By exploiting higher partial wave solutions for the Hulthén potential, constructed via the factorisation method, closed form analytical expressions of the Fredholm determinants for motion in Hulthén plus modified Graz separable potential are constructed to study on-shell scattering up to partial wave $\scr l$= 2. Phase shifts for different states of $\alpha-^3$H and $\alpha-^3$He are obtained by exploiting the expression of the Fredholm determinant. The results are found in reasonable agreement with the standard data (Spiger and Tombrello 1967).

New analytical expressions for the off-shell wave functions and T-matrix with the Manning–Rosen potential are constructed in terms of generalised hypergeometric functions. The off-shell T-matrices are computed for the neutron–proton and neutron–deuteron systems. The limiting behaviours of our expression for the off-shellT-matrix are verified and found correct.

We solve the wave equation with the Manning–Rosen plus rank one separable non-local potential to obtain exact analytical solutions through ordinary differential equation method. The regular, Jost and physical state solutions are found to involve special functions of mathematics. As an application of the Jost function and Fredholm determinant, the bound-state energies and the scattering phase parameters for the p−$^2$H$_1$ and p−$^{16}$O systems are computed. The results achieved are in good agreement with the other methods published earlier.

In this work, exact analytical expressions for regular solution and on-shell Jost function are calculated for nuclear Hulthén plus atomic Hulthén potential by imposing the same range approximation to both nuclear andatomic potentials. In this context, the regular solution is utilised to find expressions for the off-shell Jost function and half-shell T -matrix. The half-off-shell T -matrix and the elastic scattering phase shifts for the nucleon–nucleon and nucleus–nucleus systems are computed. Our results are found to be in good agreement with the standard data.

The scattering phase parameters for short-range local potentials can be evaluated by using the phase function method (PFM), regarded as an efficient approach for computing scattering phase shifts for quantum mechanical problems, without solving the Schrödinger equation. We adapt PFM to deal with the Hulthén-distorted separable non-local potentials and derive a closed form expression for the phase function with rigorous inclusion of electromagnetic effect. We demonstrate the usefulness of our constructed expression by calculating elastic scattering phase parameters for proton–deuteron (p–d) system which agree quite well with the previous results.

The aim of this paper is to find the exact solutions of the Schrödinger equation for the Manning–Rosen plus Graz separable potential through two different approaches to the problem. We express the irregular/Jost and physical solutions in terms of the special functions of mathematical physics. Numerical results of the phase shifts are obtained by utilising the properties of the Jost function and Fredholm determinants for nucleon–nucleon and nucleon–nucleus systems. The results obtained are in good agreement with earlier works.

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.

We present all the partial wave descriptions of the nucleon–nucleus system by proposing a new additive phenomenological potential with emphasis on off-energy-shell scattering. For most of the general treatment of the physical processes, the off-shell transition matrices are most expedient quantities because they carry as much information as the potential. As the off-shell Jost solution is an indispensable ingredient for deriving transition matrices, we initially construct this function by taking into account the ordinary differential equation method. Finally,we execute certain tests on our expressions with respect to various limiting conditions and present numerical results using the $MATLAB$ programme. Numerical results are in sensible conformity with the previous works.