  Some issues of recoil effects in AdS/CFT are studied from the point of view
of OPE expansions for generalized free fields. We show that the conformal group
structure encodes the relative energies and momenta at a collision center. This
is done by being careful with the analysis of Clebsch-Gordan coefficients for
an $SL(2)$ subalgebra of the conformal group. The collision fraction of kinetic
energy carried by the particles is derived from a probability distribution that
arises from these coefficients. We specifically identify a precise statement of
when recoil of a heavy particle in AdS can be ignored: the maximum probability
is for the heavy particle to be in its ground state. We also argue how a notion
of reduced mass appears in these collisions, in the limit where the particles
are moving slowly with respect to each other. This controls the notion of the
impact parameter of the collision.
