Calculations of scattering lengths in four-nucleon system on the basis of cluster reduction method for Yakubovsky equations

The cluster reduction method for the Yakubovsky equations in configuration space is used for calculations of zero-energy scattering in four-nucleon system. The main idea of the method consists in making use of expansions for the Yakubovsky amplitudes onto the basis of the Faddeev components for the two-cluster sub-Hamiltonian eigenfunctions. The expansions reduce the original equations to ones for the functions depending on the relative coordinates between the clusters. On the basis of the resulting equations the N-(NNN) zero-energy scattering problems are solved numerically with the MT I-III model for N-N forces and neglecting the Coulomb interaction between protons.