Using the complex scaling method, the low-lying three-body resonances of ${}_{}{}^6{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, and ${}_{}{}^6{}_{}{}^{}\mathrm{Be}$ are investigated in a parameter-free microscopic three-cluster model. In ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ a $2^{+}$, in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ a $2^{+}$ and a $1^{+}$, and in ${}_{}{}^6{}_{}{}^{}\mathrm{Be}$ the $0^{+}$ ground state and a $2^{+}$ excited state are found. The other experimentally known $2^{+}$ state of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ cannot be localized by our present method. We have found no indication for the existence of the predicted $1^{\mathrm{-}}$ soft dipole state in ${}_{}{}^6{}_{}{}^{}\mathrm{He}$. We argue that the sequential decay mode of ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ through the resonant states of its two-body subsystem can lead to peaks in the excitation function. This process can explain the experimental results in the case of ${}_{}{}^{11}{}_{}{}^{}\mathrm{Li}$, too. We propose an experimental analysis, which can decide between the soft dipole mode and the sequential decay mode.

• Received 12 January 1994

DOI:https://doi.org/10.1103/PhysRevC.49.3035