-body form. Numerical results are presented for five identical bosons as well as for the system containing an $$\eta $$-meson and four nucleons. Accuracy of the separable expansion is investigated. It is shown that both in $$(1+4)$$ and $$(2+3)$$ fragmentation, the corresponding eigenvalues decrease rather rapidly, what, combined with the alternation of their signs, leads to rather good convergence of the results. For the $$\eta -4N$$ system the crucial influence of the subthreshold behavior of the $$\eta N$$ amplitude on the $$\eta $$-nuclear low-energy interaction is discussed.

中文翻译：

---

$$\varvec{\eta -4N}$$问题的五体积分方程和解

五体问题的 Alt-Grassberger-Sandhas 方程在驱动二体势仅限于 s 波的情况下求解。采用分离极点展开法将方程转化为有效的拟二体形式。给出了五个相同玻色子以及包含 $$\eta $$-介子和四个核子的系统的数值结果。研究了可分离扩展的准确性。结果表明，在$$(1+4)$$和$$(2+3)$$分片中，对应的特征值下降得比较快，再加上它们的符号交替，导致了较好的收敛性结果。对于 $$\eta -4N$$ 系统，讨论了 $$\eta N$$ 振幅的亚阈值行为对 $$\eta $$-核低能相互作用的关键影响。