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Some recent results that determine an upper bound on the scattering length, whether or not composite bound states exist, are reviewed. The extension to the determination of an upper bound on (−k cotη)−1, where only one channel is open, is presented; the method used requires that the potential vanish identically beyond some given point. The results are applicable to the scattering of one compound system by another. Possible extensions and improvements of the method are discussed.
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Spruch et al. (1960) studied this question.
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