  We investigate the ground state properties of a family of $N$-body systems in
1-dimension, trapped in a polynomial potential and having long range 2-body
interaction in addition to the inverse square potential studied in the
Calogero-Sutherland model (CSM). We show that for such a Hamiltonian, the
ground state energy is similar to that of free fermions in a harmonic well with
a displacement that depends on the number of particles and depth of the well.
We obtain the ground state wave function and using random matrix results, study
the particle density and pair correlation function (PCF). We observe that the
particles are arranged in bands. Due to the presence of long range interaction,
the PCF shows a departure from the CSM.
