Optical-Model Analysis of Pion-Nucleus Scattering

Abstract

Determination of nuclear-density parameters and of the rms pion charge radius ${r}_{\ensuremath{\pi}}$ from the elastic scattering of pions by nuclei has been studied using the optical model proposed by Kisslinger. Good fits to the available data in the kinetic-energy region $24 \mathrm{MeV}\ensuremath{\le}{T}_{\ensuremath{\pi}}\ensuremath{\le}153$ MeV have been found by searching the parameter space. For ${T}_{\ensuremath{\pi}}\ensuremath{\approx}80$ MeV, i.e., ${T}_{\ensuremath{\pi}}$ large compared to nuclear binding energies but well below the ${N}^{*}$ resonance, the best-fit parameters are close to those predicted from pion-nucleon phase shifts. The nuclear radii obtained are consistent with electron-scattering radii; the calculated differential cross sections are sensitive to a second nuclear-density parameter for large angles. "Distortion" of the Coulomb amplitude in 24-MeV ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{-}\ensuremath{\alpha}$ scattering reduces ${r}_{\ensuremath{\pi}}$ from 1.8\ifmmode\pm\else\textpm\fi{}0.8 F to ${r}_{\ensuremath{\pi}}\ensuremath{\le}2.0$ F (two standard deviations), in agreement with West's recent calculation.