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 ex-
panded 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 ar-
bitrary 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.
