Elastic-scattering phenomenology by inversion. Pt. 1

We present a two-step procedure for determining the local internuclear potential which fits elastic-scattering data. The first step is the determination from the angular-distribution data of a complex S-matrix S(l) using a 'parameterized improved phase-shift' procedure, PIPS. The second stage is the determination by inversion of the corresponding complex potential. The method is used to determine the 12C+12C potential from 139.5 to 2400 MeV. We present much better fits than have previously been published; the corresponding potentials are compared with both Woods-Saxon potentials and DDM3Y folding-model potentials. We discuss certain deficiencies of Woods-Saxon potentials and inversion models based on unmodified McIntyre-Wang-Becker parameterizations. The method we present can exploit elastic-scattering data of greater precision and angular range than generally exists, accurately representing such data by a local potential. It is less computer intensive than model-independent fitting for heavy ions. (orig.)