Optical-Model Analysis of Pion-Nucleus Scattering

Abstract

Determination of nuclear-density parameters and of the rms pion charge radius $r_{\pi }$ 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 $24 \mathrm{MeV}\le T_{\pi }\le 153$ MeV have been found by searching the parameter space. For $T_{\pi }\approx 80$ MeV, i.e., $T_{\pi }$ 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 ${\pi }^{\pm }-\alpha$ scattering reduces $r_{\pi }$ from 1.8±0.8 F to $r_{\pi }\le 2.0$ F (two standard deviations), in agreement with West's recent calculation.