Four-nucleon scattering in theK-matrix approach with improved treatment of the (2+2) channels

The cross sections for elastic and rearrangement four-nucleon reactions have been calculated above the breakup threshold in the K-matrix approximation to the Grassberger-Sandhas integral equations. In the first order K-matrix approximation we find that the ${}_{}{}^2{}_{}{}^{}\mathrm{H}$(d,p${)}^3$H and ${}_{}{}^2{}_{}{}^{}\mathrm{H}$(d,n${)}^3$He cross sections at low energies are sensitive to the properties of the nuclear force and to its tensor component even at higher energies. At higher energies good agreement is obtained with experiment, but there is quantitative and qualitative disagreement with the data at lower energies. We also performed K-matrix calculations including the principal value part of the (2+2) propagators by means of the generalized-unitary-pole-expansion/energy-dependent-pole-expansion for the (2+2) subamplitudes. At lower energies this improved the agreement with data in the ${}_{}{}^2{}_{}{}^{}\mathrm{H}$(d,n${)}^3$He reaction considerably, and in the case of p${+\mathrm{}}^3$He elastic scattering even resulted in a spectacular improvement in the forward direction. The lack of structure in the differential cross section [e.g., absence of a second maximum in the ${}_{}{}^2{}_{}{}^{}\mathrm{H}$(d,n${)}^3$He cross section] persisted, however. This qualitative disagreement is probably mainly due to the omission of the contribution of the p-wave three-body subsystem amplitude in the calculations.