Super-Calogero model with OSp(2 vertical bar 2) supersymmetry: is the construction unique?

We show that the construction of super-Calogero model with OSp(2 vertical bar 2) supersymmetry is not unique. In particular, we find a new co-ordinate representation of the generators of the OSp(2 vertical bar 2) superalgebra that appears as the dynamical supersymmetry of the rational super-Calogero model. Both the quadratic and the cubic Casimir operators of the OSp(2 vertical bar 2) are necessarily zero in this new representation, while they are, in general, non-zero for the super-Calogero model that is currently studied in the literature. The Scasimir operator that exists in the new co-ordinate representation is not present in the case of the existing super-Calogero model. We also discuss the case of N free superoscillators and superconformal quantum mechanics for which the same conclusions are valid