Renormalization of the isovector $πN$ amplitude in pionic atoms

The extraction of the isovector s-wave $\pi N$ amplitude from pionic atoms is studied with special emphasis on uncertainties and their dependence on the {\it assumptions} made regarding the neutron density distributions in nuclei and on the size of the data base used . Only `global' analyses of pionic-atom data reveal a discrepancy between the extracted isovector s-wave $\pi N$ amplitude $b_1=-0.108\pm0.007 m_\pi^{-1}$ and its free $\pi N$ counterpart $b_1^{{\rm free}}=-0.0885^{+0.0010}_{-0.0021} m_\pi ^{-1}$, where the uncertainty in the neutron densities is included in the error analysis. The role of `deeply bound' pionic atom states is discussed and the reason for failure of these states to provide new information is explained.