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Pion-nucleus scattering cross sections are calculated by solving aSchr\"{o}dinger equation reduced from the Klein-Gordon equation. Localpotentials are assumed, and phenomenological potential parameters are searchedenergy-dependently for $\pi^{-} + ^{12}$C system so as to reproduce not onlyelastic differential cross sections but also total elastic, reaction and totalcross sections at 13 pion incident energies from 120 to 766 MeV. The real andimaginary parts of the local potentials thus obtained are shown to satisfy thedispersion relation. The imaginary part of the potentials as a function of thepion energy is found to peak near the $\Delta$(1232)-resonance energy. Thestrong absorption radius of the pion projectile with incident energies near the$\Delta$-resonance region is found to be about $1.6 A^{1/3}$ fm, which isconsistent with previous studies of the region where the decay of the$\Delta$'s takes place in nuclei. The phenomenological local potentials arethen compared with the local potentials exactly phase-shift equivalent toKisslinger potentials for pion energies near the $\Delta$-resonance

Phenomenological local potentials for pi-+12C scattering from 120 to 766 MeV

Phenomenological local potentials for pi^-+¹²C scattering from 120 to 766 MeV