All partial wave solutions for combined q-deformed Hulthén potentials and off-shell scattering

To deal with charged hadron scattering, we offer exact analytical derivations of some important mathematical entities for motion in the combined influence of atomic and nuclear [Formula: see text]-deformed Hulthén potentials in the context of low-energy nuclear scattering. The exact on-shell solutions for the combined potential are presented for all angular momentum states using a differential equation technique in conjunction with the appropriate application of the Gaussian hypergeometric functions. By leveraging the on-shell Jost function, the combined interaction is parameterized to compute the phase parameters, differential cross-sections and proton analyzing powers of [Formula: see text] system, which are in accord with the previous findings. Using the integral transform of the regular solution, the off-shell Jost function is derived in its maximal reduced form. Finally the half-off-shell T-matrix for the combined interaction is formulated. The results for the off-shell quantities for the q-deformed potential, to authors knowledge, are new in the literature.