Differential scattering cross sections of H+ on various noble gases and of He+ on He were measured at various energies between 3 eV-80 eV. The rainbow structure and the superimposed rapid oscillations were resolved. Differential cross sections were calculated in WKB approximation and compared with experimentally obtained cross sections. Agreement was obtained by using the modified Morse potential: U = exp{2 G1 G2(1 -ρ)} -2 exp{G1 G2(1-ρ)} , G2 = 1 for ρ>1, whit ρ=r/rm, and U=V/ε. G2 ≠ 1 for ρ ≧1, The fitting procedure discussed in part I was applied in order to obtain the parameters ε,rm, G1 and G2. Calculations with the modified Lennard-Jones potential described in part I gave the same values for ε and rm . With exception of the system H+ -Xe, a single set of parameters could describe the rainbow structure and the fine structure at all ion energies. The values for ε and rm agree fairly well with ab-initio calculations. The reduced potentials have about the same shape, G1 being between 2.7 and 2.2, G2 being between 0.8 and 0.9. In the case of H+ -Xe, ε increases significantly with decreasing proton energy, while G1 and G2 have only slightly to be changed. The potential well is narrower than for the other systems mentioned above. These effects are attributed to the crossing of the potential curves of the systems H+ -Xe and H-Xe+ .