Wave function approach to the off-shell T-matrix for the Deng–Fan potential

This paper presents a mathematical perspective on constructing the off-energy-shell transition matrix for motion in the Deng–Fan potential. As a basic prerequisite, the Deng–Fan off-shell Jost and physical solutions are derived in their maximal reduced form by considering the differential equation approach to the problem. Because of the nature of the Deng–Fan potential and the considered screened centrifugal barrier, we do some important mathematical manipulations that enable us to find the analytical expressions of these off-shell quantities, which are consistent with certain limiting conditions. To the author’s knowledge, the formulation of the Deng–Fan off-shell T-matrix is new in the literature. The effectiveness of these expressions is tested by computing the phase observables and T-matrix elements of n-p system, which confirms the previously reported findings.