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Model Independent Form Factors for Spin Independent Neutralino-Nucleon Scattering from Elastic Electron Scattering Data

Theoretical calculations of neutralino-nucleon interaction rates with various nuclei are of great interest to direct dark matter searches such as CDMS, EDELWEISS, ZEPLIN, and other experiments since they are used to establish upper bounds on the WIMP-proton cross section. These interaction rates and cross sections are generally computed with standard, one or two parameter model-dependent nuclear form factors, which may not exactly mirror the actual form factor for the particular nucleus in question. As is well known, elastic electron scattering can allow for very precise determinations of nuclear form factors and hence nuclear charge densities for spherical or near-spherical nuclei. We use charge densities derived from elastic electron scattering data to calculate model independent, analytic form factors for various target nuclei important in dark matter searches, such as Si, Ge, S, Ca and others. We have found that for nuclear recoils in the range of 1-100 keV significant differences in cross sections and rates exist when the model independent form factors are used: at 30 keV nuclear recoil the form factors squared differ by a factor of 1.06 for $^{28}$Si, 1.11 for $^{40}$Ca, 1.27 for $^{70}$Ge, and 1.92 for $^{129}$Xe. We show the effect of different form factors on the upper limit on the WIMP-proton cross section obtained with a hypothetical $^{70}$Ge detector during a 100 kg-day effective exposure. Helm form factors with various parameter choices differ at most by 10--20% from the best (Fourier Bessel) form factor, and can approach it to better than 1% if the parameters are chosen to mimic the actual nuclear density.