  Few white dwarfs, located in binary systems, may acquire sufficiently high
mass accretion rates resulting in the burning of carbon and oxygen under
nondegenerate conditions forming a O+Ne+Mg core. These O+Ne+Mg cores are
gravitationally less bound than more massive progenitor stars and can release
more energy due to the nuclear burning. They are also amongst the probable
candidates for low entropy r-process sites. Recent observations of subluminous
Type II-P supernovae (e.g., 2005cs, 2003gd, 1999br, 1997D) were able to
rekindle the interest in 8 -- 10 M$_{\odot}$ which develop O+Ne+Mg cores.
Microscopic calculations of capture rates on $^{24}$Mg, which may contribute
significantly to the collapse of O+Ne+Mg cores, using shell model and
proton-neutron quasiparticle random phase approximation (pn-QRPA) theory, were
performed earlier and comparisons made. Simulators, however, may require these
capture rates on a fine scale. For the first time a detailed microscopic
calculation of the electron and positron capture rates on $^{24}$Mg on an
extensive temperature-density scale is presented here. This type of scale is
more appropriate for interpolation purposes and of greater utility for
simulation codes. The calculations are done using the pn-QRPA theory using a
separable interaction. The deformation parameter, believed to be a key
parameter in QRPA calculations, is adopted from experimental data to further
increase the reliability of the QRPA results. The resulting calculated rates
are up to a factor of 14 or more enhanced as compared to shell model rates and
may lead to some interesting scenario for core collapse simulators.
