Shell model calculations for light supersymmetric particle scattering off light nuclei

We investigate the elastic scattering cross section of cold dark matter candidates, i.e., lightest supersymmetric particles (LSP), with light nuclei ${(}^{19}\mathrm{F},$ ${}^{23}\mathrm{Na},$ and ${}^{29}\mathrm{Si}).\mathrm{}$ These nuclei are promising targets of direct detection for such cold dark matter. We pay special attention to the spin dependence of the differential event rate. Our calculations are performed in the $s-d$ shell model space with the Wilthental interaction. We also examine the momentum transfer dependence of the differential cross section.