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

The momentum transfer dependence of the total cross section for elastic scattering of cold dark matter candidates, i.e., lightest supersymmetric particles (LSP’s), with nuclei is examined. The presented calculations of the event rates refer to a number of representative nuclear targets throughout the periodic table and have been obtained in a relatively wide phenomenologically allowed SUSY parameter space. For the coherent cross sections it is shown that, since the momentum transfer can be quite big for a large mass of the LSP and heavy nuclei even though the energy transfer is small $(<~100\hspace{0.5em}\mathrm{keV})$, the total cross section can in such instances be reduced by a factor of about 5. 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 less pronounced, since the high multipoles tend to enhance the cross section as the momentum transfer increases (for a LSP mass $<200\mathrm{}$ GeV) and partially cancel the momentum retardation. The effect of the Earth’s revolution around the Sun on these event rates is also studied by folding with a Maxwellian LSP-velocity distribution which is consistent with its density in the halos. We thus find that the convoluted event rates do not appreciably change compared to those obtained with an average velocity. The event rates increase with $A$ and, in the SUSY parameter space considered, they can reach values up to 140 yr${}^{-1}$kg${}^{-1}$ for Pb. The modulation effect, however, was found to be small (less than $\pm 5\%)$.