Interaction of Pions with Complex Nuclei

Attenuation cross sections and cross sections for scattering into a fixed angular interval have been measured in a well-defined geometry for pions of energies 33, 46, and 68 Mev. The targets were beryllium, carbon, aluminum, and copper. The results were analyzed by means of the optical model, and a strong energy dependence was found for the pion interaction mean free path in nuclear matter. A satisfactory representation of this energy dependence is the equation λₐr₀=[2b(kr₀)⁴γ²]^-1, where λₐ is the mean free path, r₀ is the pion Compton wavelength, b is a constant, k is the pion number, and γ is the total pion energy divided by its rest energy. The results of an optical model calculation with the above energy dependence were compared withe other published pion-nucleus data and agreement was found. A partial wave analysis gave essentially the same results but required mean free paths about twice as long.Published values of the pion-nucleon phase shifts at several energies were used to calculate the mean free path by means of multiple-scattering theory. The results agree with the above energy dependence and are intermediate between the mean free paths of the optical model and those of the partial wave analysis.