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 $d\leftrightarrow n+n$ and $t\leftrightarrow d+n$. By consistently excluding all particle-exchange contributions to the three-body sector, four-body integral equations are obtained for the two-to-two processes: $nt\to nt$, $nt\to dd$ as well as for $dd\to dd$ and $dd\to nt$. 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.