This work focuses on the investigation of double beta decay unstable nuceli, with the aim of exploring a new approach for the direct detection of Dark Matter (DM). Specifically, the study considers the diagram associated with neutrinoless double beta decay as a potential
technique for detecting a Majorana DM fermion. This detection method involves the inelastic scattering of the DM fermion on a double beta unstable nucleus, thereby inducing its decay. By exploiting the exothermic nature of the stimulated double beta decay, it becomes possible to directly detect a light DM fermion. This is particularly significant as traditional elastic scattering technique is not able to investigate light fermion DM candidates. The paper presents the expected signal distribution for various DM masses and compares them with the current data available for the 136Xe nucleus, establishing
upper limits on the cross sections of nucleus scattering.