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Note 1: Aperture-to-medium coupling loss is related to the ratio of the scatter angle to the antenna beamwidth. Note 2: The "very large antennas" are referred to in wavelengths; thus, this loss can apply to line-of-sight systems also.
In gamma-ray spectrometry, the Compton edge is a feature of the measured gamma-ray energy spectrum that results from Compton scattering in the detector material. It corresponds to the highest energy that can be transferred to a weakly bound electron of a detector's atom by an incident photon in a single scattering process, and manifests itself as a ridge in the measured gamma-ray energy spectrum.
In functions that involve angles, as Eq(2) does, the angles must be measured in radians. Eq(5) is a linear function that approximates, e.g., a curve in two dimensions (p=1) by a tangent line at a point on that curve, or in three dimensions (p=2) it approximates a surface by a tangent plane at a point on that surface.
To normalize the detectors, a measurement of a pure solvent is made first. Then an isotropic scatterer is added to the solvent. Since isotropic scatterers scatter the same intensity at any angle, the detector efficiency and gain can be normalized with this procedure. It is convenient to normalize all the detectors to the 90° angle detector.
The formula describes both the Thomson scattering of low energy photons (e.g. visible light) and the Compton scattering of high energy photons (e.g. x-rays and gamma-rays), showing that the total cross section and expected deflection angle decrease with increasing photon energy.
The collision causes the photon wavelength to increase by somewhere between 0 (for a scattering angle of 0°) and twice the Compton wavelength (for a scattering angle of 180°). [32] Thomson scattering is the classical elastic quantitative interpretation of the scattering process, [26] and this can be seen to happen with lower, mid-energy, photons.
Small-angle scattering from particles can be used to determine the particle shape or their size distribution. A small-angle scattering pattern can be fitted with intensities calculated from different model shapes when the size distribution is known. If the shape is known, a size distribution may be fitted to the intensity.
Then the angle of the rotation is the angle between v and Rv. A more direct method, however, is to simply calculate the trace : the sum of the diagonal elements of the rotation matrix. Care should be taken to select the right sign for the angle θ to match the chosen axis: