Non‐relativistic quantum scattering from non‐local separable potentials: the eigenchannel approach

A recently formulated version of the eigenchannel method [R. Szmytkowski, Ann. Phys. (N.Y.) 311, 503 (2004)] is applied to quantum scattering of Schrödinger particles from non‐local separable potentials. Eigenchannel vectors and negative cotangents of eigenphase‐shifts are introduced as eigensolutions to some weighted matrix spectral problem, without a necessity of prior construction and diagonalization of the scattering matrix. Explicit expressions for the scattering amplitude, the total cross section in terms of the eigenchannel vectors and the eigenphase‐shifts are derived. An illustrative example is provided.