Van Hove's theory of scattering of probe particles by a macroscopic target
is generalized so as to relate the differential cross section for atomic ej
ection via stimulated Raman transitions to one-particle momentum-time corre
lations and momentum distributions of ID trapped gases. This method is well
suited to probing the longitudinal momentum distributions of ID gases in s
itu, and examples are given for bosonic and fermionic atoms.