In any first approach toward a nuclear structure problem, one presumes the nucleons to be elementary particles. The failure or success of this approach may then instruct us something about the significance of sub-nuclear degrees of freedom. The Deng–Fan potential, although extensively used in molecular dynamics to reproduce several observables for the atomic-atomic and atomic-molecular interactions, is parametrized for nuclear systems to fit low-energy observables. By exploiting the variable phase approach (VPA) to potential scattering, phase parameters, cross-sections and analyzing powers are estimated for the nucleon–nucleon and nucleon–nucleus systems. Our results show good concurrence with the earlier theoretical and experimental data within this simple model of interaction.