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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 Si, 1.11 for Ca, 1.27 for Ge, and 1.92
for Xe. We show the effect of different form factors on the upper limit
on the WIMP-proton cross section obtained with a hypothetical 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.Comment: 20 pages, 8 figure