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Multi-MeV ion production from the interaction of a short laser pulse with a high-density plasma, accompanied by an underdense preplasma, has been studied with a particle-in- cell simulation and good agreement is found with experiment. The mechanism primarily responsible for the acceleration of ions is identified. Comparison with experiments sheds light on the ion-energy dependence on laser intensity, preplasma scale length, and relative ion energies for a multi-species plasma. Two regimes of maximum ion-energy dependence on laser intensity, I, have been identified: subrelativistic, μ I ; and relativistic, μ √I. Simulations show that the energy of the accelerated ions versus the preplasma scale length increases linearly and then saturates. In contrast, the ion energy decreases with the thickness of the solid-density plasma.