Fluctuation-correlation analysis of the Calogero-Sutherland model

We exploit the exact solution for the ground stare of the one-dimensional s pinless quantum gas of fermions with mu /x(ij)(2) interaction. The availabl e analytical pair densities for mu = -1/4, 0, and 2 allow us to analyze par ticle-number fluctuations. They are suppressed by repulsive interaction (mu >0), enhanced by attraction (mu <0), and measure the kind and strength of correlation. Other recently proposed purely quantum-kinematical measures of the correlation strength arise from the small-separation behavior of the p air density or-for fermions-from the nonidempotency of the momentum distrib ution and its large-momenta behavior. They are compared with each other and with reference-free, short-range correlation-measuring ratios of the kinet ic and potential energies.