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ELASTIC PION SCATTERING AT 50 MeV ON ⁴⁰Ca AND ⁴⁸Ca Rozon, Francis Martin


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)

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