A systematic treatment of the procedure used to construct and solve the Faddeev-Yakubovsky integral equations for three and four different particles with nonzero spin is introduced. The four-body T-matrices are written in terms of solutions of the three-body Faddeev integral equations in total angular momenta representation. General spin-angular structure of the four-body Faddeev-Yakubovsky equations is written down and reduced to a spin-angular structure of the three-body system by elimination of one body. Partial-wave expansion performed for the system of four-body integral equations gives an infinite system of one-dimensional coupled equations with integral kernels containing four types of partial components of the three-body Faddeev integral equation solutions. The given method is tested on $\mathrm{\Lambda }-NN$ and $\mathrm{\Lambda }-NNN$ systems with two-body potential written down in only separable form. Both separable NN potential and ΛN potential rewritten in separable form for s-wave are used to determine the Λ-hyperon binding energies in $\mathrm{\Lambda }-NN$ and $\mathrm{\Lambda }-NNN$ systems. Calculation also includes the hyperon conversion in $\mathrm{\Lambda }N\to \mathrm{\Sigma }N$ process. Λ-hyperon separation energies were calculated from binding energies and turned out to be 0.147 MeV in $\mathrm{\Lambda }-NN$ system and 2.04 MeV in $\mathrm{\Lambda }-NNN$ system, respectively, that is in close coincidence with experimental ones.

介绍了用于构造和求解具有非零自旋的三个和四个不同粒子的Faddeev-Yakubovsky积分方程的过程的系统处理。四体T矩阵是根据三体Faddeev积分方程在总角矩表示中的解表示的。写下四体Faddeev-Yakubovsky方程的一般自旋角结构，并通过消除一个体将其简化为三体系统的自旋角结构。对四体积分方程组执行的分波展开式给出了一个一维耦合方程组的无限系统，该方程组的积分内核包含三体Faddeev积分方程解的四种类型的部分分量。给定的方法在$\mathrm{\Lambda }-ññ$ 和 $\mathrm{\Lambda }-ñññ$具有两体势的系统只能以可分离的形式写下来。两个可分离NN电位和Λ Ñ在可分离形式改写s波电位用于确定Λ超子结合能在$\mathrm{\Lambda }-ññ$ 和 $\mathrm{\Lambda }-ñññ$系统。计算还包括Hyperon转换$\mathrm{\Lambda }ñ\to \mathrm{\Sigma }ñ$过程。由结合能计算出Λ氢的分离能，结果为0.147 MeV in$\mathrm{\Lambda }-ññ$ 系统和2.04 MeV in $\mathrm{\Lambda }-ñññ$ 分别与实验系统相吻合。