  A novel technique has been developed, which will open exciting new
opportunities for studying the very neutron-rich nuclei involved in the
r-process. As a proof-of-principle, the $\gamma$-spectra from the $\beta$-decay
of $^{76}$Ga have been measured with the SuN detector at the National
Superconducting Cyclotron Laboratory. The nuclear level density and
$\gamma$-ray strength function are extracted and used as input to
Hauser-Feshbach calculations. The present technique is shown to strongly
constrain the $^{75}$Ge($n,\gamma$)$^{76}$Ge cross section and reaction rate.
