On the formalism and upper limits for spin-dependent cross sections in
  dark matter elastic scattering with nuclei
  We revise the spin-dependent neutralino-nucleus elastic scattering comparing
the formalisms and approximations found in literature for the momentum transfer
dependent structure functions. We argue that one of the normalized structure
functions of Divari, Kosmas, Vergados and Skouras is all that one needs to
correctly take into account the detailed nuclear physics information provided
by shell-model calculations. The factorization of the particle physics degrees
of freedom from the nuclear physics momentum dependent structure functions
implied by this formalism allows for a better understanding of the so-called
model independent method for setting upper limits. We further discuss the
possibility of experiments with spin-dependent sensitivity like COUPP to test
or set limits on the proton spin-dependent cross section in the framework of
the stau co-annihilation region of the constrained minimal supersymmetric
standard model. For this model with $A_0 =0$, we provide a fitting formula by
which it is possible to convert an upper limit on the spin-independent cross
section as a function of the neutralino mass directly into an exclusion plot in
the ($m_{1/2}$, $\tan\beta$) plane.
