We perform a comparative study of the neutralino dark matter scattering on
nucleon in three popular supersymmetric models: the minimal (MSSM), the
next-to-minimal (NMSSM) and the nearly minimal (nMSSM). First, we give the
predictions of the elastic cross section by scanning over the parameter space
allowed by various direct and indirect constraints, which are from the
measurement of the cosmic dark matter relic density, the collider search for
Higgs boson and sparticles, the precision electroweak measurements and the muon
anomalous magnetic moment. Then we demonstrate the property of the allowed
parameter space with/without the new limits from CDMS II. We obtain the
following observations: (i) For each model the new CDMS limits can exclude a
large part of the parameter space allowed by current collider constraints; (ii)
The property of the allowed parameter space is similar for MSSM and NMSSM, but
quite different for nMSSM; (iii) The future SuperCDMS can cover most part of
the allowed parameter space for each model.Comment: 12 pages, 10 fig