Resonances of Multichannel Systems

Details Resonances of Multichannel Systems Resonances of Multichannel Systems

2007-02-17

arxiv.org/abs/quant-ph/0702178v1

Models and Methods in Few- and Many-Body Systems. Proc. of the DST-UNISA-JINR Symposium/Ed.: S.A.Sofianos (UNISA Press, Pretor

Physics

Quantum Physics

Based on a talk presented at the UNISA-JINR Symposium "Models and Methods in Few- and Many-Body Systems" (6-9 February 2007, S

Scientific paper

We describe structure of the T-matrices, scattering matrices, and Green functions on unphysical energy sheets in multichannel scattering problems with binary channels and in the three-body problem. Based on the explicit representations obtained for the values of T- and S-matrices on the unphysical sheets, we prove that the resonances belonging to an unphysical sheet are just those energies where the correspondingly truncated scattering matrix, taken in the physical sheet, has eigenvalue zero. We show, in addition, that eigenvectors of the truncated scattering matrix associated with its zero eigenvalue are formed of the breakup amplitudes for the respective resonant states.

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