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We present in this article an optical potential for the $\pi$-nucleusinteraction that can be used in various studies involving $\pi$-nucleuschannels. Based on earlier treatments of the low energy $\pi$-nucleus opticalpotential, we have derived a potential expression applicable from threshold upto the $\Delta$-resonance region. We extracted the impulse approximation formfor this potential from the $\pi-N$ scattering amplitude and then added to itkinematical and physical corrections. The kinematic corrections arise fromtransforming the impulse approximation expression from the $\pi-N$ center ofmass frame to the $\pi$-nucleus center of mass frame, while the physicalcorrections arise mostly from the many-body nature of the $\pi$-nucleusinteraction. By taking advantage of the experimental progress in our knowledgeof the $\pi-N$ process, we have updated earlier treatments with parameterscalculated from state-of-the-art experimental measurements.Comment: 23 pages, 12 figures. Accepted for publication in Physical Review

Pion-nucleus optical potential valid up to the Δ-resonance region