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The Anderson orthogonality exponents K + for introducing a localized perturbation into an electron gas and K(a) for displacing the localized potential by a vector a are discussed for one- and two-dimensional systems. It is shown that the smoothness of the potential enters very differently in the exponents K + and K(a). The controversial point of the boundedness of the two exponents is clarified
K. Schönhammer (Tue,) studied this question.