Type Ia Supernovae in semi-detached binary systems

We have considered scenarios for the evolution of close binaries resulting in the formation of semi-detached systems in which a white dwarf can accumulate Chandrasekhar mass by accretion from a main-sequence or subgiant companion with $M\sim 2M_{\odot }$. These white dwarfs, probably, explode as type Ia supernovae or collapse with formation of neutron stars. We have carried out a population synthesis study for these systems and have estimated the occurrence rate of such events in the Galaxy, depending on the parameter of common envelopes, mass-exchange rate in the binary, reaction of the main-sequence component on accretion of helium in the intervening phase of evolution. We have found that the model occurrence rate of SNe Ia in semi-detached systems is $\simeq 0.2 \times 10^{-3}$yr$^{-1}$,i\mathrm{.}e\mathrm{.},itdoesnotexceed$\sim 10%$ of the observational estimate of the Galactic occurrence rate of SNe Ia.