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Absolute differential cross-sections have been measured for elastic π± scattering on ¹²C, ⁴⁰Ca, and ⁴⁸Ca using the QQD Spectrometer. The ¹²C data are in good agreement with (Sob 84a), indicating that the overall normalization of the data is good. The π⁺ ⁴⁰Ca data does not agree with the previously published data of (Pre 81) but fits the potential calculation using the SET E parameters (Car 82) better. Data for ⁴⁸Ca and π⁻⁴⁰Ca have not been previously published. An optical potential model was used to describe the data. The potential parameters were fixed by fitting to the ⁴⁰Ca absolute cross-sections. The π⁻ differential cross-section ratios of the measured pair, (⁴⁸Ca, ⁴⁰Ca), were compared to calculations for which the ⁴⁸Ca neutron distribution had been fitted, either by varying the Fermi parameters, or by adding a truncated series of orthogonal polynomials to a starting Fermi form. Two forms of orthogonal polynomials were used; spherical Bessel functions as used in (Gyl 84, Bar 85)), and Laguerre polynomials as used in (Bar 85). The rms radii differences obtained from the Fermi form fitting were found not to be independent of the optical potential used and to be sensitive to the inclusion of the ratio data in the diffractive region. Difficulties were encountered in obtaining reliable results from the orthogonal polynomial fits. The rms radii difference produced by the polynomial fits were not in agreement with results from the Fermi function fit. The neutron density distribution difference obtained from the polynomial fit is similar in form to the results of (Ray 81), but the distribution peak is shifted toward the nuclear center. The rms radii differences found from the Fermi function and Fourier-Laguerre analysis are; Fermi Fourier-Laguerre Δnn',.222±.048 .110 ± .022 (fm) / Science, Faculty of / Physics and Astronomy, Department of / Graduate

In this thesis a phenomenology is given with the view to determining the electromagnetic contributions to the low energy πN S-wave phase shifts. The approach we take is to partition the Coulomb potential into a short and a long ranged part at some arbitrary cutoff radius. Subsequently we deduce expressions which allow us to estimate, in two distinct stages, first the short and then the long range electromagnetic modifications to the purely hadronic physical observable quantities. The analysis formally begins with a discussion of the single channel π+p—> π+p elastic scattering process. We then turn our attention to the two channel process π⁻p—> π⁻p, π°n. Although a more complete discussion of π⁻p low energy scattering should necessarily entail the inclusion of the third channel inelastic process π⁻p—> ƴn, we have chosen to ignore this in order that we may elucidate some of the ambiguities that have existed with the two channel analysis. Explicit calculations are done, for the energy range 11.6 Mev ≤ T[sub= π][sup= LAB] ≤ 44.0 Mev. For input we use energy dependent expressions for the hadronic phase shifts. Although our estimates to the Coulomb modifications to these quantities do display the same general features with those found in the literature, the numbers we get for the π⁻p phase shifts are considerably smaller. This we attribute to our omission of the ƴn channel. The encouraging feature we do find however is that the procedure developed for treating both the one and the two channel problems are nearly identical. The only difference is that the latter necessitates the use of the unitarity constraint on the scattering matrix. This we hope will serve as a useful guide for a future discussion of the three channel problem. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The large fluxes of positive and negative pions available in meson factories over the last few years have lead to an accumulation of precise n-nuclear data over wide ranges in energy and atomic number. Little nuclear structure information has been extracted from the data since a microscopic model for the pion interaction in the nucleus is not fully developed. However the elastic scattering differential cross sections for. low energy pions are predicted well over a wide range of atomic mass using a potential in which some parameters are empirically derived., since the potential is semi-empirical some nuclear structure information can not reliably be derived directly from the data. Measurement of differences in the nuclear structure between neighbouring nuclides, however, should be reliable if the potential produces the correct variation of differential cross section in this mass region. In the experiment reported here the differential cross section ratio for elastic scattering of 29 MeV π- on ¹³C/¹²C is measured using scintillator range telescopes. Solid carbon targets of pressed powder were used. Since a relative measurement is made the errors in the ratio are only statistical. A large peak in the distribution of the cross section ratio is produced by changes in the s-p interference minimum between ¹²C and ¹³C. The cross section ratio is sensitive to the neutron distribution of ¹³C because of the large s-wave interaction of the pion with neutrons in the nucleus. A measurement of the neutron rms. radius of ¹³C and some tests of dependence on the shape of the neutron distribution and optical potential parameters are made. The neutron distribution rms. radius of ¹³C is found to be 2.365±.025 fm. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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Differential cross sections for the elastic scattering of low energy (20 MeV) positive and negative pions from ¹²C and ⁴⁰Ca have been measured. This measurement was performed at TRIUMF using the QQD low energy pion spectrometer at 11 angles between 45° and 125°. The π⁺ ¹²C data are in good agreement with [OBG⁺83], as are the π⁻ ¹²C data with [WBB+87], indicating that the overall normalization of the cross sections is good. However, the π± ⁴⁰Ca data do not agree well with the previously published data of [WMR+88]. An optical potential model, whose parameters were determined from pionic atom data, was used to predict these differential cross sections. Two sets of parameters were used in the model. One set was determined from fits to "normal" pionic atom data, while another set was extracted from fits to "anomalous" data where level shifts and widths do not compare to theoretical values obtained when the normal set of parameters is used. In all the above cases, the experimental data best fits the optical model predictions of [FG80,Fri88b] when the normal set of parameters is used. The qualitative agreement of the data to the "normal" optical model predictions indicates that the pionic anomaly effects do not extend to positive pion energy values. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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A partial-wave analysis of pion photoproduction data up to a photon lab energy of 1.8 GeV has been performed. Both energy-dependent and energy-independent solutions have been obtained. The energy-dependent parametrization incorporates the recently determined elastic pion nucleon scattering amplitudes in such a way as to satisfy unitarity and utilize the resonance structure contained in the pion nucleon elastic amplitudes. Starting from the energy-dependent solution, energy-independent partial-wave solutions are obtained at a set of energies from threshold to 1.8 GeV. The data base used in the analysis contains 11,911 data from the reactions. The predictions of our solution are compared with the experimental data and previous analyses. Suggestions are made for future experiments. A total of sixteen resonances exist in the energy range from threshold to 1.8 GeV. These resonance states are studied using our energy-independent solutions. Photon decay couplings to the sixteen resonances are extracted. These couplings are also compared with previous solutions and quark model predictions. / Ph. D.