P-matrix description of the two-particle interaction

This paper deals with the formalism of the P-matrix description of the two-particle interaction within the framework of which the inverse scattering problem is considered. Separating, explicitly the P-matrix background part, associated with the free motion, yields a simple expression for the off-energy-shell scattering amplitude that immediately provides its separable expansion. Such separation corresponds to the partial summation of the initial P-matrix series and improves the description of physical quantities as functions of energy, provided the residual P matrix is approximated by a finite number of pole terms.