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The momentum transfer dependence of the total cross section for elasticscattering of cold dark matter candidates, i.e. lightest supersymmetricparticle (LSP), with nuclei is examined. The presented calculations of theevent rates refer to a number of representative nuclear targets throughout theperiodic table and have been obtained in a relatively wide phenomenologicallyallowed SUSY parameter space. For the coherent cross sections it is shown that,since the momentum transfer can be quite big for large mass of the LSP andheavy nuclei even though the energy transfer is small ($\le 100 KeV$), thetotal cross section can in such instances be reduced by a factor of about five.For the spin induced cross section of odd-A nuclear targets, as is the case of$^{207}Pb$ studied in this work, we found that the reduction is lesspronounced, since the high multipoles tend to enhance the cross section as themomentum transfer increases (for LSP $mass < 200 GeV$) and partially cancellthe momentum retardation. The effect of the Earth's revolution around the sunon these event rates is also studied by folding with a Maxwellian LSP-velocitydistribution which is consistent with its density in the halos. We thus foundthat the convoluted event rates do not appreciably change compared to thoseobtained with an average velocity. The event rates increase with A and, in theSUSY parameter space considered, they can reach values up to 140$y^{-1}Kg^{-1}$ for Pb. The modulation effect, however, was found to be small(less than $\pm 5%$).Comment: 23 LATEX pages, 4 Tables, 3 PostScript Figures included. Phys. Rev.  D, to be publishe

Cold dark matter in SUSY theories: The role of nuclear form factors and the folding with the LSP velocity