On the possibility to search for double beta decay of initially unstable (alpha/beta radioactive) nuclei

Possibilities to search for double beta decay of alpha/beta unstable nuclei, many of which have higher energy release than "conventional" (beta stable) double beta decay candidates, are discussed. First experimental half-life limits on double beta decay of radioactive nuclides from U and Th families (trace contaminants of the CaWO_4, CdWO_4 and Gd_2SiO_5 scintillators) were established by reanalyzing the data of low-background measurements in the Solotvina Underground Laboratory with these detectors (1734 h with CaWO_4, 13316 h with CdWO_4, and 13949 h with Gd_2SiO_5 crystals).