Among the major uncertainties involved in the Chandrasekhar mass models for Type Ia supernovae are the companion star of the accreting white dwarf (or the accretion rate that determines the carbon ignition density) and the flame speed after ignition. We present nucleosynthesis results from relatively slow deflagration (1.5 - 3 % of the sound speed) to constrain the rate of accretion from the companion star. Because of electron capture, a significant amount of neutron-rich species such as ^{54}Cr, ^{50}Ti, ^{58}Fe, ^{62}Ni, etc. are synthesized in the central region. To avoid the too large ratios of ^{54}Cr/^{56}Fe and ^{50}Ti/^{56}Fe, the central density of the white dwarf at thermonuclear runaway must be as low as ltsim 2 e9 gmc. Such a low central density can be realized by the accretion as fast as $dot M gtsim 1 times 10^{-7} M_odot yr^{-1}$. These rapidly accreting white dwarfs might correspond to the super-soft X-ray sources.
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