Properties of unitary and nonunitary $S$-matrix on the basis of causality and the completeness condition of wave functions

A study is made of the general properties of the one-charmei unitary and non-unitary $S$-matrix in the case when the interaction inside a sphere of finite radius is unknown while outside the sphere there is a centrifugal barrier plus a noaasingular potential “tail” that decreases asymptotically not weaker than exponentially. Use is made of the completeness condition of a solution of the Schrödinger equation outside the sphere of unknown interaction, symmetry, and generalized unitarity of the $S$-matrix. As illustration, the concrete example of the resonance behavior of scattering and absorption cross sections is studied; this generalizes the well-known results in model exposition. In addition, the fulfilment of the orthodox conditions of micro- and macrocausality for the final results is investigated.