Cases for DM candidates elastically interacting with nuclei with SI&SD coupling, under some given assumptions

In the most general scenario both the SI and the SD components of the cross-section are present and our DAMA/NaI set-up is sensitive to both of them. In this general scenario the result is an allowed volume in the 4-dimensional space (mW, ξσSI, ξσSD, θ).
See in the figure example of slices of the obtained DAMA/NaI 4-dimensional allowed volume for some of the possible mW and θ values in the frameworks discussed in [Riv. N. Cim. 26 n.1 (2003), 1; Int. J. Mod. Phys. D 13 (2004), 2127]. Inclusion of other existing uncertainties on parameters and models would further extend the regions; for example, the use of more favourable form factors and/or of more favourable spin factors than the considered ones would move them towards lower cross sections.
It is worth to note that experiments using either nuclei largely insensitive to SD coupling (such as e.g. natGe, natSi, natAr, natCa, natW and natO) or nuclei in principle all sensitive to such a coupling, but having a different unpaired nucleon (neutron in odd spin nuclei, such as 129Xe, 131Xe, 125Te, 73Ge, 29Si, 183W) with the respect to the proton in 23Na and 127I cannot explore most of the 4-dimensional volume allowed by DAMA/NaI.