  We present a detailed investigation of the particle pair separation process
in homogeneous isotropic turbulence. We use data from direct numerical
simulations up to Taylor's Reynolds number 280 following the evolution of about
two million passive tracers advected by the flow over a time span of about
three decades. We present data for both the separation distance and the
relative velocity statistics. Statistics are measured along the particle pair
trajectories both as a function of time and as a function of their separation,
i.e. at fixed scales. We compare and contrast both sets of statistics in order
to gain an insight into the mechanisms governing the separation process. We
find very high levels of intermittency in the early stages, that is, for travel
times up to order ten Kolmogorov time scales. The fixed scale statistics allow
us to quantify anomalous corrections to Richardson diffusion in the inertial
range of scales for those pairs that separate rapidly. It also allows a
quantitative analysis of intermittency corrections for the relative velocity
statistics.
