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The allowed parameter space for the lightest neutralino as the dark matter is explored using the Minimal Supersymmetric Standard Model as the low-energy effective theory without further theoretical constraints such as GUT. Selecting values of the parameters which are in agreement with present experimental limits and applying the additional requirement that the lightest neutralino be in a cosmologically interesting range, we give limits on the neutralino mass and composition. A similar analysis is also performed implementing the grand unification constraints. The elastic scattering cross section of the selected neutralinos on 27 Al and on other materials for dark matter experiments is discussed.

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