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Shell-model studies on the weak $\beta$-decay in nuclei relevant to astrophysical processes are carried out. The $\beta$-decay rates, as well as electron-capture rates in the $sd$- $pf$shell induced by Gamow–Teller (GT) transition, are evaluated in astrophysical environments. The weak rates for the Urca pair of nuclei with $A$= 31 in the island of inversion, which are important for the nuclear Urca processes in neutron star crusts, are investigated by shell-model calculations in the $sd$– $pf$shell. The GT strength is evaluated in the $sd$– $pf$shell for selected $\beta$-decays in the $sd$-shell nuclei, and the effects of the expansion of the configuration space on the quenching of the axial–vector coupling are examined. $\beta$-decay rates induced by first-forbidden (FF) transitions are studied by the Behrens–Bühring (BB) method for the isotones with $N$= 126 and compared with the Walecka method. The important role of the electron distortions in the $\beta$-decays of²⁰⁶Hg and²⁰⁷Tl is pointed out. 

Abstract We first discuss and determine the isospin mixing of the two 2− states (12.53 MeV and 12.97 MeV) of the16O nucleus using inelastic electron scattering data. We then evaluate the cross section of 4.4-MeV γ rays produced in the neutrino neutral-current (NC) reaction 16O(ν, ν′)16O(12.97 MeV, 2−) in a water Cherenkov detector at a low energy, below 100 MeV. The detection of γ rays for Eγ > 5 MeV from the NC reaction 16O(ν, ν′)16O(Ex > 16 MeV, T = 1) with a water Cherenkov detector in supernova neutrino bursts has been proposed and discussed by several authors previously. In this article, we discuss a new NC reaction channel from 16O(12.97 MeV, 2−) producing a 4.4-MeV γ ray, the cross section of which is more robust and even larger at low energy (Eν < 25 MeV) than the NC cross section from 16O(Ex > 16 MeV, T = 1). We also evaluate the number of such events induced by neutrinos from supernova explosion which can be observed by the Super-Kamiokande, an Earth-based 32-kton water Cherenkov detector. 

Nucleosynthesis of iron-group elements in Type Ia supernovae is studied for single-degenerate models with the use of electron-capture rates updated with the new shell-model Hamiltonian in pf -shell. An over-production problem of neutron-rich iron-group isotopes compared with the solar abundances is now found to be suppressed within a factor of about twice for the updated weak rates. Effects of screening on nucleosynthesis are investigated for explosion models of fast deflagration and slow deflagration with delayed detonation. The e-capture rates are reduced by the screening, especially by the screening effects on the ions. The production yields of most neutron-rich isotopes such as 50 Ti, 54 Cr and 58 Fe are found to be suppressed most by the screening. The inclusion of the screening is desirable for precise evaluation of abundances of neutron-rich nuclides.