We propose a scenario for the formation of DA white dwarfs with very thin helium buffers. For these stars we explore the possible occurrence of diffusion-induced CNO- flashes, during their early cooling stage. In order to obtain very thin helium buffers, we simulate the formation of low mass remnants through an AGB final/late thermal pulse (AFTP/LTP scenario). Then we calculate the consequent white dwarf cooling evolution by means of a consistent treatment of element diffusion and nuclear burning. Based on physically sounding white dwarf models, we find that the range of helium buffer masses for these diffusion-induced novas to occur is significantly smaller than that predicted by the only previous study of this scenario. As a matter of fact, we find that these flashes do occur only in some low-mass (M < 0.6M) and low metallicity (Z_ZAMS <0.001) remnants about 10^6 - 10^7 yr after departing from the AGB. For these objects, we expect the luminosity to increase by about 4 orders of magnitude in less than a decade. We also show that diffusion-induced novas should display a very typical eruption lightcurve, with an increase of about a few magnitudes per year before reaching a maximum of M_V ~ -5 to -6. Our simulations show that surface abundances after the outburst are characterized by logNH/NHe ~ -0.15...0.6 and N>C>O by mass fractions. Contrary to previous speculations we show that these events are not recurrent and do not change substantially the final H-content of the cool (DA) white dwarf. (Abridged)Comment: 16 pages, 8 figures, 3 tables. Replaced to match the final version published by MNRAS. The definitive version is available at http://onlinelibrary.wiley.com/journal/10.1111/%28ISSN%291365-296
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