Cluster reduction of the four-body Yakubovsky equations in configuration space for the bound-state problem and for low-energy scattering

A method using an expansion of the four-body Yakubovsky wave function components onto the basis of the Faddeev-equation solutions for the two-cluster sub-Hamiltonian eigenfunctions is proposed. This expansion reduces the Yakubovsky differential equations to a system of coupled-channel equations for functions depending on the relative coordinates between the subsystems of the two-cluster partitions. On the basis of the resulting equations the four-nucleon bound-state problem and the zero-energy n-t scattering problem are solved on the relatively small computer.