[en] The density matrices of excited H atoms (n=2 and 3 manifolds) resulting from electron capture in collisions of H⁺ ions with He atoms in the energy region from 1 to 100 keV/amu are investigated on the basis of the atomic-orbital--molecular-orbital matching approach. Two electrons in the system are explicitly included in the calculation. The present results for the electric dipole moment, electron current density distributions, and alignment parameters compare favorably with recent measurements by Cline (unpublished), Hippler et al. [Phys. Rev. A 43, 2587 (1991)], and Ashburn et al. [Phys. Rev. A 41, 2407 (1990)] in the entire energy regions studied, and reveal similarities of these quantities for n=2 and n=3. Some insights of the similarities are discussed