Nuclear proton radii from low energy pion scattering
Creators: name: Barnett, Bruce M.
Publisher: name: University of British Columbia
Year: 2010

description: The subject of this thesis is the study of the use of elastic scattering differential cross section ratios of positive pions on light nuclei in the determination of nuclear proton matter distribution differences and their moments. These are compared with results from electron scattering and muonic X-ray measurements of the charge density differences. The measurements are relative to nuclei whose matter distributions and absolute cross sections are considered as references. The use of the ratio of cross sections, rather than the absolute cross sections themselves, minimises the effects of uncertainties in the understanding of the pion nuclear interaction in our extraction of density difference information; these effects are investigated. A furthur advantage of the technique is that the measurement of cross section ratios is insensitive to many systematic experimental effects encountered in measurement of absolute cross sections. The ratios of elastic scattering of positive pions at 38.6 MeV and 47.7 MeV on the isotones ¹¹B, ¹²C are presented. Also, cross section ratios at 48.3 MeV and 62.8 MeV on the nuclei ¹²C, ¹⁴N, ¹⁶O and ¹⁸O are presented. The measured cross sections do not rival the quality of the cross section ratios, but are also presented. The RMS radius differences extracted from the pion elastic scattering cross section ratios at low energy are consistent (within a standard deviation) with the results of other methods. The proton matter radius ([sup N+Z] r+) differences which we obtain are as follows: [See Thesis for Formulas] The errors reflect statistical and, to a large extent, the systematic uncertainties in the quantities. The best electron scattering results are shown within braces. Analysis of the ¹²C, ¹¹B experiment in terms of RMS radius differences indicates systematic uncertainties of about the same order as the statistical uncertainties. In particular, choice of optical potential, density form and optical parameter set is of limited importance. Analyses of the ¹⁸O, ¹⁶O experiments in terms of Fourier Bessel and novel Fourier Laguerre proton matter (radial) density differences (Δρ[sub p](r))agree with precision "model independent" [NOR82] electron scattering results, in the region in which the pion can be sensitive to the nuclear proton matter distributions. (The physical limits enforce r &gt; 1.5 fm.) The effects of optical parameter uncertainties are discussed. Similar analyses of the ¹²C, ¹⁴N, ¹⁶O experiments indicate a shift in the proton matter density distribution of ¹⁴N towards the center of that nucleus, relative to that suggested by electron scattering experiments [SCH75] and at about the same radius suggested by Self-Consistent Single Particle Potential (SCSPP) calculations [HOD85]. The analyses of these electron scattering experiments were not model independent, though, and may well generate densities which are incorrect at small radius (high momentum transfer: r &lt; 2 fm.) We present these results as testimony to the ability of the π⁺ to probe Δρ[sub p](r)reliably. The optical parameter sensitivity is minimal, especially when cross section fitting is used to determine the reference nucleus optical parameters. This work provides corroboration for the analogous π⁻ neutron density measurements of [JOH79, GYL85].