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Measurements of elastic angular differential cross sections have been carried out for four quasi-one-electron collision systems at intermediate energies. Data are presented for Na++H collisions at laboratory energies of 35.94, 51.75, 63.89, and 143.75 keV, for Li++H collisions at energies of 19.44 and 43.75 keV, for Mg++He collisions at energies of 30, 66.7, and 150 keV, and for Be++He collisions at an energy of 56.25 keV. The highest energy in each case corresponds to a projectile velocity of (1/2 a.u. Born and Eikonal calculations, in which we model the projectile ion as a heavy structureless ion of charge +1e, are also presented. Our model calculations are in fair agreement with the experimental data over the range of measured scattering angles.