A theoretical investigation, based on the Klein-Nishina formula, has been made of the amount and distribution of radiation in a scattering medium. It is shown that the experimentally observed maximum in the ratio between the amounts absorbed of scattered and primary energy as the primary wavelength varies is to be expected on theoretical grounds, and that the position of the maximum depends on the atomic number of the scattering medium. For water, the theoretically predicted maximum occurs at about 100 X.U., agreeing very well with the experimental value, while for heavier substances the maximum should move towards shorter wavelengths, occurring at about 10 X.U. for lead. It has been found possible to make an exact calculation of the quantity and quality of the once-scattered radiation absorbed at any point on the axis of a parallel homogeneous beam, taking into account the effect of the wavelength and beam-width of the primary radiation, the composition and thickness of the scattering medium, and the depth of the point considered below the surface; in particular, the following quantities have been evaluated:— The intensity spectrum of the once-scattered radiation received at any point in the medium, the corresponding spectrum of the absorbed energy, and the total amount of electronic energy set free per unit volume at any point in the medium by the primary and the once-scattered radiation. Taking water as the scattering medium, owing to its close approximation in scattering properties to a tissue, these quantities have been numerically evaluated for four particular primary wavelengths, namely, 17·1, 50, 200, and 400 X.U. The results obtained are discussed and compared with experimental observations. Certain conclusions are reached regarding the effect of the beam-width on the amount of scattered radiation, the part played by scatterings of higher orders than the first, the effect of scattering on the depth-dose, and the quality of the scattered radiation. These investigations were commenced while the author was attached as physicist to the Cancer Research Committee of the University of Sydney.
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