  In this paper, a novel theoretical scheme is presented to investigate
resonant levels in weakly bound nuclear systems by the use of isospectral
potentials. In this scheme, a new potential is constructed which is strictly
isospectral with the original shallow-well potential and has properties that
are desirable to calculate resonances more accurately and easier. Effectiveness
of the method has been had been demonstrated in terms of its application to the
first $0^+$ resonances in the neutron-rich isotopes $^A$C ($\equiv
^{A-2}$C+n+n) in the three-body cluster model for A=18, 20.
