Computational Approach to the Inverse Problem in the JWKB Approximation

A previously presented method based on the JWKB approximation for constructing a local optical potential from a complete set of complex phase shifts at a single energy is further developed. The Coulomb interaction is explicitly included. By using a pointwise rational-fraction method for numerical analytic continuation the optical potential is directly computed from the experimental phase shifts. The above procedure is applied to the elastic scattering of 104-MeV $\alpha$ particles by ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, and it is found to be quite practical and reliable.