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Multiple Compton Scattering of Low Energy Gamma-Radiation

1952; American Institute of Physics; Volume: 85; Issue: 5 Linguagem: Inglês

10.1103/physrev.85.881

1536-6065

Robert O'Rourke,

Advanced X-ray Imaging Techniques

This paper contains solutions to several problems of multiple Compton scattering of low energy gamma-radiation ($E\ensuremath{\ll}\frac{1}{2}$ Mev). The results have been obtained by an approximate method proposed by Chandrasekhar. The solutions indicate an appreciable broadening of a primary monochromatic spectral distribution after it has passed through relatively small distances in the scattering medium.The results for the forward scattering spectral distributions exhibit small shifts to the violet because of an approximation employed (viz., a Taylor series development). Chandrasekhar proposed that the area of this violet shift be used as a criterion of error. If this is accepted, then the error is less than 15 percent at a distance of $x=1$ and decreases rapidly with increasing $x$. The corresponding results for the backscattering spectral distributions exhibit negative intensities near the source, i.e., for small $x$. Again the area of this negative portion of the spectral distribution curves becomes negligible as $x$ increases. It requires a great deal of graphical integration to plot the results for the backscattering in the plane parallel media over the required range of wavelength shifts which is some 20-30 Compton units. One can exhibit the negative intensities, however, by plotting the results over a range of zero to about 5 Compton units. In the case of a point source in an infinite spherical medium the backscattering spectral distribution was obtained in closed form and Fig. 5 shows the results for two values of $x$. One can see from Fig. 5 that the area of negative intensity becomes negligible as $x$ increases.The method of Chandrasekhar seems to yield qualitatively correct results if one uses only distances $x$ which are greater than about $x=2$. One cannot check the results, however, since one cannot carry out the higher approximations in any practical manner. In brief, if one tries to include either the higher derivatives in the Taylor series or to go to the higher approximations of the Gauss and Radau methods, or both, one is lead to a system of partial differential equations of high order which cannot be solved by any practical method.