Systematic features of the pion-nucleus interaction

Abstract

We analyze pion elastic-scattering data for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ using a covariant theory of the optical potential developed previously. Combining these results with the information obtained from the analysis of pion scattering from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ reported earlier, we are able to discuss the systematics of the pion-nucleus optical potential. Our model contains a first-order optical potential which is obtained from a parameter-free calculation. The parameters of a second-order potential are determined by requiring that the sum of the first-and second-order potentials provides a fit to the elastic-scattering data. The parameters of the second-order potential exhibit a smooth dependence on energy and target mass number. These parameters have a marked resonance behavior. We find that the maximum value of the magnitude of the imaginary part of the second-order potential occurs at about 150 MeV while the first-order potential has a maximum for the magnitude of the imaginary part at about 240 MeV. The imaginary part of the first-order potential has a width at half maximum of about 200 MeV. This corresponds to a kinematic broadening of the (3,3) resonance due to the effects of the Fermi motion of the target nucleons. (This increased width is unrelated to the effects of the true absorption process or of collision broadening.) We also find a significant isospin violation in the second-order potential. For example, the imaginary part of the second-order potential for ${\pi }^{-}$ scattering is found to be systematically larger than that for ${\pi }^{+}$ scattering for nuclei with $N=Z$. An explanation for this feature of the optical potential is presented.