Scenarios for the formation of systems in which a carbon-oxygen white dwarf accretes helium from a nondegenerate companion that burns helium in its core are considered. The mass transfer rate in such systems is about 300 times larger than that anticipated for classical hydrogen-transferring cataclysmic variables with orbital periods less than two hours, and the lifetime is some 200 times smaller than that of short-period classical cataclysmics. After the transfer of about 0.15 solar mass of helium onto a dwarf of initial mass 0.6-1 solar, a thermonuclear runaway occurs in the accreted layer. If the mass of the accretor is about 0.6 solar, the system may appear as a short-lived helium PN. If it remains visible for about 100 yr, there may be one such supernova at any time in the Galaxy at a luminosity of the order 10,000 solar. If the mass of the accretor is 1 solar or larger, an explosion of weak supernova magnitude will occur. Perhaps two in 10 supernovae may be of this variety.
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Icko et al. (1991) studied this question.