Off-Shell quantities for the q -Deformed Hulthen Potential

This work presents an analytical investigation of the scattering properties of the q-deformed Hulthén potential within the framework of non-relativistic quantum mechanics. Exact solutions of the Schrödinger equation are obtained for arbitrary partial waves, allowing for the derivation of explicit expressions for the off-shell Jost functions, as well as the half-off-shell and full off-shell transition matrices. The developed formalism is applied to nucleonnucleon systems to examine both on-shell and off-shell effects. Optimized potential parameters corresponding to different states are determined through a systematic fitting procedure. The results exhibit good agreement with standard data available in the literature. Overall, this study provides a unified analytical framework for scattering dynamics and establishes reliable benchmarks for future investigations of off-shell effects in nuclear interactions.