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.