An approximate solution for the nuclear Hulthén plus atomic Hulthén potentials is constructed by solving the associated Volterra integral equation by series substitution method. Within the framework of supersymmetry-inspired factorisation method, this solution is exploited to construct higher partial wave interactions. The merit of our approach is examined by computing elastic scattering phases of the $\alpha−\alpha$ system by the judicious use of phase function method. Reasonable agreements in phase shifts are obtained with standard data.

Exact analytical expression of the Fredholm determinant with outgoing wave boundary condition for motion in Hulthén-distorted non-local separable potential is constructed and expressed in the maximum reduced form. Using boundary conditions (regular and irregular), two approximate energy-dependent interactions corresponding to the parent non-local potential are also constructed. The phase shifts for the $\alpha–\alpha$ elastic scattering are computed by using (i) exact expression for the Fredholm determinant and (ii) energy-dependent local interactions by exploiting the phase function method. The merits of our constructed equivalent energy-dependent potentials are judged by comparing the $\alpha–\alpha$ elastic scattering phases with our exact calculation and standard data.

The approximate phase-equivalent potentials to Manning–Rosen one are constructed using supersymmetric algebra. Using the supersymmetric factorization method, four SUSY transformations T$_1$, T$_2$, T$_3$ and T$_4$ are operated in pairs on Manning–Rosen potential to construct three different phase-equivalent potentials. These methodologies are verified by computing scattering phase shifts for different partial waves of nucleon-nucleon and α–nucleon systems using the newly constructed phase-equivalent potentials. Good agreement with standard phase-shift data prove the merits of our approaches.