Role of resonances in building collision cross-sections: Mittag-Leffler-based study

Abstract

The method of complex dilation is used to define the partial wave S-matrix in the sector of the fourth quadrant of the complex energy plane. Two ways of obtaining the expansion coefficients—the partial wave S-matrix residues—are studied. The Mittag-Leffler decomposition of the partial wave S-matrix as a sum of residue terms and an integral contribution is used to define the contributions of a number of the partial wave S-matrix poles, related to a 1-D potential, to the corresponding S-wave cross-section. The obtained expansion demonstrates a way of describing the contribution from a single pole to the partial wave S-matrix and thereby to various types of cross-sections. Our model study shows how peaks in a cross-section not only can be attributed to so-called isolated resonances but also to a set of overlapping barrier-type resonances. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004