Nuclear Statistical Equilibrium (NSE) abundance (i.e., the abundance specified by $\rho$, $T$, and $Y_{\rm e}$) rather than fully solving the reaction network, as the NSE is reached in this regime of high density and temperature. In order to correctly follow the evolution of $Y_{\rm e}$, weak interactions are computed along with the NSE abundance.

Throughout this paper, the initial C+O WD composition is assumed as follows: X($^{12}$C) $= 0.475$, X($^{16}$O) $=0.5$, and X($^{22}$Ne) $= 0.025$ in mass fractions. This is consistent with the compositions used in the W7 model, roughly corresponding to the initially solar CNO composition: Metallicity is represented by $^{22}$Ne, assuming that the CNO cycle in the H-burning has converted all heavy elements to $^{14}$N, and then it is reprocessed to $^{22}$Ne by $^{14}$N($\alpha, \gamma$)$^{18}$F(${\rm e}^{+}, \nu_{\rm e}$) $^{18}$O($\alpha, \gamma$)$^{22}$Ne in the He-burning.

The reaction network (Thielemann et al. 1996) includes 384 isotopes up to $^{98}$Mo. The electron capture rates, which strongly affect nucleosynthesis at the beginning of the deflagration stage, are taken from Langanke & Martinez-Pinedo (2000) and Martinez-Pinedo et al. (2000). Detailed comparisons between the new rates and those of Fuller et al. (1982, 1985) are presented by Brachwitz et al. (2000) for the spherical 1D 