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 $\frac{{\lambda }_a}{r_0}={\left[\frac{2b{\left(k{r}_0\right)}^4}{{\gamma }^2}\right]}^{-1\mathrm{}},$ where ${\lambda }_a$ is the mean free path, $r_0$ is the pion Compton wavelength, $b$ is a constant, $k$ is the pion number, and $\gamma$ 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.