Unified analysis of pionic atoms and low-energy pion-nucleus scattering: Phenomenological analysis

The ${\pi }^{-}$-atom and low-energy $\pi$-nucleus elastic scattering data have been analyzed systematically in order to examine their information content with respect to the structure of the $\pi$-nucleus optical potential. We have firmly established the existence of the data's insensitivity to the potential structure and have examined its consequences in detail. The insensitivity is manifested in the form of correlations between the coefficients of $\rho$ and ${\rho }^2$ in the potential. We have found that such correlations vary slowly as a function of the pion energy ($T_{\pi }$) from the threshold (the ${\pi }^{-}$ atoms) through 50 MeV and that, exploiting the correlations, one can define an effective nuclear density, ${\rho }_e$, at which the pion effectively interacts with nuclei. ${\rho }_e$ was also found to increase slowly as $T_{\pi }$ increases. In contrast, no correlation was observed between the coefficient of the local term and that of the nonlocal (momentum dependent) term. As a consequence of the above nature of the correlations, we have established a form of the optical potential which contains the minimum number of parameters in order to describe the information content of the data.