Analyses of pion-⁴⁰Ca elastic scattering data using the Klein–Gordon equation

The elastic scattering data for incident pion energies of 130, 163.3, 180, and 230 MeV on ⁴⁰Ca have been analyzed using the full Klein–Gordon equation (KGE), as opposed to its approximate form which renders it to the format of a Schroedinger equation with an energy-dependent potential (RSE). Calculated angular distributions, using KGE and RSE, for all four cases are nearly the same up to about 70° but differ significantly at larger angles. To fit the large-angle data of 163.3 MeV, the nature of the old potential determined by using RSE needs to be revised. The new potentials in four cases are presented and they are compatible with those determined from the inverse scattering theory at a fixed energy in the surface region. (author)