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A regular solution for the Manning–Rosen potential is constructed by adapting the differential equation approach to the problem. The Jost solution and the Jost function are found by exploiting the relation between regular and irregular solutions. The Jost function thus obtained is applied for the first time to find bound state energies and the scattering phase shifts for nuclear systems.

Although often used in molecular dynamics, in this work the Manning–Rosen potential is parameterized to compute the scattering phase shifts for the nucleon–nucleon and the alpha-nucleon systems by exploiting the standard phase function method. We obtain excellent agreement in phase shifts with the more sophisticated calculations up to partial waves

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A new expression for the Hulthén off-shell Jost function in all partial waves is constructed in its maximal reduced form. As a basic requirement the on-shell solutions are first developed by following the differential equation approach to the problem together with judicious exploitation of the properties of certain special functions of mathematical physics. Utilizing the properties of the Jost function, the binding energies and phase shifts for N-N and n-d systems are computed and found excellent agreement with standard data.