  Abstract: The interaction of dark matter particles (WIMPs) with the odd-mass
$^{73}$Ge and $^{131}$Xe target nuclei ,{ {that is the recoil rates
corresponding to the elastic scattering of WIMPs by these nuclei}}, is analysed
in the context of the minimal extensions of the SUSY model. The BCS+QRPA
technique plus the quasiparticle-phonon coupling scheme is used to describe the
nuclear structure part of the calculations. The resulting values for the
nuclear spin content of both nuclei are compared to values previously reported
in the literature.
