Low energy π± interactions with S-D shell nuclei
A magnetic spectrometer has been commissioned for use in performing low energy pion scattering experiments. It has been used to measure the differential cross sections for the elastic scattering of 50 MeV π± from 12[sub C], 18[sub O], and 26[sub Mg] targets, as well as the inelastic scattering to the 2₁₊ states of these nuclei. The analysis of the elastic scattering data has been performed with an optical potential model. It is found that the π± elastic cross sections for 12[sub C] and 18[sub
... sub C] and 18[sub O] are well described by calculations employing a global parameter set (CMS 82), which has been previously shown to reproduce π± elastic scattering data for a range of nuclei. The π± elastic data for ²⁶Mg require a variation of the p-wave potential parameters. A similar requirement is seen with π± ³²S elastic data (Sob 84a). Distorted wave calculations, inputting separate neutron and proton transition densities, have been performed for the analysis of the inelastic data. These calculations demonstrate a strong sensitivity of π+ to protons, and π- to neutrons, present in the nucleus. By varying the strengths of the neutron and proton transition densities, in order to reproduce the π± inelastic cross sections, it is possible to determine the ratio of neutron to proton matrix elements (M[sub n]/M[sub p]) for the given 2+ states. It is shown that the value of M[sub n]/M[sub p]) obtained in this way is independent of the optical potential parameters used in the calculation. The extracted values of (M[sub n]/M[sub p]) are: 0.97 ± 0.08, 1.81 ± 0.15, and 0.90 ± 0.07 for 12[sub C], 18[sub O], and 26[sub Mg] respectively. These values are in agreement with those obtained by other means.