  Recent studies have shown that alpha Centauri B might be, from an
observational point of view, an ideal candidate for the detection of an
Earth-like planet in or near its habitable zone (0.5-0.9AU). We study here if
such habitable planets can form, by numerically investigating the
planet-formation stage which is probably the most sensitive to binarity
effects: the mutual accretion of km-sized planetesimals. Using a
state-of-the-art algorithm for computing the impact velocities within a test
planetesimal population, we find that planetesimal growth is only possible,
although marginally, in the innermost part of the HZ around 0.5AU. Beyond this
point, the combination of secular perturbations by the binary companion and gas
drag drive the mutual velocities beyond the erosion limit. Impact velocities
might later decrease during the gas removal phase, but this probably happens
too late for preventing most km-sized objects to be removed by inward drift,
thus preventing accretion from starting anew. A more promising hypothesis is
that the binary formed in a crowded cluster, where it might have been wider in
its initial stages, when planetary formation was ongoing. We explore this
scenario and find that a starting separation roughly 15 AU wider, or an
eccentricity 2.5 times lower than the present ones are required to have an
accretion-friendly environment in the whole HZ.
