One of the main challenges for the better understanding of nucleosynthesis in the rapid neutron capture process (r-process) concerns the enormous amount of very exotic neutron-rich nuclei involved in this kind of cataclysmic scenario, and the scarce information available about their nuclear properties. In particular, theoretical calculations in the mass region around N=126 are difficult to validate on the basis only of the experimental information available close to stability so far. Such information becomes relevant for a reliable interpretation of the third peak in the r-process abundance distribution. Present and next generation radioactive-beam facilities (RIB) will be instrumental towards the systematic measurement of such nuclei, for improving theoretical nuclear models, and for enhancing the accuracy of the nuclear physics input in r-process model calculations. Here we present an experiment carried out recently at Fragment Separator (FRS) at the GSI Helmholtz Center for Heavy Ion Research in Darmstadt (Germany), which allowed us to measure for the first time relevant nuclear properties of several neutron-rich isotopes in the region around Hg and Tl. Preliminary results about the identified species and their implantation statistics are reported in this contribution. The experimental setup was comprised of an array of silicon implantation detectors (SIMBA) and the BEta deLayEd Neutron detector (BELEN). The main advantage compared to previous experiments was due to an innovative self-triggered acquisition system, which allowed us to enhance the neutron detection probability when compared to conventional analogue acquisition systems. This setup has been developed in the framework of the NuSTAR (Nuclear Structure, Astrophysics and Reactions) in the DESPEC (DEcay SPEC-troscopy) collaboration which will perform experiments at the future Super Fragment Separator (SuperFRS) at FAIR (Facility for Antiproton and Ion Research).