Using a nonrelativistic field theoretic formalism a soluble model of the four-nucleon system is developed and solved numerically. Two- and three-body scattering proceeds through intermediate quasiparticles and the resulting $T$ matrices are separable in momentum space and satisfy two- and three-body unitarity. The 2 + 2 subamplitudes are treated exactly by the convolution method. The resulting four-body equations reduce to single variable integral equations following partial wave decomposition and can be solved numerically by rotation of contour together with matrix inversion. A complete phase shift calculation is performed for the isospin triplet interaction. The differential cross sections for all two-to-two processes initiated by $p$+${}_{}{}^3{}_{}{}^{}\mathrm{He}$, $n$+${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and $d+d$ are compared with experiment for energies up to 25 MeV in the center of mass. Total elastic and reaction cross sections for the processes initiated by $n$+${}_{}{}^3{}_{}{}^{}\mathrm{H}$ are also calculated and compared with experimental data.

NUCLEAR REACTIONS Four-body calculation of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$($n$,$n$)${}_{}{}^3{}_{}{}^{}\mathrm{H}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$($p$,$p$)${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}$($d$,$d$)${}_{}{}^2{}_{}{}^{}\mathrm{H}$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}$($d$,$n$)${}_{}{}^3{}_{}{}^{}\mathrm{He}$

• Received 16 June 1978

DOI:https://doi.org/10.1103/PhysRevC.19.1711