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 expantions 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 neglegting the Coulomb interaction between protons.