Ghost components in the Jost function and a new class of phase-equivalent potentials

We show that the introduction of components, in the Jest function, that cre ate new bound states while leaving the S-matrix unchanged, generates potent ials behaving as r(-2) at large distances. We demonstrate that the modified Jest functions can be obtained by applying two successive supersymmetric t ransformations to the original potential. We further show that transparent potentials, with S-l(k) equivalent to 1, can also be obtained by successive supersymmetric transformations. They are characterized by the property tha t their SUSY-2 partners resemble centrifugal barriers. Finally, the relatio n of these transformations to the asymptotic normalization constants of the inverse scattering problem is discussed. We show that the two supersymmetr ic transformations that remove a bound state provide a potential which is t he same as that obtained via the Marchenko inverse scattering procedure, wh en the asymptotic normalization constant is set to zero.