Angle transformation for theπ-nucleus optical potential

The transformation of the $\pi$-nucleon $T$ matrix from the $\pi$-nucleon to the $\pi$-nucleus center-of-mass systems is investigated. The correct angle transformation is presented, and it is shown to yield straightforward corrections to the usual Kisslinger and local Laplacian potentials consisting of terms proportional to ${\nabla }^2\rho$ and ${\nabla }^4\rho$ where $\rho$ is the target density. Numerical results are presented for ${\pi }^{-}-{}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ elastic scattering at 120- and 180-MeV lab kinetic energy.