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.
Volume 94, 2020
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