Abstract
The analytic properties of the partial wave S-matrix and related quantities are studied and numerically investigated. The analysis is carried out by means of integration along paths in the complex k-plane. The domain for the choice of integration contours can be rigorously defined by the use of complex scaling techniques. A generalization of Levinson's theorem incorporating the poles in the lower half k-plane is proved and exemplified. An expansion theorem for the partial wave S-matrix in terms of its poles and residues is derived and analyzed. The connections between poles and associated residues and their relationships with the Breit-Wigner ansatz and the Fano line shape parameters are discussed and numerically realized. Finally, the implications of the present development in connection with the inversion problem are indicated.
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Rittby, M., Elander, N., Brändas, E. (1979). On the analytical continuation of the partial wave S-matrix using complex scaling techniques. In: Brändas, E., Elander, N. (eds) Resonances The Unifying Route Towards the Formulation of Dynamical Processes Foundations and Applications in Nuclear, Atomic and Molecular Physics. Lecture Notes in Physics, vol 325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50994-1_39
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DOI: https://doi.org/10.1007/3-540-50994-1_39
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