  By using the technique of supersymmetric quantum mechanics, we study a quasi
exactly solvable extension of the N-particle rational Calogero model with
harmonic confining interaction. Such quasi exactly solvable many particle
system, whose effective potential in the radial direction yields a
supersymmetric partner of the radial harmonic oscillator, is constructed by
including new long-range interactions to the rational Calogero model. An
infinite number of bound state energy levels are obtained for this system under
certain conditions. We also calculate the corresponding bound state wave
functions in terms of the recently discovered exceptional orthogonal Laguerre
polynomials.
