Simple Hulth$\grave{e}$n-type potential models are proposed to treat the $\alpha−\alpha$ and $\alpha−He^3$ elastic scattering. The merit of our approach is examined by computing elastic scattering phases through the judicious use of the phase function method. Reasonable agreements in scattering phase shifts are obtained with the standard data.

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.

Two simple models based on the Coulomb-distorted phase function and supersymmetry-inspired factorisation methods are adapted to deal with the nucleon–light nuclei elastic scattering at low energies. The first one is associated with the derivation of a closed-form expression of the scattering phase shift for motionin Coulomb-distorted separable non-local potentials. The second one deals with the development of an energy dependent phase equivalent local potential to the non-local one for s-wave and its subsequent generation of higher partial wave interactions through the formalism of supersymmetric quantum mechanics. The usefulness of our models is demonstrated through the computation of α–nucleon scattering phase shifts at low energies up to partialwaves $\ell$ = 2. Certain energy-dependent correction factors are also incorporated into energy-dependent higher partial wave potentials to achieve an excellent agreement with the 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 closed-form analytical expressions for the off-shell solutions for Hulthén-distorted Yamaguchi potential are derived to deal with the charged hadron systems. To construct these solutions, the particular integrals of the non-homogeneous Schrödinger equations are utilised in conjunction with the interacting Green’s functions. The Jost functions thus obtained, both on- and off-shell, are exploited to find the half-off-shell T -matrix. The off shell Jost function exists but off-shell Jost solution for the said potential has not yet been discussed in the literature. The merits of the T -matrix are examined through some model calculations. Exploiting the expressions for on and half-shell transition matrices, the s-wave elastic and inelastic scattering cross-sections are also estimated. Our results for the proton–proton and proton–oxygen systems are in close agreement with other calculations.