Abstract
The ND −1 equations for the elastic scattering of two identical particles without spin are written under the hypothesis that the partial wave amplitude satisfies a dispersion relation with one subtraction. The N and D functions satisfy a set of two coupled singular integral equations and depend on the left hand discontinuity and on the inelasticity factor. These quantities are the basic parameters for model theories, and if they satisfy suitable asymptotic conditions, the solution of the ND −1 equations exists and is unique. The asymptotic behaviour of the real part of the phase shift is studied and gives a possible generalization of Levinson's theorem. Some simple models are examined, which illustrate various points of the method.
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