Study of resonances in exotic drip-line nuclei by the use of super-symmetric quantum mechanics

In this paper, a nice theoretical scheme is presented to investigate resonant and bound states in weakly bound nuclear systems by the use of isospectral potentials together with hyperspherical harmonics expansion. In this scheme, a new potential is constructed which is strictly isospectral with the original shallow potential and has properties that are desirable to calculate resonances more accurately and elegantly. The effectiveness of the method has been checked in terms of its application to the $0^{+}$ resonances in the neutron-rich isotopes ${}^{18,20}$C in the two-neutron plus core three-body cluster model. The results are in excellent agreement with the available data.