Inverse Problem for Heavy-Ion Elastic Scattering and the Connection Between Parametrized Phase-Shift and Optical-Potential Models

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Abstract
A method based on the JWKB approximation is presented for constructing a local potential from a complete set of complex phase shifts at a single energy. By introducing the Sabatier transformation the problem is reduced to solving an Abel integral equation, the solution of which is closely connected with the potential. The resulting optical potential is uniquely determined in the noncritical domain, and its range of validity is in keeping with the JWKB approximation. A direct connection between the phase shifts and the optical potential is thereby established. The above procedure is tested for the scattering of medium-energy α particles, and it is found to be quite reliable over an angular range encompassing the diffraction region. Possible applications of the above method to the elastic scattering of medium-energy heavy ions are discussed.