Super-Calogero-Moser-Sutherland systems and free super-oscillators: a mapping

We show that the supersymmetric rational Calogero-Moser-Sutherland (CMS) model of AN+1-type is equivalent to a set of free super-oscillators, through a similarity transformation. We prescribe methods to construct the complete eigenspectrum and the associated eigenfunctions, both in supersymmetry-preserving as well as supersymmetry-breaking phases, from the free super-oscillator basis. Further we show that a wide class of super-Hamiltonians realizing dynamical OSp(2 vertical bar 2) supersymmetry, which also includes all types of rational super-CMS as a small subset, are equivalent to free super-oscillators. We study BCN+1-type super-CMS model in some detail to understand the subtleties involved in this method