On the inverse problem for the scattering theory of charged particles when there is a linear relationship between the energy, the square of the orbital angular momentum, and the Coulomb coupling constant

A generalized algebraic variant is proposed for solving the inverse problem of the potential scattering of charged particles for the case when the initial scattering data are taken in the presence of a linear relationship between the energy $E$, the square of the orbital angular momentum $l$ and the Coulomb coupling constant $a$. Expressions are obtained for constructing a central $E$-, $l$-, and $a$-independent potential corresponding to a Jost function characterized by rationality with respect to the parameters $E$, $l$, and $a$.