Soluble model involving four identical particles

Using a nonrelativistic field theoretic formalism, a soluble model of scattering involving four identical spinless particles is developed and solved numerically. In addition to the elementary "nucleon" (the n), two composite particles meant to approximate the deuteron and triton are introduced with the couplings d↔n+n and t↔d+n. By consistently excluding all particle-exchange contributions to the three-body sector, four-body integral equations are obtained for the two-to-two processes: nt→nt, nt→dd as well as for dd→dd and dd→nt. Numerical solutions of the equations are found to satisfy unitarity constraints above the two-, three-, and four-body thresholds. The positions of the four-body bound states are obtained and a complete phase shift calculation is performed. The sum of the total three- and four-body breakup cross sections predicted by the model are displayed as a function of energy and the angular distributions for all 2 {→} 2 reactions are compared with the four-nucleon data.NUCLEAR REACTIONS Four-body problem. Spinless model of the four-nucleon system.