Jost function for coupled channels

Almost any textbook on the scattering theory has a chapter devoted to the Jost function, but none of them gives a practical recipe for its calculation. Thus one usually gets a feeling that the Jost function is a pure mathematical object, elegant and useful in formal theory, but impractical in computations. This is even more so in the case of multi-channel problems, where the Jost function is, in fact, a matrix. Recently, we proposed an exact method for direct calcu- lation of the Jost function for central potentials (which may have Coulombic tails) [1, 2] and the Jost matrix for non-central short range potentials [3]. This method works for all real or complex momenta of physical interest, including the spectral points corresponding to bound and Siegert states. In this work we extend it for potentials which couple channels with different thresholds.