  Electron capture and beta-decay rates for nuclear pairs in sd-shell are
evaluated at high densities and high temperatures relevant to the final
evolution of electron-degenerate O-Ne-Mg cores of stars with the initial masses
of 8-10 solar mass. Electron capture induces a rapid contraction of the
electron-degenerate O-Ne-Mg core. The outcome of rapid contraction depends on
the evolutionary changes in the central density and temperature, which are
determined by the competing processes of contraction, cooling, and heating. The
fate of the stars are determined by these competitions, whether they end up
with electron-capture supernovae or Fe core-collapse supernovae. Since the
competing processes are induced by electron capture and beta-decay, the
accurate weak rates are crucially important. The rates are obtained for pairs
with A=20, 23, 24, 25 and 27 by shell-model calculations in sd-shell with the
USDB Hamiltonian. Effects of Coulomb corrections on the rates are evaluated.
The rates for pairs with A=23 and 25 are important for nuclear URCA processes
that determine the cooling rate of O-Ne-Mg core, while those for pairs with
A=20 and 24 are important for the core-contraction and heat generation rates in
the core. We provide these nuclear rates at stellar environments in tables with
fine enough meshes at various densities and temperatures for the studies of
astrophysical processes sensitive to the rates. In particular, the accurate
rate tables are crucially important for the final fates of not only O-Ne-Mg
cores but also a wider range of stars such as C-O cores of lower mass stars.
