The forward amplitude for pion-nucleus scattering in the $N^{*}$ region is studied using a Glauber formalism with a cluster model of the nucleus. It is found that the major features of the data for light nuclei (${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$) are reasonably well reproduced by using a simple parametrization of the cluster structure. These results are in sharp contrast to predictions of a nucleon model at a comparable level of simplicity. We argue that a Glauber series representation of the amplitude is viable in a cluster model but not reliable in a nucleon model essentially because the interlocking effects of multiple scatterings and strong particle correlations inside the nucleus are easy to approximate in the former model and are difficult to account for in the latter model. Several modifications of the basic cluster model are considered and estimated to be small. More studies, experimental and theoretical, on angular distributions are urged.

NUCLEAR REACTION ${}_{}{}^2{}_{}{}^{}\mathrm{H}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$; forward amplitude in the $N^{*}$ region calculated with a cluster model using a Glauber approximation and compared to data.

• Received 5 August 1974

DOI:https://doi.org/10.1103/PhysRevC.11.73