  We calculate the momentum distribution and the second-order correlation
function in momentum space, $g^{(2)}({\bf p},{\bf p}',t)$ for molecular dimers
that are coherently formed from an ultracold atomic gas by photoassociation or
a Feshbach resonance. We investigate using perturbation theory how the quantum
statistics of the molecules depend on the initial state of the atoms by
considering three different initial states: a Bose-Einstein condensate (BEC), a
normal Fermi gas of ultra-cold atoms, and a BCS-type superfluid Fermi gas. The
cases of strong and weak coupling to the molecular field are discussed. It is
found that BEC and BCS states give rise to an essentially coherent molecular
field with a momentum distribution determined by the zero-point motion in the
confining potential. On the other hand, a normal Fermi gas and the unpaired
atoms in the BCS state give rise to a molecular field with a broad momentum
distribution and thermal number statistics. It is shown that the first-order
correlations of the molecules can be used to measure second-order correlations
of the initial atomic state.
