  It is commonly held that quantum states with energy $E = 0$ would belong to
the continuum. However, several situations have been reported when a
zero-energy state becomes bound subject to certain restrictions on the coupling
constants defining the potential. In the present work, we present another
evidence of the existence of regular zero-energy normalizable solutions for a
system of QES potentials that correspond to rationally extended many-body
truncated Calogero-Sutherland model. Our procedure is based upon the potential
group approach with an underlying so$(2, 1)$ structure that utilizes the three
cases guided by it on profitably carrying out a point canonical transformation.
We deal with each case separately by suitably restricting the coupling
parameters.
