Analytic structure of the multichannel Jost matrix for potentials with Coulombic tails
- Department of Physics, University of Pretoria, Pretoria 0002 (South Africa)
- Division of Chemical Physics, Department of Physics, Stockholm University, Stockholm, SE-106 91 (Sweden)
A quantum system is considered that can move in N two-body channels with the potentials that may include the Coulomb interaction. For this system, the Jost matrix is constructed in such a way that all its dependencies on the channel momenta and Sommerfeld parameters are factorized in the form of explicit analytic expressions. It is shown that the two remaining unknown matrices are single-valued analytic functions of the energy and therefore can be expanded in the Taylor series near an arbitrary point within the domain of their analyticity. It is derived a system of first-order differential equations whose solutions determine the expansion coefficients of these series. Alternatively, the unknown expansion coefficients can be used as fitting parameters for parametrizing experimental data similarly to the effective-range expansion. Such a parametrization has the advantage of preserving proper analytic structure of the Jost matrix and can be done not only near the threshold energies, but around any collision or even complex energy. As soon as the parameters are obtained, the Jost matrix (and therefore the S-matrix) is known analytically on all sheets of the Riemann surface, and thus enables one to locate possible resonances.
- OSTI ID:
- 22217740
- Journal Information:
- Journal of Mathematical Physics, Vol. 54, Issue 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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