Constraining electron capture rates in core-collapse supernovae for nuclei near N{\$}$=${\$}50.

Electron captures on medium-heavy nuclei play an important role in the late stages of the evolution of core-collapse supernovae, just prior to the explosion. In particular, nuclei around N$=$50, just above $^{\mathrm{78}}$Ni, have been identified as especially important for the deleptonization of the core. The astrophysical simulations require accurate electron-capture rates. One has to largely rely on theoretical models, which must be benchmarked and guided by experimental data. This work describes a broad effort to improve the electron capture-rates for nuclear astrophysical simulations, focusing on nuclei near N$=$50. This includes (t,$^{\mathrm{3}}$He) charge-exchange experiments for extracting Gamow-Teller strengths, the comparison with theoretical models used for calculating electron-capture rates for the astrophysical simulations, and results from sensitivity studies by using 1D core-collapse simulations.