PHASE-EQUIVALENT COMPLEX POTENTIALS

Potentials providing the same complex phase shifts as a given complex potential but with a shallower real part are constructed with supersym metric transformations. Successive transformations eliminate normaliza ble solutions corresponding to complex eigenvalues of the Schrodinger equation with the full complex potential. Two numerical techniques, fi nite differences and Lagrange meshes, are applied to the determination of these normalizable solutions. With respect to real potentials, a n ew feature is the occurrence of normalizable solutions with complex en ergies presenting a positive real part. Such solutions can be removed hut may lead to complicated equivalent potentials with little physical interest. The derivation of equivalent potentials is tested on comple x Poschl-Teller potentials for which analytical solutions are availabl e. As a physical application, a deep optical potential for the alpha+O -16 scattering is transformed into an I-dependent equivalent shallow o ptical potential.