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Equivalence of the adiabatic approximation and the Born approximation for excitations in slowly colliding asymmetric systems

Within a full quantum-mechanical description the authors show that the recoil term in the Born approximation can be identified with the perturbation by the target motion in the first-order adiabatic approximation if Z1/Z2 to 0. Moreover, when the excitation is restricted to a small internuclear distances, the approximations are equivalent.