We consider models with a gauged U(1){'}, to which is coupled a fermionic standard-model singlet ψ. If ψ's close the Universe, a Lee-Weinberg calculation gives the four-fermion coupling G^' from the mass m_ψ. We can then calculate the germanium scattering cross section as a function of m_ψ. The results are nearly model independent and close to experimental limits for 10 GeV≤m_ψ≤100 GeV. In the region 400 GeV≤m_ψ≤40 TeV the scattering cross section depends on M_Z^', and again approaches experimental limits if M_Z^'≤2 TeV.
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Brahm et al. (1990) studied this question.
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