  The present work is designed to explore the evolutionary and pulsational
properties of low-mass white dwarfs with carbon/oxygen cores. In particular, we
follow the evolution of a 0.33 Msun white dwarf remnant in a self-consistent
way with the predictions of nuclear burning, element diffusion and the history
of the white dwarf progenitor. Attention is focused on the occurrence of
hydrogen shell flashes induced by diffusion processes during cooling phases.
The evolutionary stages prior to the white dwarf formation are also fully
accounted for by computing the conservative binary evolution of an initially
2.5-Msun Pop. I star with a 1.25 Msun companion, and period P_i= 3 days.
Evolution is followed down to the domain of the ZZ Ceti stars on the white
dwarf cooling branch. We find that chemical diffusion induces the occurrence of
an additional hydrogen thermonuclear flash which leads to stellar models with
thin hydrogen envelopes. As a result, a fast cooling is encountered at advanced
stages of evolution. In addition, we explore the adiabatic pulsational
properties of the resulting white dwarf models. As compared with their
helium-core counterparts, low-mass oxygen-core white dwarfs are characterized
by a pulsational spectrum much more featured, an aspect which could eventually
be used for distinguishing both types of stars if low-mass white dwarfs were in
fact found to pulsate as ZZ Ceti-type variables. Finally, we perform a
non-adiabatic pulsational analysis on the resulting carbon/oxygen low-mass
white dwarf models.
