Analytic structure of the multichannel Jost matrix for potentials with Coulombic tails

被引:13
|
作者
Rakityansky, S. A. [1 ]
Elander, N. [2 ]
机构
[1] Univ Pretoria, Dept Phys, ZA-0002 Pretoria, South Africa
[2] Stockholm Univ, Div Chem Phys, SE-10691 Stockholm, Sweden
基金
新加坡国家研究基金会;
关键词
EFFECTIVE-RANGE THEORY; SCATTERING; RESONANCES;
D O I
10.1063/1.4853855
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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. (C) 2013 AIP Publishing LLC.
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页数:17
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