Roles of nuclear weak rates on the evolution of degenerate cores in stars

Electron-capture and β-decay rates in stellar environments are evaluated with the use of new shell-model Hamiltonians for sd-shell and pf-shell nuclei as well as for nuclei belonging to the island of inversion. Important role of the nuclear weak rates on the final evolution of stellar degenerate cores is presented. The weak interaction rates for sd-shell nuclei are calculated to study nuclear Urca processes in O-Ne-Mg cores of stars with 8-10 M⊙ (solar mass) and their effects on the final fate of the stars. Nucleosynthesis of iron-group elements in Type Ia supernova explosions are studied with the weak rates for pf-shell nuclei. The problem of the neutron-rich iron-group isotope over-production compared to the solar abundances is shown to be nearly solved with the use of the new rates and explosion model of slow defraglation with delayed detonation. Evaluation of the weak rates is extended to the island of inversion and the region of neutron-rich nuclei near 78Ni, where two major shells contribute to their configurations