Nuclear shell model calculations of neutralino-nucleus cross sections forSi29andGe73

We present the results of detailed nuclear shell model calculations of the spin-dependent elastic cross section for neutralinos scattering from ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$. The calculations were performed in large model spaces which adequately describe the configuration mixing in these two nuclei. As tests of the computed nuclear wave functions we have calculated several nuclear observables and compared them with the measured values and found good agreement. In the limit of zero momentum transfer we find scattering matrix elements in agreement with previous estimates for ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ but significantly different than previous work for ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$. A modest quenching, in accord with shell model studies of other heavy nuclei, has been included to bring agreement between the measured and calculated values of the magnetic moment for ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$. Even with this quenching, the calculated scattering rate is roughly a factor of 2 higher than the best previous estimates; without quenching, the rate is a factor of 4 higher. This implies a higher sensitivity for germanium dark matter detectors. We also investigate the role of finite momentum transfer upon the scattering response for both nuclei and find that this can significantly change the expected rates. We close with a brief discussion of the effects of some of the non-nuclear uncertainties upon the matrix elements.