The three-cluster generator coordinate method is used to investigate the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$${(}^3$He,2p${)}^4$He and ${}_{}{}^3{}_{}{}^{}\mathrm{H}$${(}^3$H,2n${)}^4$He reactions at low energies. The three-body exit channels are simulated by distortion effects in the wave functions. We test the model through the experimental ${}_{}{}^3{}_{}{}^{}\mathrm{He}$${+}^3$He elastic cross sections, and discuss the different contributions to the S factors. We show that, in the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$${(}^3$He,2p${)}^4$He cross section, the (α+p)+p sequential breakup dominates the α+(p+p) process. A systematic search for resonances in ${}_{}{}^6{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ is carried out, but we do not find any evidence for a new resonance.

• Received 2 June 1994

DOI:https://doi.org/10.1103/PhysRevC.50.2635