  The half-lives of isotopes around the $N=82$ shell closure are an important
ingredient in astrophysical simulations and strongly influence the magnitude of
the second $r$-process abundance peak in the $A\sim130$ region. The most
neutron-rich $N=82$ nuclei are not accessible to the current generation of
radioactive beam facilities and $r$-process simulations must therefore rely on
calculations of the half-lives of the isotopes involved. Half-life measurements
of the experimentally accessible nuclei in this region are important in order
to benchmark these calculations. The half-life of $^{130}$Cd is particularly
important as it is used to tune the Gamow-Teller quenching in shell-model
calculations for the $\beta$ decay of other nuclei in this region. In this
work, the GRIFFIN $\gamma$-ray spectrometer at the TRIUMF-ISAC facility was
used to measure the half-life of $^{130}_{~48}$Cd$_{82}$ to be $T_{1/2}=
126(4)$ ms. In addition, the half-lives of the three $\beta$ decaying states of
$^{131}_{~49}$In$_{82}$ were measured to be $T_{1/2}(1/2^-)=328(15)$ ms,
$T_{1/2}(9/2^+)=265(8)$ ms, and $T_{1/2}(21/2^+)=323(50)$ ms, respectively,
providing an important benchmark for half-life calculations in this region.

Nuclear Experiment