Background: $beta$-delayed multiple neutron emission has been observed for some nuclei with A$leq$100, with $^{100}$Rb being the heaviest $beta$2n emitter measured to date. So far, only 25 P$_{2n}$ values have been determined for the $sim$300 nuclei that may decay in this way. Accordingly, it is of interest to measure P$_{2n}$ values for the other possible multiple neutron emitters throughout the chart of the nuclides. It is of particular interest to make such measurement for nuclei with A$>$100 to test the predictions of theoretical models and simulation tools for the decays of heavy nuclei in the region of very neutron-rich nuclei. In addition, the decay properties of these nuclei are fundamental for the understanding of astrophysical nucleosynthesis processes such as the $r$-process, and safety inputs for nuclear reactors. Purpose: To determine for the first time the two neutron branching ratio, P$_{2n}$ value, for $^{136}$Sb through a direct neutron measurement, and to provide precise P$_{1n}$ values for $^{136}$Sb and $^{136}$Te. Method: Pure beams were provided by the JYFLTRAP at the IGISOL facility of the University of Jyvaskyla, Finland. The purified ions were implanted into a moving tape at the end of the beam line. The detection setup consisted of a plastic scintillator placed right behind the implantation point, and the BELEN detector, based on neutron counters embedded in a polyethylene matrix. The analysis was based on the study of the $beta$- and neutron- growth-and-decay curves and the $beta$-one-neutron and $beta$-two-neutron time correlations. Results: The P$_{2n}$ value of $^{136}$Sb was found to be 0.14(3)% and the measured P$_{1n}$ values for $^{136}$Sb and $^{136}$Te were found to be 32.2(15)% and 1.47(6)%, respectively. The measured P$_{2n}$ value is a factor 44 smaller than predicted by the FRDM+QRPA model used for $r$-process calculations.
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