  We use direct numerical simulations to calculate the joint probability
density function of the relative distance $R$ and relative radial velocity
component $V_R$ for a pair of heavy inertial particles suspended in homogeneous
and isotropic turbulent flows. At small scales the distribution is scale
invariant, with a scaling exponent that is related to the particle-particle
correlation dimension in phase space, $D_2$. It was argued [1, 2] that the
scale invariant part of the distribution has two asymptotic regimes: (1) $|V_R|
\ll R$ where the distribution depends solely on $R$; and (2) $|V_R| \gg R$
where the distribution is a function of $|V_R|$ alone. The probability
distributions in these two regimes are matched along a straight line $|V_R| =
z^\ast R$. Our simulations confirm that this is indeed correct. We further
obtain $D_2$ and $z^\ast$ as a function of the Stokes number, ${\rm St}$. The
former depends non-monotonically on ${\rm St}$ with a minimum at about ${\rm
St} \approx 0.7$ and the latter has only a weak dependence on ${\rm St}$.
