  Hydrogen-rich matter has been added to a CO white dwarf of initial mass 0.516
\msun at the rates $10^{-8}$ and $2\times 10^{-8}$ \msun \yrm1, and results are
compared with those for a white dwarf of the same initial mass which accretes
pure helium at the same rates. For the chosen accretion rates, hydrogen burns
in a series of recurrent mild flashes and the ashes of hydrogen burning build
up a helium layer at the base of which a He flash eventually occurs. In
previous studies involving accretion at higher rates and including initially
more massive WDs, the diffusion of energy inward from the H shell-flashing
region contributes to the increase in the temperature at the base of the helium
layer, and the mass of the helium layer when the He flash begins is
significantly smaller than in a comparison model accreting pure helium; the He
shell flash is not strong enough to develop into a supernova explosion. In
contrast, for the conditions adopted here, the temperature at the base of the
He layer becomes gradually independent of the deposition of energy by H shell
flashes, and the mass of the He layer when the He flash occurs is a function
only of the accretion rate, independent of the hydrogen content of the accreted
matter. When the He flash takes place, due to the high degeneracy at the base
of the He layer, temperatures in the flashing zone will rise without a
corresponding increase in pressure, nuclear burning will continue until nuclear
statistical equilibrium is achieved; the model will become a supernova, but not
of the classical type Ia variety.
