  We are investigating the properties of vacancies in solid 4He with the exact
zero temperature SPIGS method. Our aim is to study the possibility of
phase--separation between vacancies and the perfect crystal. We find a
significant correlation among vacancies both in two and in three dimensional
solid 4He. In 3D we have considered up to 5 vacancies in a hcp crystal at a
density rho = 0.0293 AA^-3, close to the melting, and in 2D we have considered
up to 6 vacancies in a triangular crystal at rho = 0.0765 AA^-2. In all the
considered cases the correlation among vacancies seems to display an
exponential decay that would suggest the presence of a bound state. The
systematically sublinear dependence on the number of vacancies found for the
activation energy strengthens the indication of an attractive interaction, even
if we have direct evidence that vacancies do not form a single compact cluster.
