Resonances of Multichannel Systems
Abstract
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.
Cite
@article{arxiv.quant-ph/0702178,
title = {Resonances of Multichannel Systems},
author = {Alexander K. Motovilov},
journal= {arXiv preprint arXiv:quant-ph/0702178},
year = {2007}
}
Comments
Based on a talk presented at the UNISA-JINR Symposium "Models and Methods in Few- and Many-Body Systems" (6-9 February 2007, Skukuza, Kruger National Park, South Africa