Spin-independent WIMP-nucleus scattering (${\sigma }_A(0)={\sigma }_p({\mu }_A/{\mu }_p{)}^2{A}^2$ for equal proton/neutron couplings)

An elastic recoil interaction whose leading coherent nuclear amplitude does not depend on nuclear spin. At low momentum transfer, proton and neutron amplitudes add; equal couplings give an $A$-fold amplitude and the displayed cross-section scaling, with reduced masses ${\mu }_A$ and ${\mu }_p$. A finite-momentum nuclear form factor reduces coherence. Unequal nucleon couplings or other interactions change how experiments on different targets should be compared.