  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.
