Shell-Model Study of Nuclear Weak Rates relevant to Astrophysical Processes in Stars

New shell-model Hamiltonians which can successfully describe spin responses in nuclei are used to evaluate nuclear weak rates in stellar environments. The e-capture and beta-decay rates for the nuclear pair with Mg-31-(31) Al, in the island of inversion, which have been pointed out to be important for the cooling of neutron star crusts, are studied by shell-model calculations with the effective interaction in sd-pf shell obtained by the extended Kuo-Krenciglowa (EKK) method. The weak rates induced by the Gamow-Teller transitions between the low-lying states in the nuclear pair lead to a nuclear Urca process. The spin-dipole strengths and e-capture rates for Ni-78 are evaluated by shell-model with full pf-sdg shells including up to 5p-5h excitations outside filling configurations of Ni-78. The e-capture rates obtained are compared with RPA calculations and the effective rate formula. Weak rates for the second-forbidden transition in Ne-20 are evaluated by the multipole expansion method of Walecka as well as the Behrens-Buhring method within sd-shell. Difference in the rates between the two methods is found to be rather small as far as the conserved-vector-current (CVC) relation is satisfied. Possible important contributions of the forbidden transition to the heating of the ONeMg core by double e-captures on Ne-20 in a late stage of the evolution of the core and implications on the final fate of the core, whether core-collapse or thermonuclear explosion, are discussed.