The resonance states embedded in the three-cluster continuum of ${}^6\mathrm{He}$ and ${}^6\mathrm{Be}$ are obtained in the algebraic version of the resonating group method. The model accounts for a correct treatment of the Pauli principle. It also provides the correct three-cluster continuum boundary conditions by using a hyperspherical harmonics basis. The model reproduces the observed resonances well and achieves good agreement with other models. A better understanding for the process of formation and decay of the resonance states in six-nucleon systems is obtained.

• Received 14 April 2000

DOI:https://doi.org/10.1103/PhysRevC.63.034607