The Fredholm determinant for Hulthén-distorted non-local separable potential: Application to $$ \alpha {-}\alpha $$ elastic scattering

Abstract

Exact analytical expression of the Fredholm determinant with outgoing wave boundary condition for motion in Hulthen-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.