Using a two-body separable $t$ matrix between pairs, we solve the resulting four-body equations for four spinless bosons in the form that the 2+2 subsystem contribution is treated exactly by the convolution method. The 3+1 subamplitudes are represented as finite rank operators. We compare the utility of these methods both in four-body bound state and scattering calculations. We also develop an approximation that neglects four-body intermediate states in the 2+2 subsystem contribution and compare it with exact results. Finally, we present the results for a four-nucleon calculation with spin dependent $s$-wave separable interactions between pairs. These formally exact four-body equations are subsequently used to develop one parameter models to describe low energy phase shifts and cross sections for the reactions n ${}_{}{}^3{}_{}{}^{}\mathrm{H}$→n ${}_{}{}^3{}_{}{}^{}\mathrm{H}$, dd→dd, and dd→p ${}_{}{}^3{}_{}{}^{}\mathrm{H}$.

• Received 1 August 1983

DOI:https://doi.org/10.1103/PhysRevC.30.35