Scattering matrix, Fredholm matrix and Jost matrix in a multichannel scattering process by a finite-rank potential

Summary

In a multichannel scattering by a finite-rank potential, the Fredholm matricesM ^± andM _ϕ, relative to physical and regular boundary conditions, are defined in the natural space of the problem, labelled by the couple of indicesn (rank index) andc (channel index). We define then the new matricesN ^± andN _ϕ, called the images ofM ^± andM _ϕ, from spacenc to subspacec. Simple expressions are found to relate the scattering matrixS and the Jost matrixf ^± to the above-defined images.