  The super-Eddington wind scenario has been proposed as an alternative way for
producing type Ia supernovae (SNe Ia). The super-Eddington wind can naturally
prevent the carbon--oxygen white dwarfs (CO WDs) with high mass-accretion rates
from becoming red-giant-like stars. Furthermore, it works in low-metallicity
environments, which may explain SNe Ia observed at high redshifts. In this
article, we systematically investigated the most prominent single-degenerate
WD+MS channel based on the super-Eddington wind scenario. We combined the
Eggleton stellar evolution code with a rapid binary population synthesis (BPS)
approach to predict SN Ia birthrates for the WD+MS channel by adopting the
super-Eddington wind scenario and detailed mass-accumulation efficiencies of
H-shell flashes on the WDs. Our BPS calculations found that the estimated SN Ia
birthrates for the WD+MS channel are ~0.009-0.315*10^{-3}{yr}^{-1} if we adopt
the Eddington accretion rate as the critical accretion rate, which are much
lower than that of the observations (<10% of the observed SN Ia birthrates).
This indicates that the WD+MS channel only contributes a small proportion of
all SNe Ia. The birthrates in this simulation are lower than previous studies,
the main reason of which is that new mass-accumulation efficiencies of H-shell
flashes are adopted. We also found that the critical mass-accretion rate has a
significant influence on the birthrates of SNe Ia. Meanwhile, the results of
our BPS calculations are sensitive to the values of the common-envelope
ejection efficiency.
