Multi-channel analog of the effective-range expansion

Abstract

Similarly to the standard effective range expansion that is done near the threshold energy, we obtain a generalized power-series expansion of the multi-channel Jost-matrix that can be done near an arbitrary point on the Riemann surface of the energy within the domain of its analyticity. In order to do this, we analytically factorize its momentum dependencies at all the branching points on the Riemann surface. The remaining single-valued matrix functions of the energy are then expanded in the power-series near an arbitrary point in the domain of the complex energy plane where it is analytic. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This means that near an arbitrary point in the domain of physically interesting complex energies it is possible to obtain a semi-analytic expression for the Jost-matrix (and therefore for the S-matrix) and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles.

33 pages, 10 figures

References in corpus (6)

• Causality and the effective range expansion
• Applicability of Modified Effective-Range Theory to positron-atom and positron-molecule scattering
• Pade approximation of the S-matrix as a way of locating quantum resonances and bound states
• Analyzing the contribution of individual resonance poles of the S-matrix to the two-channel scattering
• Canonical quantum potential scattering theory
• Shape resonances in modified effective range theory for electron-molecule collisions

Cited by in corpus (6)

• Effective field theory description of halo nuclei
• Marrying {\it ab initio} calculations and Halo-EFT: the case of ${}^7\mathrm{Li}+n\to {}^8\mathrm{Li}+\gamma$
• Analytic structure and power-series expansion of the Jost function for the two-dimensional problem
• A method for extracting the resonance parameters from experimental cross section
• Jost-matrix analysis of the resonance 5He*(3/2+) near the dt-threshold
• Resonance states 0+ of the Boron isotope B8 from the Jost-matrix analysis of experimental data