Verification of Molière's Theory of Multiple Scattering for Heavy Ions

Abstract

The multiple-scattering distributions of 164-MeV ${\mathrm{O}}^{16}$ ions from Au, Ni, and Al foils and of 400-MeV ${\mathrm{Ar}}^{40}$ ions from Al and Zapon foils have been measured. These measurements are of interest because they involve large values (2.9 to 30.8) of the Born parameter $\alpha =\frac{Z_{1}Z}{137\beta }$. The $\frac{1}{e}$ widths found in this experiment are in complete agreement with those calculated from Molière's theory and verify its accuracy to within 2% for large values of $\alpha$. However, the accuracy is not sufficient to verify the detailed shape of the calculated distributions. The results of earlier experiments involving values of $\alpha >1\mathrm{}$ have also been compared with Molière's theory. These results, with a few exceptions, agree to within 5 or 10% with calculations based on the theory, and are scattered about the theoretical values in such a way that no systematic differences can be inferred. Molière's theory agrees well with experiment for large values of $\alpha$ because it relies on a classical calculation of scattering to account for deviations from the Born approximation. The theory of Nigam, Sundaresan, and Wu, which uses a second Born approximation, overestimates the widths of the distributions by as much as 60%.