Statistical Properties of the Scattering Amplitude and Cross Sections Using the Statistical Collision Matrix

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Abstract
The statistical collision matrix is used to study the statistical distribution of the random part of the partial scattering amplitude and the partial fluctuation cross section. Using simplifying assumptions, explicit expressions are obtained for the lower moments of the partial scattering amplitude for the inelastic processes. It is shown that the real and imaginary parts of the fluctuating scattering amplitude have a Gaussian distribution with the same variance. Using ensemble averages of the resonance parameters of the statistical collision matrix, an expression is obtained for the partial reaction fluctuation cross section in the region of overlapping resonances. A remark is made about the partial elastic fluctuation cross section.