Half-Lives of the Neutron-Rich $N\approx82$ Isotopes $^{128-130}$Cd and $^{131}$In

Half-lives of $N=82$ nuclei below doubly-magic $^{132}$Sn are key input parameters for calculations of any astrophysical $r$-process scenario and play an important role in the formation and shape of the second $r$-process abundance peak. Shell-model calculations of neutron-rich nuclei near the $N=82$ neutron shell closure that are not yet experimentally accessible have been performed by adjusting the quenching of the Gamow-Teller (GT) operator to reproduce the $^{130}$Cd half-life. The calculated half-lives of other nuclei in the region are known to be systematically too long. Recently, a shorter half-life for $^{130}$Cd was measured that resolves this discrepancy by scaling the GT quenching by a constant factor for all of the nuclei in the region. However, the reduced quenching of the GT operator creates a new discrepancy in the calculated half-life of $^{131}$In. The measurement of $^{131}$In is complicated due to the presence of three known $\beta$-decaying states with roughly the same half-life, making photopeak gating an ideal method to measure each of these half-lives. In this talk, the half-lives of $^{128-130}$Cd and $^{131}$In, as well as the spectroscopy of $^{131}$Sn, measured using the GRIFFIN $\gamma$-ray spectrometer at TRIUMF will be presented.