  We consider the inequivalent quantizations of a $N$-body rational Calogero
model with a Coulomb type interaction. It is shown that for certain range of
the coupling constants, this system admits a one-parameter family of
self-adjoint extensions. We analyze both the bound and scattering state sectors
and find novel solutions of this model. We also find the ladder operators for
this system, with which the previously known solutions can be constructed.
