Measurements of the angular distribution and total reaction rate in neutron-proton scattering are described. The emphasis of this work has been to obtain an accurate normalization of the distribution, which is difficult to achieve with neutral beams. Nearly monoenergetic neutrons from the d(p,n)pp reaction were scattered from a liquid hydrogen target. The neutron beam energy was determined from the time of flight with respect to the radio frequency signal of the TRIUMF cyclotron. The differential cross section was measured at 319 and 493 MeV from 10 to 180 degrees in the centre of mass (CM.). Calibrated neutron beam monitors upstream of the scattering target provided an absolute normalization over the whole angular range. Between 10 and 100 degrees CM. a neutron detector consisting of a charged particle veto, a carbon convertor and two trigger scintillators sandwiching 7 multiwire proportional chambers was used to select elastic neutrons by time of flight techniques. The neutron angular distribution was measured with an average precision of 5% and an uncertainty on the normalization of 1.3%. An associated particle experiment (neutrons and recoil protons detected in coincidence) determined the efficiency of the neutron detector and the monitors were calibrated by measuring the incident neutron flux with the neutron detector in the beam, i.e. at zero degrees. The recoil protons were detected in the angular range between 60 and 180 degrees CM. with a precision of 1% to 2% and an error on the normalization of 2.8% at 319 MeV and 3.7% at 493 MeV. Elastic events were selected by time of flight and by either a measurement of magnetic rigidity (momentum) or total energy. The absolute normalization of the two experimental techniques is verified by the overlap of the two measurements and by comparing the integrated differential cross section with the measured total cross section. The neutron-proton total cross section was measured at six energies between 200 and 500 MeV by a transmission type experiment to a precision of 1% to 3%. The systematic corrections were small, of the order of 1%, and the statistical errors were increased to include monitor and beam instabilities. The measurements show a smooth quadratic energy dependence. The data was included in a phase shift analysis and a dispersion relation analysis along with the previous world data. Agreement between the real part of the forward scattering amplitude predicted by the phase shift analysis and by the dispersion relation analysis is improved. The errors on the 1=0 (isoscalar) phase shifts are decreased and to a lesser extent on the 1=1 phase shifts. There is a marked improvement in the smooth variation with energy of the 1=0 phase shifts and a better agreement of the higher partial waves with the theoretical predictions of the Paris potential. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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The secant method is applied to an iterative algorithm of electromagnetic scattering from planar surfaces with periodic structure. The theory of convergent solutions for iterative techniques is discussed and examined. The Secant method is applied to the spectral iteration approach to accelerate and assure convergence of the basic iterative scheme. The derivation of the method as applied to surfaces containing parallel thin wire gratings is presented, and the conditions for achieving convergence are explored. This new method is also applied to gratings made of coated wires. The reflection characteristics of the grating as a function of wire spacing, wire conductivity, and polarization of the incident field are computed, and the results are compared with those of previous works. Suggestions and recommendations for applying the method to more complicated structures are also included.

The design, analysis, and performance of a small-angle scatterometer are presented. The effects of the diffraction background, geometrical aberrations and system scatter at the small-angles are separated. Graphs are provided that quantify their contribution. The far-field irradiance distributions of weakly truncated and untruncated Gaussian beams are compared. The envelope of diffraction ringing is shown to decrease proportionately with the level of truncation in the pupil. Spherical aberration and defocus are shown to have little effect on the higher-order diffraction rings of Gaussian apertures and as such will have a negligible effect on most scatter measurements. A method is presented for determining the scattered irradiance level for a given BRDF in relation to the peak irradiance of the point spread function. A method of Gaussian apodization is presented and tested that allows the level of diffraction ringing to become a design parameter. Upon sufficient reduction of the diffraction background, the scattered light from the scatterometers' primary mirror is seen to be the limiting component of the small-angle instrument profile. The scatterometer described was able to make a meaningful measurement close enough to the specular direction at 0.6328μm in order to observe the characteristic height and width of the scatter function. This allowed the rms roughness and autocorrelation length of the surface to be determined from the scatter data at this wavelength. The inferred rms roughness agreed well with an independent optical profilometer measurement of the surface. The BRDF of the samples were also measured at 10.6μm. The rms roughness inferred from this scatter data did not agree with the other measurements. The BRDF did not scale in accordance with the scaler diffraction theory of microrough surfaces. The scattering in the visible was dominated by the effects of surface roughness whereas the scattering in the far-infrared was apparently dominated by the effects of contaminants and surface defects. The model for the surface statistics is investigated. A K₀ (modified Bessel function) autocorrelation function is shown to predict the scattered light distribution of these samples much better than the conventional negative-exponential function. Additionally, a sampling theory is developed that addresses the negative-exponentially correlated output of lock-in amplifiers, detectors, and electronic circuits in general. It is shown that the optimum sampling rate is approximately one sample per time constant and at this rate the improvement in SNR is √(N/2) where N is the number of measurements.

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