Three-Body Calculations of A = 9 Nuclei with Supersymmetric α-α Potentials

Abstract.

The three-body α-α-N system is considered as a model for the ⁹Be and ⁹B nuclei. Two alternative models for the α-α interaction, which are approximate supersymmetric partners of each other, are tested. One model is a shallow agr;-α potential with l-dependent repulsive core, while the other one is a deep attractive potential with Pauli-forbidden states. All static observables have been calculated for the ⁹Be ground state together with its spectrum, elastic and inelastic (to the ${5^-\over 2}$ state) longitudinal electromagnetic form factors and the Coulomb displacement for the ⁹B ground state. The shallow repulsive-core α-α potential turns out to provide an almost quantitative description of all these observables.