Limits on active-sterile neutrino mixing parameters using heavy nuclei abundances

The production of heavy-mass elements due to the rapid neutron-capture mechanism (r-process) is associated with astrophysical scenarios, such as supernovae and neutron-star mergers. In the r-process the capture of neutrons is followed by $\beta$-decays until nuclear stability is reached. A key element in the chain of nuclear weak-decays leading to the production of isotopes may be the change of the parameters controlling the neutrino sector, due to the mixing of active and sterile species. In this work we have addressed this question and calculated $\beta$-decay rates for the nuclei involved in the r-process chains as a function of the neutrino mixing parameters. These rates were then used in the calculation of the abundance of the heavy elements produced in core-collapse supernova and in neutron-star mergers, starting from different initial mass-fraction distributions. The analysis shows that the core-collapse supernova environment contributes with approximately $30\%$ of the total heavy nuclei abundance while the neutron-star merger contributes with about $70\%$ of it. Using available experimental data we have performed a statistical analysis to set limits on the active-sterile neutrino mixing angle and found a best-fit value $\sin^2 2\theta_{14}=0.22$, a value comparable with those found in other studies reported in the literature.