An impact-parameter treatment is carried out for the process H(1s) + He(1s2) -> H(2s or 2p) + He(1s2), with incident hydrogen atom energies E in the range 1 kev <or= E <or= 100 kev. Full account is taken of distortion, back-coupling, rotational coupling and the virtual transition sequence 1s l harp over r 2p l harp over r 2s. The calculated inelastic cross sections and the percentage polarization of the emitted Lyman-α radiation show satisfactory agreement with the recent experimental results of Ankudinov et al. and of Dose et al. The effect of simultaneous excitation of both the target and the projectile atoms is discussed.