Three-cluster approximation in the algebraic version of the resonating-group method: The ground state of the 9Li nucleus

The three-cluster approximation for describing light nuclei is formulated in the algebraic version of the resonating-group method. The overlap integral and matrix elements of the Hamiltonian between the generating invariants are obtained for the 9Li nucleus. All allowed (by the Pauli exclusion principle) permutations of nucleons belonging to different clusters that form the 9Li nucleus are taken into account in the calculations. The results can easily be generalized to any three-cluster system up to the 12C nucleus. Expressions obtained for the matrix elements are used in variational calculations of the energies and the structure features of the 9Li nucleus in the ground state. It is shown that the ground state of the 9Li nucleus is not described by the shell model and that it has a well-pronounced three-cluster structure. 16 refs., 2 figs., 3 tabs