Potentials providing the same complex phase shifts as a given complex potential but with a shallower real part are constructed with supersymmetric transformations. Successive transformations eliminate normalizable solutions corresponding to complex eigenvalues of the Schrödinger equation with the full complex potential. Two numerical techniques, finite differences and Lagrange meshes, are applied to the determination of these normalizable solutions. With respect to real potentials, a new feature is the occurrence of normalizable solutions with complex energies presenting a positive real part. Such solutions can be removed but may lead to complicated equivalent potentials with little physical interest. The derivation of equivalent potentials is tested on complex Pöschl-Teller potentials for which analytical solutions are available. As a physical application, a deep optical potential for the α+16O scattering is transformed into an l-dependent equivalent shallow optical potential.
ASJC Scopus subject areas
- Nuclear and High Energy Physics