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Vibrational excitation cross-sections σn←m(E) in resonant e-N2, e–CO and e–H2 scattering are calculated from transition matrix elements Tn←m(E) obtained using Fourier transform of the cross correlation function <[lowercase_phi_synonym]n(R)|ψm(R,t)> where ψm(R,t); e-iHA-(R)t/h[lowercase_phi_synonym]m(R). Time evolution under the influence of the resonance anionic Hamiltonian HA-(A- = N2-/CO/H2-) is effected using Lanczos and fast Fourier transforms and the target (A) vibrational eigenfunctions [lowercase_phi_synonym]m(R) and [lowercase_phi_synonym]n(R) are calculated using Fourier grid Hamiltonian method applied to PE curve of the neutral target. The resulting vibrational excitation cross-section profiles provide reasonable agreement with experimental results and the cross correlation functions offer an unequivocal differentiation between the boomerang and impulse models. [ABSTRACT FROM AUTHOR]