  Numerical simulations of structure formation have suggested that there exists
a good correlation between the halo concentration c (or the characteristic
density delta_c) and the virial mass Mvir for any virialized dark halo
described by the Navarro, Frenk & White (1995) density profile. In this Letter,
we present an observational determination of the c-Mvir (or delta_c-Mvir)
relation in the mass range of 10^14< Mvir <10^16 (solar mass) using a sample of
63 X-ray luminous clusters. The best-fit power law relation, which is roughly
independent of the values of Omega_M and Lambda, is c propto Mvir^(-0.5) or
delta_c propto Mvir^(-1.2), indicating n=-0.7 for a scale-free power spectrum
of the primordial density fluctuations. We discuss the possible reasons for the
conflict with the predictions by typical CDM models such as SCDM, LCDM and
OCDM.
