  The inelastic scattering of fast electrons by metastable hydrogen atoms in
the presence of a linearly polarized laser field is theoretically studied in
the domain of moderate field intensities. The interaction of the hydrogen atom
with the laser field is described by first-order time-dependent perturbation
theory, while the projectile electrons interacting with the laser field are
described by the Gordon-Volkov wave functions. An analytic expression is
obtained for the differential scattering cross section in the first-order Born
approximation for laser-assisted inelastic e-H(2s) scattering for the 2s-nl
excitation. Detailed analytical and numerical results are presented for
inelastic scattering accompanied by one-photon absorption, and the angular
dependence and resonance structure of the differential cross sections is
discussed for the 2s -4l excitation of metastable hydrogen.
