Using the method of effective nuclear density, we apply a simple, $\pi$-nucleus optical potential (without ${\rho }^2$ terms and the Lorentz-Lorenz effect) to ${\pi }^{-}$ atoms and low-energy $\pi$-nucleus elastic scatterings. Data of both phenomena are analyzed in a unified, hybrid (phenomeno-logical and theoretical) manner: The ${\pi }^{-}$-atom data are analyzed first to determine phenomenologically the potential parameters at threshold. The parameters are then extrapolated successfully up to 50 MeV incident pion laboratory energy by a microscopic calculation in which the energy-dependence correction is made after including the Fermi-averaging and Pauli-blocking effects. In contrast to other work, our potential includes the minimum number of the parameters that describe the full information content of the data. We can thus conclude that these effects are the important microscopic corrections for the extrapolation, but neither the Lorentz-Lorenz effect nor some highly nonlocal effects are crucial ones. The potential we have used has angular transformation terms which are also found to be crucial in the unified treatment. During the course of this work we have found an interesting behavior of the terms. A short account of its discussion is also presented.

NUCLEAR REACTIONS Unified analysis and calculation; strong-interaction shifts and widths in ${\pi }^{-}$ atoms and differential cross sections of elastic $\pi$-nucleus scattering up to 50 MeV; $\pi$-nucleus optical potential.

• Received 2 August 1982

DOI:https://doi.org/10.1103/PhysRevC.27.2817