Analysis ofπ−-Mesonic Atoms

A phenomenological analysis of the ${\pi }^{-}$-mesonic atom in light nuclei has been made by use of a new approximation technique for the exterior wave function outside of the region of strong interaction. This approximation is a series expansion of the Coulomb wave function in terms of the energy-level-shift ratio $\frac{\Delta E_{1S}}{E_{1S}}$. From the new measurements of Jenkins, Kunselman, Simmons, and Yamazaki of the shifts and spreads of the $2P\to 1S$ transition energy in ${\pi }^{-}$-mesonic atoms, we have calculated the complex ${\pi }^{-}$-nucleus potential and the exact ${\pi }^{-}$-nucleus scattering length. The ${\pi }^{-}$-nucleus scattering lengths are found not to satisfy the hypothesis that they are the sums of ${\pi }^{-}$-nucleon scattering lengths. Also the scattering lengths do not exhibit any apparent isotopic-spin dependence. It is also found that level shift depends only on the volume integral of the potential and not on its shape. Using this potential, the ${\pi }^{-}$-mesonic wave function inside the nucleus is obtained in analytic form, and it is found that the probability that the ${\pi }^{-}$-meon is inside the nucleus has only about half the value given by a first-order perturbation calculation.