Analytical properties of theS-matrix in many-channel-scattering

This work is an extension of previous work byNewton ^1–3 andWeidenmüller ^4,5 to a more realistic case of many-channel scattering: We consider arbitrary orbital angular momenta and a potential matrix of the Yukawa type. The analytical properties of the modifiedS-matrix are investigated. The modifiedS-matrix is meromorphic in certain strips around the real axes of the Riemann surface. This surface is determined solely by the kinematical branchpoints. The region of analyticity can be extended further for the diagonal and the squared nondiagonal elements of theS-matrix to include the entire Riemann surface except cuts on the imaginary axes. These cuts can possibly include part of the real axes. The one-pole approximation of theS-matrix is of a Breit-Wigner form. An exact expression for the partial widths and a sum rule for the partial widths are derived. A generalized Levinson theorem is proved.