  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 ejection
via stimulated Raman transitions to one-particle momentum-time correlations and
momentum distributions of 1D trapped gases. This method is well suited to
probing the longitudinal momentum distributions of 1D gases in situ, and
examples are given for bosonic and fermionic atoms.
