A weak-rate library aimed at investigating the sensitivity of astrophysical environments to variations of electroncapture rates on medium-heavy nuclei has been developed. With this library, the sensitivity of the core-collapse and early post-bounce phases of core-collapse supernovae to nuclear electroncapture is examined. The rates are adjusted by factors consistent with uncertainties indicated by comparing theoretical rates to those deduced from charge-exchange and β-decay measurements. To ensure a model-independent assessment, sensitivity studies across a comprehensive set of progenitors and equations of state are performed. We find a+16/−4% range in the mass of the innercore at shock formation and a ±20% range of peak e n luminosity during the deleptonization burst. These ranges are five times as large as those seen from a separate progenitor study, where we evaluate the sensitivity of these parameters to 32 presupernova models. Additionally, the simulations are found to be more sensitive to a reduction in electron-capture rates than an enhancement, and specifically to the reduction in rates for neutron-rich nuclei near the N = 50 closed neutronshell. As measurements for medium-heavy (A 65 > ) and neutron-rich nuclei are sparse, and because accurate theoretical models that account for nuclear structure considerations of individual nuclei are not readily available, rates for these nuclei may be overestimated. If more accurate estimates confirm this, results from this study indicate that significant changes to the core-collapse trajectory are expected. For this reason, experimental and theoretical efforts should focus on this region of the nuclear chart.

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