Stellar electron capture rates on neutron-rich nuclei and their impact on stellar core collapse

During the late stages of gravitational core-collapse of massive stars, extreme isospin asymmetries are reached within the core. Due to the lack of microscopic calculations of electron-capture (EC) rates for all relevant nuclei, in general simple analytic parametrizations are employed. We study here several extensions of these parametrizations, allowing for a temperature, electron density, and isospin dependence as well as for odd-even effects. The latter extra degrees of freedom considerably improve the agreement with large-scalemicroscopic rate calculations. We find, in particular, that the isospin dependence leads to a significant reduction of the global EC rates during core collapse with respect to fiducial results, where rates optimized on calculations of stable fp-shell nuclei are used. Our results indicate that systematic microscopic calculations and experimental measurements in the N approximate to 50 neutron-rich region are desirable for realistic simulations of the core collapse.