Solving the differential Yakubovsky equations for p 3He scattering by the cluster-reduction method

The cluster-reduction method has been used to solve numerically the differential equations for the s-wave Yakubovsky components in the nppp system. Proton scattering on a ³He nucleus has been considered for energies below the three-body threshold in the singlet and triplet spin states of the system. Nucleon-nucleon interaction has been simulated by the MT I–III potential, and the Coulomb interaction between the protons has been taken into account. Effective equations that describe the relative motion of clusters have been derived. The low-energy behavior of phase shifts has been analyzed. The values of ¹ A=8.2 fm and ³ A=7.7 fm have been obtained for, respectively, the singlet and triplet scattering lengths. The calculated phase shifts agree well with experimental data.