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Analytical calculations of multiple scattering for high-energy photons and neutrons

机译：高能光子和中子多重散射的解析计算

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Abstract: Radiography of large dense objects often require the use of highly penetrating radiation. For example, a couple of centimeters of steel attenuates 50 keV x-rays by a factor of approximately 10$+$MIN@14$/ whereas this same amount of steel would attenuate a 500 keV photon beam by only a factor of about 0.25. However, this increase in penetrating power comes with a price. In the case of x-radiation there are two bills to pay: (1) For projection radiography, this increase in penetration directly causes a corresponding decrease in resolution. (2) This increase in penetration occurs in a region where the interaction of radiation and matter is changing from absorption to scattering. In the above example the fraction of scattering goes from about 0.1 at 50 keV to over 0.99 at 500 keV. These scattered photons can significantly degrade contrast. In order to overcome some of these difficulties, radiography using scattered photons has been studied by myself and numerous other authors. In all the above cases, calculation of the intensity of scattered radiation is of primary importance. In cases where scattering is probable, multiple scattering can also be probable. Calculations of multiple scattering are generally very difficult and usually require the use of extremely sophisticated Monte Carlo simulations. It is not unusual for these calculations to require several hours of CPU time on some of the worlds largest and fastest supercomputers. In this paper I will present an alternative approach. I will present an analytical solution to the equations of double scattering, and show how this solution can extended to the case of higher order scattering. Finally, I will give numerical examples of these solutions and compare them to solutions obtained by Monte Carlo simulations. !4
机译：摘要：大型密集物体的射线照相通常需要使用穿透力强的射线。例如，几厘米的钢将50 keV x射线衰减约10 $ + MIN @ 14 $ /倍，而相同量的钢将500 keV光子束衰减仅约0.25倍。但是，这种穿透力的提高是有代价的。对于X射线，需要支付两个费用：（1）对于投影X射线照相术，这种透射率的增加直接导致分辨率的相应降低。 （2）渗透率的增加发生在辐射与物质相互作用从吸收变为散射的区域。在以上示例中，散射分数从50 keV时的约0.1变为500 keV时的超过0.99。这些散射的光子会大大降低对比度。为了克服其中的一些困难，本人和许多其他作者已经研究了使用散射光子的射线照相技术。在上述所有情况下，散射辐射强度的计算至关重要。在可能发生散射的情况下，也可能发生多次散射。多次散射的计算通常非常困难，并且通常需要使用极其复杂的蒙特卡洛模拟。这些计算在一些世界上最大，最快的超级计算机上需要几个小时的CPU时间并不少见。在本文中，我将提出一种替代方法。我将为双散射方程式提供解析解，并展示该解决方案如何扩展到高阶散射的情况。最后，我将给出这些解的数值示例，并将它们与通过蒙特卡洛模拟获得的解进行比较。 ！4

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