| Summary: | Recent electron scattering measurements and muonic atom studies have allowed precise determinations of the charge distributions of nuclei. Measurements of the neutron distributions, however, have not progressed to this degree of sophistication, largely because of the uncertainties in the hadron-nucleus interaction. Charge distribution measurements provide good tests of nuclear structure calculations, but measurements of neutron distributions will provide independent constraints on these calculations and the potentials used.
In this experiment, π⁻ differential cross section ratios were measured on pairs of isotopes (³⁶S, ³²S), (³⁴S,³²S) with 50 MeV pions and (²⁶Mg, ²⁴Mg) with 45 MeV pions. Absolute differential cross sections were also measured for ³²S and ²⁴Mg. Magnetic spectrometers were used to collect the data.
The cross section ratios were compared to optical model calculations in which the parameters of a Fermi function representing the neutron distribution of the larger isotope of each pair were varied. The rms radius difference between the two isotopes producing the best fit was found to be independent of the details of the optical potential used, as long as the potential produced a fit to the absolute cross sections. The neutron distribution of the larger isotope was also represented as a Fermi function modified by a sum of spherical Bessel functions, the coefficients of which were allowed to vary. The results for the rms radius differences were consistent with the Fermi function fits, except for ³⁴S -³²S, where the results differed by a full standard deviation. The rms radius differences found for the sulfur isotopes agreed with the results of shell-model calculations by Hodgson (Str82,Hod83). The extracted rms radius difference of the magnesium isotopes was one standard deviation less than the shell-model prediction. The results for the Fermi function fits, Fourier Bessel fits and the single particle potential (SPP) calculations by Hodgson (Hod83) are: [See Thesis for Diagram]. === Science, Faculty of === Physics and Astronomy, Department of === Graduate
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