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Particle dark matter coherent scattering direct searches rely on the scattering of the DM particle off a nucleus (Xe, Si, Ge, NaI etc). The wisdom is this is coherent scattering: so the rate ~atomic mass squared, since $q^2 \approx zero$. Is this completely sensible? Despite $q^2 \approx 0$ for galactic wind DM particles, thus with a size of interaction supposedly $\approx \hbar/q^2 > R$ nucleus, is it really sensible for a tiny heavy object exchanging a similarly tiny object to extend over the entire nucleus??? Argument for no:

  1. $\approx 100$ GeV particle: Compton wavelength < 1F the size of a single nucleon.
  2. object exchanged, Z or H, also on shell size < 1F.
  3. neutralino - esp. if it could be a 4th gen. Dirac or Majorana neutrino**, will have an oscillation length < 1 F - i.e. its wavefunctions will be changing on a scale small with the nucleus
  4. compared with e-m scattering, like e, mu, proton off nuclei, the e-m field clearly could encompass the entire nucleus at low $q^2$.
  5. compared with light neutrino scattering, even though W,Z heavy, the neutrino itself at low q^2 is larger than the nucleus.

** if the neutrino mixing angles $\sin^2\theta \approx (1/\Delta m^2)^2$ or $(1/\Delta m^2)1.5$, which they do for gen 1-3, then a 4th gen 100 GeV neutrino has a lifetime $\approx T_{top} \times 10^{44} > T_{universe}$, assuming the charged partner mass $ > M_{ne_u}$.

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Coherent scattering of nuclei and nucleons at $ \hbar/q^2 \ll R$ is a fairly mundane and well understood phenomena (it was, for instance, the tool we attempted to use to probe the onset of perturbative physics in my dissertation project) despite the fact that it seems to violate the size scaling rule. – dmckee Jul 17 '11 at 19:13
BTW-- Welcome to Physics.SE! You'll note that I have edited your question to make the formatting conform to the two tools we have available (MarkDown for text styling and MathJax for LaTeX alike mathematical expressions). You can find some help on the tools in the FAQ and in the sidebar of the editing page. However, I was a little unclear on exactly what you wanted in the (**) footnote, so I have probably not written what you meant. – dmckee Jul 17 '11 at 19:21

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