Pade approximation of the S-matrix as a way of locating quantum resonances and bound states

Details Pade approximation of the S-matrix as a way of locating quantum resonances and bound states Pade approximation of the S-matrix as a way of locating quantum resonances and bound states

2011-10-22

arxiv.org/abs/1110.4988v1

J. Phys. A: Math. Theor. 40 (2007) 14857-14869

Physics

Nuclear Physics

Nuclear Theory

20 pages, 6 figures

Scientific paper

It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the S-matrix along the real positive energy axis. No calculations of the S-matrix at complex energies or a complex rotation are necessary. The proposed method is therefore universal in that it is applicable to any potential (local, non-local, discontinuous, etc.) provided that there is a way of obtaining the S-matrix (or scattering phase-shifts) at real collision energies. Besides this, combined with any method that extracts the phase-shifts from the scattering data, the proposed rational parametrization technique would be able to do the spectral analysis using the experimental data.

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