  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.

Quantum Physics;Nuclear Theory;Atomic Physics