Nuclear weak rates in stellar environments are obtained by shell-model calculations including Gamow-Teller (GT) and spin-dipole transitions, and applied to nuclear weak processes in stars. The important roles of accurate weak rates for the study of astrophysical processes are pointed out. The weak rates in sd-shell are used to study the evolution of ONeMg cores in stars with 8-10 M⊙. Cooling of the core by nuclear Urca processes, and the heating by double e-captures on 20Ne are studied. Especially, the e-capture rates for a second-forbidden transition in 20
Nearby in the stack
Ne are evaluated with the multipole expansion method of Walecka and Behrens-B
u
hring, and the final fate of the cores, core-collapse or thermonuclear explosion, are discussed. The weak rates in
pf
-shell are applied to nucleosynthesis of iron-group elements in Type Ia supernovae. The over-production problem of neutron-rich iron isotopes compared with the solar abundances is now reduced to be within a factor of two. The weak rates for nuclear Urca pair with
A
=31 in the island of inversion are evaluated with the effective interaction obtained by the extended Kuo-Krenciglowa method. The transition strengths and e-capture rates in
78
Ni, important for core-collapse processes, are evaluated with the
pf
-
sdg
shell, and compared with those obtained by the random-phase-approximation and an effective rate formula.
β
-decay rates of
N
=126 isotones are evaluated with both the GT and first-forbidden transitions. The half-lives are found to be shorter than those obtained by standard models. Neutrino-nucleus reaction cross sections on
13
C,
16
O and
40
Ar are obtained with new shell-model Hamiltonians. Implications on nucleosynthesis, neutrino detection, neutrino oscillations and neutrino mass hierarchy are discussed.