Within the frame work of time independent non-relativistic quantum scattering theory the importance of the nucleon-nucleon, nucleus-nucleus scattering by additive interactions have been discussed. Within the formalism of separable model electromagnetic-distorted nuclear scattering has been treated to construct closed form analytical expressions for off-shell quantities in their maximal reduced form via different approaches to the problem and make them amenable to numerical treatment. The integral representations for on- and off-shell Jost functions for all partial waves in the representation space approach have been reconstructed by exploiting the particular solution of the inhomogeneous Schrödinger equation together with the transpose operator relation and interacting Green's functions. Research workers as well as graduate students of physics and mathematical physics will find these topics interesting.