ALTERNATIVE DESCRIPTIONS OF BORROMEAN NUCLEI: HYPERSPHERICAL AND PSEUDOPOTENTIAL APPROACHES

Three-body systems, i.e., Borromean nuclei, are studied in the framework of the Boundary Condition Model, in which the relevant interactions are expressed in terms of the scattering lengths of the two-body subsystems. We present two alternative descriptions of such systems: a hyperspherical coordinate approach and a molecular approach. We demonstrate the role of virtual states in the two-body subsystems in producing a weekly bound three-body system, i.e., a Borromean nucleus. We obtain relations between the spatial extension of the three-body bound state, its energy, and the scattering lengths in the subsystems. The results are compared with experimental data for the Borromean nucleus 11Li and 14Be.