  Results from Direct Numerical Simulations of particle relative dispersion in
three dimensional homogeneous and isotropic turbulence at Reynolds number
$Re_\lambda \sim 300$ are presented. We study point-like passive tracers and
heavy particles, at Stokes number St = 0, 0.6, 1 and 5. Particles are emitted
from localised sources, in bunches of thousands, periodically in time, allowing
to reach an unprecedented statistical accuracy, with a total number of events
for two-point observables of the order of $10^{11}$. The right tail of the
probability density function for tracers develops a clear deviation from
Richardson's self-similar prediction, pointing to the intermittent nature of
the dispersion process. In our numerical experiment, such deviations are
manifest once the probability to measure an event becomes of the order of -or
rarer than- one part over one million, hence the crucial importance of a large
dataset. The role of finite-Reynolds effects and the related fluctuations when
pair separations cross the boundary between viscous and inertial range scales
are discussed. An asymptotic prediction based on the multifractal theory for
inertial range intermittency and valid for large Reynolds numbers is found to
agree with the data better than the Richardson theory. The agreement is
improved when considering heavy particles, whose inertia filters out viscous
scale fluctuations. By using the exit-time statistics we also show that events
associated to pairs experiencing unusually slow inertial range separations have
a non self-similar probability distribution function.
