ИСТИНА

The new method for the solution of multi-channel scattering problems in discretized L2 representation without solving the scattering equations is given. The technique allows to construct the discrete analog of the spectral shift function (SSF) for the total and free Hamiltonians which is the object of the general spectral theory of the perturbations. The main advantage of this discrete version of the SSF formalism is that it can be directly generalized to the multi-channel case. Here the set of different discrete SSFs corresponding to different spectral branches could be defined, in contrast to the conventional theory in continuum. Moreover, each such disretized spectral shift function is directly interrelated to the corresponding eigenchannel phase shift similarly to one-channel case. Finally, each element of the multi-channel S-matrix can be found at many energies simultaneously from the one-fold diagonalization of the Hamiltonian matrix in the multi-channel L2 basis. As an illustration, numerical results for several multi-channel scattering problems in nuclear and atomic physics are presented.