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 $$ \alpha $$ α – $$\alpha $$ α 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 $$ \alpha $$ α – $$\alpha $$ α elastic scattering phases with our exact calculation and standard data.

中文翻译：

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Hulthén 失真的非局部可分离势的 Fredholm 行列式：应用于 $$ \alpha {-}\alpha $$ 弹性散射

在 Hulthén 畸变的非局部可分离势中运动的具有出射波边界条件的 Fredholm 行列式的精确解析表达式被构建并以最大简化形式表示。使用边界条件（规则和不规则），还构建了对应于母体非局部势能的两个近似能量依赖相互作用。$$ \alpha $$ α – $$\alpha $$ α 弹性散射的相移是通过使用 (i) Fredholm 行列式的精确表达式和 (ii) 通过利用相位函数方法计算的依赖能量的局部相互作用. 我们构建的等效能量依赖势的优点是通过将 $$ \alpha $$ α – $$\alpha $$ α 弹性散射相位与我们的精确计算和标准数据进行比较来判断的。