Resonances and Their Relations to Spectral Densities and Scattering Cross Sections in the Schrödinger Formulation

Abstract

The concept of resonances for a two-body single and many channel Schrodinger problem is discussed with respect to the Titchmarsh–Weyl theory. It is argued that the contributions from the entire set of resonances together with the free particle spectral density build the entire spectrum. The implication of this statement on the influence of resonances on a two-body scattering cross section is discussed. It is described how the residues of the S-matrix at a complex resonance energy, i.e. two complex numbers, is used to define its contribution to the cross section. The limitations of the Breit–Wigner approximation is discussed.