  The nature of the progenitors of type Ia supernovae (SNe Ia) remains a
mystery. Binary systems consisting of a white dwarf (WD) and a main-sequence
(MS) donor are potential progenitors of SNe Ia, in which a thermonuclear
explosion of the WD may occur when its mass reaches the Chandrasekhar limit
during accretion of material from a companion star. In the present work, we
address theoretical rates and delay times of a specific MS donor channel to SNe
Ia, in which a He star+MS binary produced from a common envelope event
subsequently forms a WD+MS system without the He star undergoing mass transfer
by Roche lobe overflow. By combining the results of self-consistent binary
evolution calculations with population synthesis models, we find that the
contribution of SNe Ia in this channel is around 2.0e-4 per year. In addition,
we find that delay times of SNe Ia in this channel cover a range of about
1.0-2.6 Gyr, and almost all SNe Ia produced in this way (about 97%) have a
delay time of > 1 Gyr. While the rate of SN Ia in this work is about 10% of the
overall SN Ia rate, the channel represents a possible contribution to the old
population (1-3 Gyr) of observed SNe Ia.
